Rekhaganit

Author(s): Atmaram Babu
Publisher: Atmaram Babu
Catalog link: https://jainqq.org/explore/020605/1

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rored bthe provincial Text Book Com. N.-1.-P. & Oudk / kitAba ko provinpAla Tekasa buka kameTo mumAlika magarabI va zumAlI va avadha mumAnika mutavasmita ne pasaMda karake dAkhila korsa kiyA Missaicolchelocioleelaalmaidalamlakha A NEW EDITION OF FULD'S ELEMENTS OF GEOMETRY IN HINDI INTENDED FOR THE STUDENTS OF VERNACULAR & NORMAL SCHOOLS BY The late B. Atma Ram B. A. HEAD MASTER HIGH SCHOOL ALIGARII. BOOKS I--11. rekhAgagiAla pahilA aura dUsarA adhyAya Tippana va345 prazanoM aura savAlAta imtihAna sahita jisako 'da maMzA janAba phaiz2amAbaemakemsanasArababahAdaema.e. DArakara sAvika dAriza tAlIma mumAlika prAmAlI garabI va avadha bAbU AtmArAma bI. e. haiDamAsUra hAI skUla alIgar3ha bagara ja phAyadai tulabA naurmila ra kUla va madArisa tahasIlI va ilakAbandI umdA 2 aMgarejI kitAbo se tAlIpa viyA Revised and enlarged Edition. cauthI bAra sana 1000 I0 kImata phI jilda 000 jilda haqa tAlIpha mahaphUja hai / . 10 pAne jalajalajalAlAbalalalalallana kyarA presa meM sunzI rAma nArAyaNa bhArgava ke pravandha se chapa SH&D & SOLD BY KACKER & RROS Noiwei-lhi.. For Private and Personal Use Only

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PREFACE In thus presenting to students and teachers a new elementary work in Urdu on the principles of Geometry, it can hardly be necessary to defend ourselves for having made Euclid's Elements the basis ofthework. For while it cannot de nied that many defects and difficulties occurin the Elements, and that these become more obvious the more closely we examine the work, it must, onthe other hand, be acknowledged that notwithstanding the numerous attenpets which have been made by our best modern geometers to find an appropriate substitute, the " Elements " of Euclid has ever held the chief place in our Universities and Colleges, and is never likely to be superseded. Nearly every oificial programme of instruction or examination expressly includes some portion of this honoured work The present edition of Euclid's Elements is prepared especially for those studying for the Normal School Certificate and the Middle Class Vernacular Examination in the North - Western Provinces and Oudh, It differsin several important particulars from other editions of the same work intended to be used as text books in the Vernacular Schools of India. First, the style has been simplified as far as possible by discarding much of the usual technical phraseology and in places where this has been necessarily retained, copious explanations have been added, especially in the Definitions. A list of all the technical terms used in the work, together with their English and Hindi equivalents, is also attache d. Secondly muy now aaisin olor Demonstrations of the proposition have been given, in addition to those of Euclid, in order to bring the subject within the comprehension of different capacities. In nota few cases where Euclid has given only the indirect method of proof or what is culled Reductio ad absurdum--(themethod generally employed by Euclid for the ion of converse propositions)--a direct method of p valis more satisfying and more convincing to the student hast, .n appended murdly to almost all the propositions, there have been added new rollaries, Exercises and Annotations of various k. ds, tending to render the additions a species of short running om atary on the immori "rk of Euclid. Fourthly, in order tor move one of the most prac. 1 objections which have been urged aganist the Elements, namely, its want of methodical arrangement, a classified index: 'n appended by means of which the propositions in the relat g to any particular subject may be immediate In conclusion we must not omit to mention the ps .cipal works which have been cosulted, and to which the prest edition is mainly indebted for anyador ta: vb ch it may possess overits rivaIs in the same field. T works i eferred to are the edition of the Elements by Todhunter, Potts, Wallace, Playfair, Smith and Law. It only remains for us to offer our thanks to the friends who have helpd us with their advice in the preparation of this work, and to assure each student and teacher that any suggestion for its improvement will be thankfully received by us. ALIGARH, October 1894 AR For Private and Personal Use Only

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Shri Mahavir Jain Aradhana Kendra Definitions Dimension Point Locus Line aMgarez2I Straight line Parallel straight line Curve Superficies Plane superficies Solid Verter Arm www.kobatirth.org perpendicular Boundary istalAha paribhASA vistAra bindu nidhi hindI plane angle koNa plane rectilincalangle | sarala koNa Right angle khama ko Obtuse angle adhika koNa Acute angle Re-entering angle Adjacent angle Interior Angle Exterior angle Opposite angle Alternate angla Supplement Complement rekhA sIdhI yA sarala rekhA samAnAntara sIdhI rekhA vakra yA kuTila rekhA dharAtala darpaNodara gharAtala piMDa nyUna koNa punaryukta koNa vyAsanna koNa grantaH koNa hi koNa pUraka koTi zIrSa bhuJa samma ukha koNa ekAntara koNa lamba sImA urdU Hdwd mtdd lkhTyn nqT@ mqm lnqT khT khT mstqym khTwT mstqym mtwzyh khT mnHny sTH sTH mstry jsm zryh msTHh zryh msTHh mstqym zryh qy'mh zryh mnfrj@ zryh Hd@ zryh mkrrh zryh mtSlh zwyh dkhlh zwyh khrjh zwyh mtqblh zryh mtbdlh sh tmmy qy'm@ sq t`dwd jaika

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( 3 ) aMgarez2I hindI urdU mHyT tr qws Dl` Figure grAkRti yA kSetra Circle vRtta Circumference paridhi Centre kendra Diameter yAsa Radius yAsaI yA trijyA Arc cApa Chord cApa karNa yA jIvA Side mana Rectilincal fiyure | Rju maja kSetra Trianglo limuna Equilateral triangle samatri bAhu tribhuja Isosceles triangle samabAhu tribhuja Scalene triangle vighamabAha tribhuja Right-angled triangle | samakoNa tribhuja Hypotenuse samakoNa trimaja kA karNa Obtuse-angled triangle| adhika koNa vimuja Acute-angled triangle nyUnakoNa tribhuja Qnadrilatera figure caturbhaja kSetra Square varga Oblong yAyata yA nAtyAyata Rhombus viSamakoNa samacaturmuna Rhomboid grajAtyAyata Parallelogram samAnAntara caturmuja Trapezium bidhama catubhuna Complement Trapezoid samalamba caturmaja Polygon bahubhuja kSetra shkl mstqym lDl` mthlh mthlth mtswy lDl` mthlth mtswy lsqyn mthlth mkhtlf Dl` mthlth qy'm lzwyh wtr mthlth qy'm lzwy@ mthlth mnfrj lzwyh mthlth Hdh lzwy@ shkhl nwrb`@ lDl` mstTyl m`yn shbyh blm`yn mtwzy l'Dl` mnHrf pUraka nwzlf@ shkhl khthyr lDl` For Private and Personal Use Only

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(5) ozma bhUmikA AME TRENCECHASAN patthara kA Tola jo kisI caTTAna se kATA gayA hai eka Thosa cIka hai jaba saMgatarAza ne isako gar3hakara isakA Daula durusta kara liyA to yaha eka piMDa kI zakla banagaI aba faz2a karo ki yaha zakla aisI hai ki isa Taula meM chaha tarapha haiM jo ApasameM saba taraha se barAbara haiM agara koI zakhasa khar3A hokara isa Taula ke eka kone para naz2ara DAle to usako tIna taraphe jaisI ki isa tasvIra meM naz2ara par3atI haiM dikhalAI deMgI isa zakla kI haraeka tarapha ko dharAtala kahate haiM aura jaba yaha dharAtala aisA hamavAra aura cikanA hai ki isameM kahauM khurakhurApana nahIM hai to yaha darpaNodara dharAtala hai tez2a aura paine kinAre jahAM koI do taraphai milatI haiM rekhA kahalAtI hai vaha jagaha jahAM kahauM tIna kinAre milate hai bindu hai| rAzi use kahate haiM jisake kula aura Tukar3oM kI eka hI nAma se pukAra sakeM masalan rekhA eka rAzi hai kyoMki hama usake kula aura usake haraeka Tukar3e ko rekhA kahate haiM hara cIz2a kI lambAI, caur3AI aura muTAI yA gaharAI yA uMcAI) ko bistAra kahate haiM aba hama piMDa, dharAtala, rekhA aura biMdu ke Apasa kA phaka isa taraha bayAna karate haiM piMDa meM tInoM vistAra hote haiM yAnI lambAI , caur3AI aura muTAI dharAtala meM do vistAra hote hai yAnI lambAI aura cauDAI rekhA meM eka vistAra hotA hai yAnI nirI lambAI For Private and Personal Use Only

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vidu meM koI vistAra nahIM hotA hai rekhAgaNita vaha vidyA hai jisameM piMDoM, dharAtalo, konoM aura rekhAoM kI paimAyaza se bahasa kI jAtI hai aura unake Apasa ke sambandha bayAna hote haiN| ukta dasa eka bar3A mazahUra gaNitajJa thA jisane mulaka mitha meM haz2arata IsA ke pezatara san 323 aura 283 ke darmiyAna zuharata pAI aura skandariyA kI gaNita pAThazAlA kI buniyAda kAyama kI isane rekhAgaNita kI aisI tIba dI ki isakA nAma kI rekhAgaNita kA dUsarA nAma hogayA For Private and Personal Use Only

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rekhAgaNita pahilA adhyAya paribhASA yAno kiso coz2a ko khAsiyatoM kA aisA bayAna ki usase bahI cIz2a samajha meM bhAye (1) vinda vaha hai jisakI koI jagaha mukararahI lekina usake Tukar3e na hosake Tippana kitAboM meM bindu kA yaha nizAna (* ) hai yaha nizAna kitanA hI choTA kyoM na ho to bhI isake Takar3e ho sakta haiM isase yaha na samajhanA cAhiye ki bindu ke jisakA bayAna rekhAgaNita meM huaA hai Tukar3e hosakta haiM rekhAgaNita kA binTu eka aise choTe se TevayaM kI jagaha ko khayAna ko z2Ahira karatA hai jisakA vistAra hama gumAna meM nahIM le sakta hai| (2) rekhA vaha hai jisakI koI jagaha ho aura jisameM lambAI ho lekina caur3AI yA muTAI na ho Tippana bindu ke kisI dazA meM hapati karane se rekhA paidA hotI hai aura rekhA ke samajhane meM la vidhi sUcaka lambAI aura nidhedha sUcaka caur3AI kA zAmila hai rekhA do taraha kI yAnI saudhau aura kuTila hosaktI hai (3) rekhA ke sire bindu hote haiM Ti. rekhA ke siroM se murAda isa jagaha rekhAke Adi granta se hai jahAM eka rekhA dUsarI rekhA ko kATatI hai vahAM bhI bindu hotA hai (4) sarala yA sIdhIrekhA vaha hai jo apane donoM siroM ke vIca hamavAra (yAnI ekAhI dizA meM) ho Ti. agara bindu bagara apanI rizA ke badale hue harakata kare to vaha sIdhI rekhA paidA karegA aura agara vaha apanI harakata lagAtAra badalatA jAya to usa harakata se kuTila yA vakra rekhA banegI isase yaha natIjA nikalatA hai ki do binduoM ke darmiyAma sirpha eka sIdhI rekhA khIMcI jAkhato hai For Private and Personal Use Only

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(8) (5) dharAtala vaha hai jisakI koI jagaha ho aura jisameM lambAI aura caur3AI hoM lekina muTAI na ho Ti. jahA~ eka dharAtala dUsare ko kATatA hai vaha rekhA hai (6) dharAtala ke kinAre rekhAI Ti. do sIdhI rekhAoM kI eka dharAtala meM hone ko kada isa jagaha para isaliye nahIM kI gaI hai ki do saudhau rekhA jo Apasa meM milatI hai hamezA eka hI dharAtala meM hotI haiM (7) samadharAtala vA darpaNodara dharAtala para dharAtala hai ki jisapara koI do bindu liye jAMya aura una binduoM ke bIca sodhIrekhA khIMcI jAya tovaha sIdhI rekhA bilakula dharAtala meM hI Ti. sama dharAtala Thahare hue pAnI yA cikane pharNa ke dharAtala ke samAna vijakala capaTA zaura hamavAra hotA hai (8) kona aisI do rekhAoM ke eka dUsarI tarapha ke mukAva kI kahate haiM jo eka dharAtala meM Apasa meM milatI haiM lekina milakara eka rekhA nahIM bana jAtI haiM Ti. kona do vakra rekhA yA eka vakra rekhA aura eka sIdhI rekhA yA do sIdhI rekhAoM ke eka dharAtala meM milane se paidA hotA - hai jo milakara eka rekhA nahIM bana jAtI hai (e) saralakona usa kona ko kahate haiM jo aisI do sIdhI rekhAoM ke eka dusarI kI tarapha jhukAva se paidA ho jo milakara eka sIdhI rekhA nahIM bana jAtI hai Ti. (1) jaba kisI bindu para eka hI koga ho to vaha eka akSara se jo usa para likhA huyA ho / bayAna ho sakatA hai jaisA ki kona a kA hai magara / jaba eka bindu para eka se jiyAdA kone hoM to a ba ja una meM se hara eka kona tIna akSaroM se isa taraha bayAna kiyA jAtA hai ki bIca kA akSara bindu para likhA huyA hotA hai aura eka akSara una donoM sIdhI rekhAyoM ke jinase kona banatA hai kisI jagaha para likhA hotA hai masalan jo kona rekhA ba a aura sabase banatA hai usako ba asa kona aura jo kona sa a aura daa rekhAyoM se banA hai usako saada kona aura jo kona va a aura da arekhAoM se banA hai usako ba ada kona kahate hai For Private and Personal Use Only

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(2) Ti0 (2) jisa dindu para kona kamAne vAlI rekhA milatI hai usako kona kA zaurSa aura una rekhAoM meM se hara eka ko kona kI kahate hai vidyArthiyoM ko bAda rakhanA cAhiye ki bhuja jina rekhAyoM se kona banatA hai unake ghaTane bar3hane se kona ghaTatA bar3hatA nahIM hai jaise ba ma sa aura da a ya eka hI kona hai Ti. (3) isa kitAba meM mUkSma rUpa se sarala kona kI jagaha sirpha kona zabda liyA jAyagA ba (10) jaba eka sodhI rekhA dUsarI sIdhI rekhA para khar3I hokara apane Asa pAsa ke kona jinheM Asanna kona kahate haiM barAbara banAve to una konoM meM se hara eka kona samakona hogA aura khar3I sIdhI rekhA ko dUsarI sIdhI rekhA para lamba kahate haiM . Ti0 ( 1 ) samakona kI paribhASA isa prakAra bhI kI gaI hai ki vaha samakona kA vyAdhA hai jisake eka rekhA vyapane kisI sire para agara baha rekhA usa sire kI tarafa bar3hAI jAve apane bar3e hue hisse ke sAtha paidA karatI hai aura isa pichale kona ko sIdhA kona kahate haiM ( 11 ) adhika kona vaha kona hai jo sama kona se bar3A ho Ti0 ( 2 ) jaba eka sIdhI rekhA dUsarI sIdhI rekhA para lamba ho to dUsarI sIdhI rekhA bhI pahalI para lamba hogI Ti0 adhika kona do sama kona se choTA bhI honA cAhiye ( 12 ) nyUnakona vaha kona hai jo samakIna se choTA ho < Ti. 0 agara kisI kona kA eka bhuja kona ke zIrSa kI tarafa bar3hAyA jAve to eka dUsarA kona paidA hogA yaha kona pahale kona ke barAbara yA usase choTA yA bar3A hogA agara barAbara hai to pahalA kona mamakona aura agara choTA hai to vyadhika kona aura jo bar3A hai to nyUna kona hogA (13) sImA kisI cIja ke kinAre ko kahate haiM For Private and Personal Use Only (14) kSetra vaha hai jo eka yA jiyAdA sImAoM se ghirA ho (15) vRtta vaha ca etra hai jo eka rekhA se jisakA nAma paridhi

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(10) hai ghirA ho aura jisake andara eka khAsa bindu aisA ho ki usase jitanI sIdhI rekhA paridhi taka khauMcI jAveM saba ApasameM barAbara hoM (16) vRtta kA kendra eka aisA bindu vRtta ke andara hai ki usa binT se jitanI sIdhI rekhA paridhi taka khauMdhI jAyeM saba Apasa meM barAbara hoM Ti. vRttoM ko unake kendroM ke nAma se jAhira karanA gara mAmalI bAta nahIM hai masalan vRtta jisakA ma kendra hai usako ma itta kahate haiM (17) vRtta kAvyAsa vaha sIdhI rekhA hai jo kenTra para hokara jAya aura jisake donoM sire paridhi para hoM Ti. jo sIdhI rekhA vRtta ke kendra se usakI paridhi taka khIMcI jAtI hai usako vyAsArddha vA trijyA kahate haiN| Ti0 (2) agara eka sIdhI rekhA apane eka Thahare hue sire ke girda kisI dharAtala meM ghUmakara apanI grasala jagaha para lauTa Ave to dharAtala jisapara yaha rekhA dhamI hai itta kahalAtA hai aura vaha rekhA jo sIdhI rekhA ke dUsare sire ke bindu kI harakata se paidA huI hai vRtta kI paridhi kahalAtI hai aura ghUmane vAlI sIdhI rekhA vRtta kI trijyA aura Thahare hue sire ke bindu ko ta kA kendra kahate haiM (18) vRttArddha vaha kSetra hai jo vyAsa aura paridhi ke usa bhAga se ghirA ho jo vyAsa se kaTA hai . Ti. vRttAI kA kendra vahI hai jo vRtta kA kendra hai (19) dhanuSa kSetra vaha kSetra hai jisako kisI sodhI rekhA aura paridhi ke usa hisse ne jo usa sIdhI rekhA se kaTA hai 6 ho Ti0 dhanuSa kSetra kA pahile aura dUsare adhyAya meM kahIM kAma nahIM par3A hai vRttAI dhanuSa kSetra hai lekina hara dhanugha kSetra vRttAI nahIM hai ___ (20) Rja bhaja kSetra vaha kSetra hai jo sIdhI rekhAoM se ghirA ho Ti. jina sIdhI rekhAoM se Rju bhuja kSetra ghirA hotAhai unako ukha kSetra ko bhuja kahate haiM aura jo jagaha una bhajoM se ghirI hotI hai vaha kSetra kA kSetraphala yA rakabA kahalAtA hai For Private and Personal Use Only

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(21) tribhuja vaha kSetra hai jo tIna sIdhI rekhAoM se ghirA ho / Ti. jina sIdhI rekhAyoM se tribhaja ghirA hotA hai unameM se eka ko AsAnI ke liye tribhuja kA aAdhAra aura bAkI do ko tribhaja kI muja kahate haiM aura usa biMdu ko jahAM donoM bhaja milatI hai tribhuja kA zIrSa kahate hai (22) catarmajavaha kSetra hai jo cAra sodhI rekhAoM se ghirA ho __ (23) bahamuja vaha kSetra hai jo cAra se z2iyAdA sIdhI rekhAoM se ghirA ho Ti. jisa bahumaja kSetra kI saba bhajA aura maba kona yApasameM barAbara hote haiM usako samAna kona sama bhuja kSetra kahate haiM (24) samavibAhu tribhuja vaha vibhuja hai jisakI tInoM bhujA ApasameM barAbara hoM ( 25 ) samadibAhu trimaja vaha tribhuja hai jisakI . do bhuja aApasameM barAbara hoM Ti. samavivAhu tribhuja samavivAhu bhI hotA hai lekina samavivAha vibhuja samatrivAha nahIM hosaktA hai| (26) biSama bAha tribhuja vaha vibhuja hai / jisakI koI eka bhujA dUsarI bhujA ke barAbara na ho/ (27) samakona tribhaja vaha trimaja hai jisakA eka kona samakona ho Ti. samakona tribhuja meM samakona ke sAmane vAlo bhuja ko karNa aura bAkI do bhujAoM meM se eka ko bhAdhAra yA bhami aura dUsarI ko koTi yA laMba kahate hai (28) adhika kona tribhuja vaha tribhuja hai / jisakA eka kona adhika kona ho (28) nyana kona tribhuja vaha tribhuja hai jisake . saba kona nyana kona hoM Ti. (1) nyUna kona tribhuja meM tInoM kona nyana kona hone ko kada isaliye rakhI gaI hai ki samakona tribhuja aura adhika kona tribhujoM meM For Private and Personal Use Only

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(jaisA ki pahale adhyAya kI satrahoM sAdhya ke papane se mAlUma hogA) dI ho kona nyUnakona hote haiN| Ti. (2) agara vibhuja kI sirpha bhujoM para qhayAla kiyA jAya to vaha sIna kisma kA hotA hai yAnI samavibAhu tribhuja, samaDivAhu tribhuja, aura viSamabAhu tribhuja aura tIna hI kisma kA usa sUrata meM hotA hai jaba upake si konoM para qhayAla kiyA jAya yAnI samakona tribhuSa, adhika kona tribhuja au ranyU nakona tribhuja phira tribhuja kI aura bhI kismeM ho saktI haiM jaba usakI bhujAoM aura konoM donoM para khayAla kiyA jAya (30) vargava vaha catarbhujakSetra hai jisakI cAroM bhujA ApasameM barAbara hoM aura cAroM kona sama kona ho Ti. vargakSetra kI paribhASA meM eka hI kona kA samakona kahanA kAphI hai kyoMki jisa catubhuja kSetra kI cAroM bhujA yAyasameM barAbara hoM aura eka koma samakona ho to usake saba kona jaisA ki pahile adhyAya kI chiyAlIsauM sAdhya meM sAbita huA hai samakona hote haiM (31) Ayata kSetra vaha caturbhuja kSetra hai jisake cAroM kona samakona hoM lekina usakI saba bhujA ApasameM barAbara na hoN| Ti* jisa caturbhuja kSetra kI Amane sAmane kI sajAbarAvara ho aura eka kona samakona ho usako aAyata yA samakona caturbhuja kahate hai (32) viSamakona sama catarbhaja vaha caturbhuja / kSetra hai jisakI cAroM bhujA ApasameM barAbara hoM aura // usake kona samakona na hoM (33) ajAtyAyata vA viSamakona Ayata vaha caturbhuta kSetra hai jisakI Amane sAmane kI bhujA ApasameM barAbara hoM lekina saba bhujA ApasameM barAbara na hoM aura kone bhI samakona na hoM (34) ina cAra caturbhuja kSetroM ke sivAya hara caturbhaja kSetra ko viSama catabha ja kSetra kahate haiM Ti. (1) kabhIra viSama caturmuja jisakI do bhujA samAnAntara hotI hai samalamba caturbhana kahalAtA hai caturbhuja / For Private and Personal Use Only

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(13) Ti. (2) hara caturbhuja kSetra ko yA to cAra prakSaroM se sa jo usake cAroM konoM para likhe hote haiM yA sirpha do akSaroM / se jo usake Amane sAmane ke konoM para likhe hote haiM bayAna meM karate haiM jaisA ki isa kSetra ko aba sa da vA a sa yA bada se bayAna karate haiM ( 35 ) samAnAntara sIdhI rekhA vaha sIdhI rekhA haiM jo eka dharAtala meM hoM aura donoM tarapha bar3hAIjAne se kabhI eka dUsarI se na mileM Ti0 (1) isase yaha samajhanA cAhiye ki uma dharAtala kI co samAnAntara rekhAyoM ke bIca meM hotAhai caur3AI hara jagaha mamAna hotIhai Ti. (2) yaha samakina hai ki do sIdhI rekhA jo eka dUmArI se kabhI nahIM mileM go vaha kitanI hI banAI jAra mamAnAntara nahoM imo samaya rakhAtroM ko eka dharAtala meM hone ko ka da rakkho gayI hai (a) samAnAntara catamaja vaha kSetra hai jisakI Amane sAmane kI bhuja samAnAntara hoM aura jo sodhI rekhA kisI samAnAntara caturbhaja ke Amane sAmane ke konoM ke darmiyAna khauMco jAto hai usako usa kSetra kA karNa kahate haiM Ti.(,) samAnAntara kSetra vaha hai jisake Amane sAmane ke saja samAnAntara hoM-samAnAntara kSetra meM 4, 6,8 yA yugama saMkhyA ke suja ho saka hai jisameM grAmane sAmane ke hara do bhuja samAnAntara hote haiM . Ti. (2) agara samAnAntara caturbhuja aba sa da kA karNa asa ho aura ya ka fa aura ja ka la rekhA samAnAntara caturbhuja kI aba aura Ada bhujoM kI samAnAntara hoM to usa samAnAntara caturbhaja meM cAra samAnAntara caturbhaja baneMge jinameM se do yAnI a ja ka ya yaura ka fasa la . meM kaNa guz2aratA hai aura do bAnau ya ka la da aura jaba pha ka meM karNa nahIM guz2aratA hai jina samAnAntara caturbhujoM meM karNa nahIM guz2aratA hai unako a ja ka ya aura ka fa sa la samAnAntara caturbhujoM kA pUraka kahate haiM va sa abAyopakrama Ti-avAdhyApakrama baha vastupapAdaya mAdhya hai jisakA subUta aisA mApha aura jAhira hai ki subUta kI hANata nahIM rakhatA yAda rakhanA cAhiye ki uko dama ne avAdhyopakrama se kAma nirpha prameyopapAdaya mAdhyoM ke liye yAmala karane yA vasta papAya sAdhyoM ke hala karane meM liyA hai lekina unakA For Private and Personal Use Only

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(14) kAma una nAdhyoM ke usa hisse meM jisako sabUta kaho haiM haragiz2a nahI liyA hai aura na umase subUta meM kisI kisma kI madada lI jA saktI hai mAnalI 1-kisI eka bindu se kisI dUsare bindu taka rekhA khIMca sakte haiM Ti.. hama khapAla karate haiM ki koI sIdhI rekhA do niyata binduyoM ke darmiyAna jinako hama umke grAdivyanta samameM upasthita hai to uma sIdhI rekhA ko hama parimita khA kahate haiM lekina jaba hama usako aAdi anta ko khayAla meM nahIM lAte haiM to vaha mIdhI rekhA aparimita kahalAtI hai 2- parimita rekhA ko usakI sIdha meM cAheM jitanA bar3hA sakta hai Ti (1) hara sIdhI rekhA donoM tarafa vilA kisI idda sukararA ke bAda saktI hai isa pravAdhyo pakrama kI madada se hama parimita sIdhI rekhA ko usake hara sire kI tarapha gitanA cAheM vafA khato hai Ti. ( 2 ) vyavAdhyopakrama 1 , 2 se eka sIdhe mistara (rUla) kA kAma meM lAyA jAnA mukaddama pAyA jAtA hai yaha z2arUra nahIM hai ki vaha mistara mAyazI paimAnoM yA hiramoM meM bAMTA gayA ho ki usase kisI khAsa lambAI kI rekhA nApI jA sake 3- ki jisa keMdra se aura usa keMdra se jisa dUrI para cAheM vRtta khoMca sakta haiM Ti. isa avadhyopakrama kamyAsa yAnI parakAra kA eka khAsa kAma meM lAmA phaz2a karanA yAnI yaha ki usa ke vasIle se mitta khIMce jAiz2a mAna liyA gayA hai lakina yaha ijAz2ata hagiz2a nahIM dI gayI hai ki hama usake vasIle se kisI dUrI ko nA yA usa dUrI ko eka mukAma se dUsare sukAma para le jAveM / svayaMsiddhi Ti. svayaMsiddhi vaha prameyopapAda sAdhya hai jinameM subUta ko gaMjAyA nahIM hai lekina jinakI sacAI mosI jAhira hai ki phaurane mAna lainI pa. khatI hai kisI prameyopapAya sAdhya ko sirpha isa vajaha se ki vaha jAhira bAta hai svayaM sivina khayAla karanA cAhiye unako svayaM miDikhayAla karane ke liye yaha bhI jarUra hai ki usakA muvata aisI dalIloM ke vasIle se jisakI buniyAda jiyAdA jAhira prameyopapAda sAdhya para hai nahosa ke kyoMki yaha sanAmida hai ki khayaMsiddhi kI tAdAda jahAM taka samakima hai kama ho aura isI vajaha se bIsavIM sAdhya aura bAjara aura sAdhya go vaha sAdhya dasarI svayaMsiDiyoM kI taraha jAhira bAteM haiM svayaM siddhi meM dAkhila nahIM ko gayo hai saphasila taura para donoM meM se sAbita kI gayA haiM For Private and Personal Use Only

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(1) jo cIz2a eka ho cIja ke (yA barAbara cIz2oM ke barAbara hoM vaha ApasameM bhI barAbara hotI haiM Ti. vaha svayaM middhi saba kisma kI rAziyoM se sambandha rakhatI hai aura yahI yAta svayaM siDi 2,3,4,5,6,7 aura para saccI AtI hai lekina svayaMsiddhi 8,10,11 aura 12 sirpha rekhAgaNita kI rAziyoM se sambandha rakhatI hai ( 2 ) agara barAbara cIz2oM meM ( yA eka hI cIz2a meM) barAbara2 jor3A jAya to bAda jor3ane ke jo cIjeM hAsila hogI vaha mI mApasameM barAbara hoMgI (3) agara barAbara cIz2oM meM se (yA eka cIz2a meM se ) barAbara 2 nikAla liyA jAya to bAda nikAlane ke jo cIjeM hAsila hoMgI baha bho Apasa meM barAbara hoMgI (8) agara nAbarAbara cIz2oM meM barAbara2 z2iyAdA kiyA jAya tI bAda z2iyAdA karane ke jo cIjeM hAsila hoMgI vaha bhI nA barAbara hoMgI (5) agara nAbarAbaracIz2oM meM se barAbara 2 nikAla liyA jAya to bAda nikAlane ke jo cIjeM hAsila hoMgo vaha bhI nAbarAbara hoMgI (6) jo cIjeM eka hI cIz2a kI (yA barAbara cauloM kI ) dvanI hoM vaha Apasa meM barAbara hotI haiM (7) jo cIjeM eka hI cIz2a kI (yA barAbara cIz2oM kI) AdhI hoM vaha ApasameM barAbara hotI haiM (8) jo rAzeM eka dUsarI ko Dhaka letI haiM yAnI ekahI jagaha gheratI haiM vaha ApasameM barAbara hotI haiM Ti0 ( 1 ) isa ke viloma kA istemAla bhI yAnI barAbara rAzi jaba eka dUsarI para eka hI taura para rakkhI jAyaM to eka dUsarI ko eka letI haiM ukaladasa ne kiyA hai Ti. (2) eka rAzi para dUsarI rAzi ko rakhane ko maru lan ra ka rekhA ko TramarI rekhA para yA eka kona ko dUsare kona para yA eka vibhuja ko dUsare vibhuja para yA eka vRtta ko dUsare vRtta ghara bagara hara rakhane ko kAkAdaga kahate haiM yAcchAdana jo rekhAgaNita meM istemAla hulyA sirpha khathAlI hai yAnI yaha ki hama dila meM khayAla karate haiM ki eka rAzi dUsarI rAzi para rakkhI gayI hai aura taba agara hama sAbita kara sakeM ki vaha rAzi ra ka TUsarI ko pUrA 2 8ka letI haiM yaha natIjA nikAlate haiM ki vaha rAzi grApasa meM barAbara haiM masalana agara do sIdhI rekhA eka dUsarI para isa taraha rakkhI jAnA khayAla kareM ki eka ke donoM sire dUsarI ke donoM siroM For Private and Personal Use Only

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para par3e to baha saudhau rekhA vyApama meM barAbara hotI haiM aura agara do konoM ko hama eka dUsare para isa taraha apane dila meM rakha sakeM ki eka kA zIrSa dasare ke zIrSa para ho aura eka ko bhunoM kI dizAeM bhI dasare ko bhujoM kI dizAnoM para par3e to vaha kona vyApasameM barAbara hote haiM kyoMki bhujoM kI lambAI ke ghaTane vAlane se jaisA ki hama navIM paribhASA meM bayAna kara cuke hai kona ghaTatA bar3hatA nahIM hai agara do dharAtaloM kA eka dUsare para isa taraha rakhe jAnA khayAla kareM ki eka kI mujoM kI dizAeM aura lambAI dUsare kI bhujoM kI dizAoM aura lambAiyoM ko pUrA 8ka leve to vaha dharAtala aApasameM varAvara hote haiM Ti03 yaha svayaMmiddhi rekhAgaNita sambandhI barAbarI daryAta karane kI kasauTI hai aura isameM aura aGkagaNita sambandhI barAbarI ke kAMTe meM bahuta bar3A phA hai rekhAgaNita sambandhI dorAzi usa sarata meM barAbara hotI hai jaba vaha eka dUsarI ko eka leveM yA eka sakeM aura do saMkhyA usa sarata meM barAbara hotI hai jaba una donoM meM ikAiyoM ke yoga ekase hoM aura caMki ukale dasa ne rekhAyoM, konoM yA dharAtaloM vagairaha kI rApiyoM kI koI ikAI sakarara nahIM kI hai isaliye rekhAgaNita sambandhI rAzi kI barAbarI ke sabUta meM saMkhyA se kAma lenA jAyaz2a nahIM hai (c) kula apane TakaDe se bar3A hotA hai| Ti.1- DAkara TAmasana ne apanI ukaleTsa meM isa khayaM siddhi ke sAtha yaha svayaM sivi z2iyAdA kI hai ki kula apane sava himoM ke yoga ke barAbara hotA hai hama yaha svayaMsiddhi bhI z2iyAdA kara sakta haiM ki hisse kA hissA kula kA bhI hissA hotA hai Ti02- navIM svayaMsiddhi mAhirA pAThavoM kI ulaTI hai yAnI yaha ki do rAzi jina meM se eka dUsarI se bar3I ho eka dUsarI ko eka nahIM saktI hai (10) do sodhI rekhA dharAtala ko nahIM ghera saktoM Ti01 - isake yaha mAnI haiM ki do sauMdhI rekhA jinameM se eka ke koI do bindu dasarI ke do binda proM para par3eM ve eka dUsarI ko sarAsara kalaMgA yahAM taka ki bar3hAI jAne para bhI eke raheMgI Ti0 2. sIdhI rekhA kI khAsiyata jo hamane svasiddhi 10 meM bayAna ko hai saudho rekhA kI paribhASA hI se z2AhirA Ta pakatI hai kyoMki chagara do modhI rekhAyoM kA jagaha ko gheranA mumakina hotA to ve apane sire ke binduoM ke darmiyAna eka dUsarI ko pUrA nahIM eka saktI Ti. 3. dharAtala ke gherane ke liye kama se kama tIna sIdhI rekhAtroM kA honA z2arUra hai (12) saba samakona Apasa meM barAbara hote haiM For Private and Personal Use Only

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Ti. 1- kyoMki kona eka kisma kI rAzi hai isaliye yaha khayaMmiddhi dhAThI vayaMsiddhi ko eka khAsa sUrata he Ti. 2- kahA jAtA hai ki yaha svayaMsiddhi eka prameyopapAdya sAdhya hai aura mubUta isakA isa taraha ho sakatA hai ki kula sIdhe kona kyoMki ve prA. cchAdana se eka dUsare para rakta jAmatI hai aura eka dUmare ko eka sA haiM cApamameM barAbara hote haiM (svayaMsiddhi 8) le kina samakona sIdhe kona kA aAdhA hotA hai (paribhASA 10) aura barAbara cIz2oM ke Adhe Apasa meM barAbara hote hai (khayaMsiddhi 7) isaliye kula samakona aApasameM barAbara hote haiM (12) agara eka sIdhI rekhA do sIdhIrekhAoM se milakara apano eka taraphA do antaH kona aise aise paidA kare ki vaha donoM kona mila kara do samakona se choTe hoM to vaha do sIdhI rekhA lagAtAra bar3hAI jAne se kahIM na kahIM usa tarafa meM mila jAyagI jisa tarafa ke kona do samakona se choTe haiM Ti0 - yaha svayaMsiddhi pahale adhyAya kI satrahavauM sAdhya kA viloma hai aura aisI jAhira bAta nahIM hai jisake sAbita karane ke liye dalIla kI hAjata na ho jo zata kula svayaM miDDiyoM ke liye z2arUra hai isa svayaM siddhi ke badane ple feyara sAhaba ne apanI kitAba meM yaha svayaM siddhi likhI hai "agara ho mIdhI rekhA rA ka bindu para eka dUsarI ko kATatI hoM to vaha donoM rekhA kimI ekahI rekhA kI samAmAntara nahIM ho sakI hai| lekina yaha khayaMsiddhi bhI etarAja se khAlI nahIM hai kyoMki yaha pahale adhyAya ko tIsavIM sAdhya kA eka jAhira natIjA hai| rekhAgaNita kau sAdhyoM kA varNana sAdhya yaha hai jisameM kisI cIz2a ke banAne vA kisI siddhAnta ke sAvita karane kI garaz2a bayAna ko jAya aura jaba sAdhya ke yaha bhAnI haiM to usakI do kismeM haiM vasta papAdya (sopapAdya ) aura prameyopapAdya (upapAda) ira sAdhya meM kucha cIja yA miTAnta diye hue hote haiM aura unase kaka. daryAta karane kA bayAna hotA hai agara dAla karane se kisI cIz2a ke banAne kA matalaba hai to usako vastUpapAdya sAdhya kahate haiM aura agara hAla karane se kisI siddhAnta ke siddha karane kA matalaba hai to usako pramayopapAdya sAdhya kahate haiM vastUpapAda sAdhya meM dI huI cIz2oM ko nirdiSTa yora jina cIz2oM ko banAnA cAhate haiM unako karaNIya aura prameyopayA mAdhya meM diye hue mitAnta ko kalpitaartha aura jo siddhAnta unase sAbita karanA cAhate haiM usako phala kahate haiM rekhAgaNita kI sAdhya meM z2iyAdA se z2iyAdA chaH hisse huA karate hai For Private and Personal Use Only

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(18) 1 sAdhAraNa sUtra (dAvA yAma) jisameM sAdhya kI zarte yAma khaura para bayAna kI jAtI hai 2 vivaraNa sUtra (dAvA qhAsa) jisa meM eka khAsa zakka khoMca kara usa para matra kI zateM bayAna karake jAhira karate haiM 3 icchAprakAza (iz2ahAra muddA) apane amalI matalavako bayAna karanA ki hama yaha banAnA yA sAbita karanA cAhate haiM aura usa para mArA dhyAna denA 8 aMkana yA kRta amala) sAdhya ke hala karane yA mAvita karane ke liye avAdhyopakrama ke anusAra jarUrI rekhAyoM yA vRttoM ko khIMcanA 5 upapatti (suvUta) dalIloM ke silmile se dAve ko hala karanA yA sAbita karanA yAnI yaha daryAta karanA ki dAvA hamArA sahI thA yA galata yA no matalaba hamArA thA usakA hAsila honA mumakina hai yA nahIM phala (natIjA) jisameM dAva ko phira bayAna karake jAhira karanA ki vo cIz2a hamako vanAnI thI yA jo bAta hamakosAbita karanI thI vaha bana gaI yA sAbita hogaI dUsa kitAba meM saMkSepa ke liye nIce likhe saMketa kAma meM lAye jAyaMge. paribhASA ke liye avAdhyopakrama ke liye vA. svayaMsiddhi ke liye kha. dusare adhyAya kI tIsarI sAdhya ke liye a02 sA03 pa0 savAlAta itihAna (1) rekhAgaNita kI paribhASA likho (2) rekhAgaNita meM kina kina cIjoM se bahasa kI jAtI hai (javAba) bindu, rekhA, dharAtala, piMDa se (3) vidu meM kyA cIz2a Avazya ko hai (javAba) jagaha (4) rekhA kI tArIpha karo caura batAyo ki rekhA ke prakAra kI hotI hai (5) rekhA ke se banatA hai aura sAbita karo ki do rekhAyoM ke kaTane se bindu paidA hotA hai (6) dharAtala ke vistAra vatAyo aura. batAyo dharAtala ke taraha kA hotA hai (7) jaba eka dharAtala dUsare dharAtala ko kATatA hai to kaunasI rAzi rekhAgaNitIya paidA hotI hai (8) sama dharAtala kisa taraha se banatA hai (javAba ) jaba eka sIdhI rekhA dUsarI sIdhI rekhA ko kATe aura usa para guz2aratI huI apanI sIdha ko binA badale harakata kare to usase sama dharAtala banatA hai For Private and Personal Use Only

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(18) - (6) mama dharAtala meM binTuM kI jagaha niyata karane ke vAste kitanI pa kI jarUrata hai ( javAba )do kI kyoMki minTu sido vakta yA sIdhI rekhAoM ke eka dUsare ke kaTane se paidA hotA hai| (10) rekhA kA sthAna mukarrara karane ke liye kitanI pAtoM kI z2arUrata hai (javAba) do kI yAnI do bindu jima meM hokara vaha gujaratA hai yA eka binda jinameM hokara vaha guz2aratA hai aura eka rekhA jisakI vaha samAnAntara yA lamba yAdi ho (11) sarala kona kI tArIfa karo aura yaha bhI batAyo ki usakI tArIpha meM laphaz2a " eka hI dharAtala meM ho" jo rekhAgaNita ke darpaNodara kAna kI tArIpha meM kyoM ur3A diye gaye (12) do yA tIna konoM ko jo eka hI bindu ba para haiM kisa taraha jAhira kara sakta haiM aura eka kona ko jo eka vinda para hai kisa taraha para bayAna karate haiM (13) vRtta aura kendra kI tArIpha karo (14) vRtta ke bayAna meM kina kina pratoM kA honA jarUrI hai (javAba) tIna yAnI kendra ko jagaha ki jisake liye do zatoM kA honA jarUrI hai sosare trijyA kI lambAI (15) vRttAI aura dhanugha kSetra meM kyA pharka hai (16) tribhuja kI tArIfa karo aura batAyo ki agara tribhuja kI bhuja - aura konoM para qhayAla kiyA jAve to usakI kitanI kismeM ho saktI haiM (17) caturmaja kSetra kI kisma bayAna karo (18) varga, viyama kona, sama caturbhaja, aura varga, bAyata aura prAyata ajAtyAyata aura vighama kona samacaturbhaja, ajAtyAyata meM kina kina bAtoM meM ekatAhai aura kauna kaunasI bAtoM meM virodhatAhai (18) do sIdhI rekhA jo donoM tarafa banAI jAne se kabhI eka dUsarI se nahIM milatI haiM hara sUrata meM samAnAntara nahIM hotI haiM isakI koI zrAma misAla do (20) ina caturbhuja kSetroM ko jinakA bayAna rekhAgaNita kI 30, 31, 32, 33 paribhASA me huyA hai kisa eka qhAsa nAma se pukAra sakate hai (javAba) samAmAntara caturbhaja (22) yavAdhyopakrama aura svayaM siddhi meM kyA pharka hai| (22) rekhAgaNita kI tIsarI avAdhyopakrama me kaunasI bAta mAna lI gaI hai aura rekhAgaNita kI tIna svayaM siDDiyoM ko jo rAzoM kI barAbarI se sambandha rakhatI hai bayAna karo (23) rekhAgaNita meM rAzoM kI barAbarI kI kyA jAMca hai-rekhAgaNita kI una svayaMsiddhiyoM ko jA sIdhI rekhA aura samakona se sambandha rakhatI haiM bayAna karo For Private and Personal Use Only

Page #22
(20) ((24) rekhAgaNita kI vaha svayaMsiddhi bayAna karo ki jo aisI rekhAoM se sambandha rakhatI ho jo bAhAne se mila jAtI haiM (25) kyA rekhAgaNita meM kucha svayaMsiddhi aisI haiM jinakA nAma svayaM siddhi rakhanA manAsiba nahIM hai (26) yAcchAdana kriyA kise kahate haiM kyA aAcchAdana kriyA kI rekhAgaNita meM koI khAsa z2arUrata hai (27) mAdhya kI tArIfa karo, mAthya vasta pAya aura proyo papAdya kA pAka batAyo (28) mAdhya sUtra kise kahate hai aura vastupapAya aura prameyopapAdya meM kauna se do hisma hote haiM misAla dekara bayAna karo sAdhya 1 vastapapAdya sAdhAraNa satra dI huI parimiti sIdhI rekhAoM para samatribAhu vibhuja banAo vivaraNasatra phaz2a karI ki aba do huI sIdhIrekhA hai aba para samavivAha vibhaja banAnA hai aMkala aM keMdra se abadarI ghara basada da ba chatta khA~co gravA03 ba keMdra se aba kI dUrI asa ya vRtta khA~co vyavA03 sa bindu se jisapara eka vRtta dUsare ko kATatA hai aaura babindu. oM taka sa a aura saba sIdhI rekhA khauMco vA 01 to abasa samavibAhu tribhuja hogA upapatti cUMki a keMdra basada hatta kA hai isaliye asa barAbara hai aba ke pa. 15 aura cUki bakeMdra asaya vRtta kA hai isaliye basa barAbara hai ba ake pa. 15 lekina sAbita hocakA hai ki asa barAbara hai aba ke isaliye asa aura basa meM se hara eka aba ke barAbara hai lekina jo cIz2a eka hI cIja ke barAbara ho vaha saba ApasameM barAbara hotI haiM isaliye asa barAbara hai basa ke / isaliye aba aura basa aura sa aApasa meM barAbara chaha vA For Private and Personal Use Only

Page #23
(21) isaliye abasa samAvibAha vibhuja huSA aura vaha do huI aba sIdhI rekhA para banagayA aura isI ke banAne kI jarUrata thI Ti. isa sAdhya meM ukta dasa ne isa svayaM sivi ko mAna liyA hai ki jaba eka vRtta kA keMdra dUsare vRtta kI paridhi meM ho to usa vRtta kA kucha hissA dUsare vRtta ke andara hogA aura kucha hissA bAhara isaliye una vRttoM kI paridhi eka dUsarI ko do binduoM para kATeMgI caMki una biMduoM meM se eka bindu do huI rekhA ke eka tarapha aura dUsarA dUsarI tarafa hogA isaliye do samatribAhu tribhuja usa rekhA para baneMge aura donoM vibhuja milakara eka viSamakona samacaturbhuja banajAyagA jisakA karNa dI huI rekhAhogI abhyAsa (1) pahilI sAdhya meM agara aba donoM tarapha itanA bar3hAyA jAya ki yaha vRttoM se bindu da aura ya para mile aura sa da aura saya milAe jAya to sAbita karo ki vibhuna sa ada aurasa baya samadvibAhu tribhuja hai (2) dI huI parimita sIdhI rekhA para eka aisA samadvibAhu tribhuna banAyo jisakI hara eka bhujA dI huI rekhA se dUnI ho sAdhya 2 vastUpapAdya sA0 satra-diye hue bindu se eka aisI sIdhI rekhA khIMco jo do huI sodhI rekhA ke barAbara ho vi0matra-pharja karo ki adiyA huA biMdu aura ba sa dI huI rekhA hai ase basa kI barAbara eka sIdhI rekhA / khauMcanI hai aM0-a se ba taka sodho rekhA sauMcI aura usa para samavibAha vibhuja adaba banAo ba kendra se basa dUrI para sa ya fa vRtta khA~co savA03 daba ko ya taka bar3hAo da kendra se daya dUrI para yajaha vRtta khauM cI avA.3 daa ko ha taka bar3hAo pradhA. to aha barAbara hogI basa ke sA.1 dhavA.2 For Private and Personal Use Only

Page #24
(22) pari0 15 upa0-- caMki saya fa vRtta kA va kendra hai isaliye basa barAbara hai ba ya ke aura cUMki yajaha vRtta kA dondra hai isaliye daha barAbara hai da ya ke pari0 15 aura inake hisse da a aura da ba barAbara haiM pari0 24 isaliye bAkI hissA aha barAbara hai bAko hisse ba ya ke sva03 lekina sAbita ho cukA hai ki basa barAbara hai ba ya ke isaliye aha aura basa meM se hara eka barAbara hai ba ya ke lekina jo cIjeM eka hI cIz2a ke barAbara hoM vaha saba ApasameM barAbara hotI haiM sva01 isaliye aha barAbara hai basa ke isaliye aha sIdhI rekhA diye hue biMdu ase dI huI basa sIdhI rekhA ke barAbara khiMcAyI aura isI rekhA ke khIMcane kI z2arUrata thI Ti. (1) isa sAla meM jaba diyA huA bindu nato dI huI rekhA meM ho aura na usa rekhA kI sIdha meM ho to isa sAla kI grATha marateM paidA hogI yAnI eka hI binda se vyAurekhA pATha tarapha khiMca-sato haiM 1- dI huI rekhA ke do sire haiM aura dive hue viMdu ko hara sire se milAne ke liye eka rekhA khIMcI jA sakatI hai 2- hara milAne vAlI rekhA kI hara tarafa samatribAhu tribhuja bana sakatA hai 3- samatribAhu tribhuja kI vaha bhujA jo zaka meM pahale bar3hAyI jAtI hai apane hara sire kI tarafa bAra satI hai lekina jaba diyA huA biTu dI huI rekhA meM yA usakI mIdha meM ho to do sUrateM jo bindu ko rekhA ke hara sire ke milAne se paidA hotI haiM eka ho jAyagau aura isaliye zAla ko sirpha cAra sUrate raha jAyagI jaba diyA huaA viMdu dI huI rekhA ke sira para hoto pala bahuta AsAna hai biMdu ke kendra mAnakara usa rakhA kI dUrI para vRtta khIMco yora rekhA ko vRtta kI paridhi taka bahAno baphA huA hissA dI huI rekhA ke barAbara hogA mudarisa ko cAhiye ki apane lar3akoM se isa pAka kI saba sUrata khicavAve For Private and Personal Use Only

Page #25
(23) Ti. (2) amalI taura se hama isa zakla ko isa taraha hala kara sakta haiM ki parakAra se va samodhI rekhA kI lambAI nApeM aura phira agara parakAra kI eka zAkha kI noka biMdu a para rakkheM to dUsarI zAkha kI noka aise biMdu para par3egI to sIdhI rekhA jo vidu a se usa bidu taka khIMcI jAtI hai basa sIdhI rekhA ke barAbara hogI magara rekhAgaNita meM isa taura para parakAra ke istemAla kI ijAjata nahIM dI gayI hai parakAra kA sirpha vahI istemAla jAyaz2a samajhA gayA hai jo avAdhyopakrama 3 meM bayAna huA hai yAnI hama usake kamI le se eka vRtta khIMceM jisakI paridhi eka diye hue biMdu meM hokara kisI dUsare diye hara viMdu ke girda jisako hama kendra kahate haiM guz2are yaha qhayAla karanA cAhiye ki parakAra ke para yAnI pAAkha kAgaz2a ke dharAtala para se haTate hI phaurana apane grApa banda hojAte haiM ki kisI dUrI ko hama uma ke vamIle se eka jagaha se dUsarI jagaha para nahIM le jAsakta parakAra ke isa khAsa aura mahadUda istemAla para gaura karane se tAla bailma ko isa adhyAya kI pahalI tIna sAdhyoM kI jarUrata mAlama hojAyagI abhyAsa (3) agara dUsarI sAdhya meM choTe vRtta kA yAma bar3e vRtta kI trijyA ho to batAo ki diyA huA viMTu gauravagAye hue tribhuja kA zIrgha kahAM hogA (4) dI huI parimita mIdhI rekhA para aimA samadibAhu tribhuja banAyo jisakI pratyeka muja kimI dI huI dUsarI rekhA ke barAbara ho sAdhya 3 vastU papAdya lA. satra dI huI do sIdhI rekhAoM meM se jo bar3I ho usameM se choTo ko barAbara hissA kATI vi0 sUtra farz2a karo ki aba aura sa da do (pha dI huI sIdhI rekhA haiM jinameM aba bar3I hai aba meM se sa da kI barAbara eka hissA kATanA hai aM0 a bindu se sa da ke bArAbara aya sIdhIrakhA khoMcI sA0 2 a keMdra se aya dUrI para ya phaja vRtta aba sIdhI rekhA kI ja biMdu para kATatA huA khauMco abA03. to aja barAbara sada ke hogI For Private and Personal Use Only

Page #26
(24) upa. cUMki ya phaja itta kA akeMdra hai isaliye aja barAbara hai aya ke pa0 15 lekina a ya barAbara sa da ke banAyI gaI hai isaliye aja aura sa da meM se hara eka aya ke barAbara hai isaliye aja barAbara hai sa da ke isaliye aba dI huI bar3I rekhA meM se eka hissA ajabarA. bara sada choTI rekhA ke kaTa gayA aura isI hisse ke kATane kI janarata thI Ti isI prakAra se hama do choTI bar3I rekhAoM meM se choTo ko isa kadara bATAsakta hai ki bahakara bar3I ke barAbara hojAya aura eka aisausIdhI rekhA bhI khIMca sakta hai jo do sIdhI rekhAoM ke yoga yA ghantara ke barAbara ho sAdhya 4 pramayopapAdya sA0 satra- agara do vibhujoM meM eka tribhuja ko do bhuja dUsare vibhuja kI do bhujoM ke alaga 2 barAbara ho aura una bhujoM se bane hue kona bhI Apasa meM barAbara hoM to una vibhujoM ke AdhAra yAnI tosarI bhuja bhI Apasa meM barAbara hoMgI aura donoM niraja bhI Apasa meM barAbara hoMge aura eka vibhuja ke bAkI kona alga alaga dasare tribhuja ke bAko konoM ke barAbara hoMge yAnI vaha kona Apasa meM barAbara hoMge jinake sAmane ko bhaja barAbara hai vi0 satra- pharja karo ki abasa aura dayapha tribhuja haiM avasa vibhuja kI do bhuja aba aura asa alagada yapha vibhuja kI daya aura daphabhujoM ke barAbara haiM / yAnI aba barAbara hai daya ke aura asa barA / / bara hai daphake aura ba asa kona barAbara hai| iyapha kona ke basa yaka to basa AdhAra barAbara hogA ya fa AdhAra ke aura abasa tribhujadayapha tribhuja ke barAbara hogA aura bAkI kona jinake sAmane kI bhuja barAbara haiM alaga2 barAbara hoMge yAnI aba sa kona bara; For Private and Personal Use Only

Page #27
(25) vara hogA dayapha kona ke aura asaba kona barAbara hogA daphaya kona ke __ upa. kyoMki agara aba sa tribhuja dayapha vibhuja ke Upara isa taraha se rakkhA jAya ki ba biMda ya biMda para ho aura aba sIdhI rekhAdaya sIdhI rekhA para to caMkiaba barAbara hai daya ke (vabhUjiba faz2a ) prabiMTu da biMda para par3egA / __ aura jaba aba sIdhI rekhA ne kula daya sodhI rekhA ko Dhaka liyA to cUMki ba asa kona barAbara hai ya da fa kona ke isa liye asa sIdhI rekhA da fa sIdhI rekhA para par3egI aura cUMki asa barAbara hai dapha ke ( bamujiba phaja ) sa biMda pha biMda para par3egA lekina yaha bayAna ho cukA hai ki ba biMdu ya biMdu ke Upara hai isaliye kula basa AdhAra kula ya pha AdhAra ko Dhaka legA kyoMki jaba ba bindu ya para huA aura sa bindu pha bindu para agara kula basa AdhAra kula ya pha AdhAra para nahauM par3atA hai to do sIdhI rekhA ba sa aura ya pha eka dharAtala ko ghereMgI aura yaha bAta nAmumakina hai sva1. isa liye ku la ba sa AdhAra kula ya pha AdhAra para par3atA hai aura usake barAbara hai ora kula aba sa tribhuja kula da ya pha vibhaja para par3atA hai aura usake barAbara hai aura eka vibhuja ke bAkI kIna dUsare tribhuja ke bAkI konoM ko yUrA pUrA Dhaka lete haiM aura unake barAbara haiM yAnI aba sa kona barAbara hai da ya fa kona ke aura a sa ba kona barAbara hai daphaya kona ke phala isaliye agara do tribhujoM meM eka tribhuja kI do bhuja TUsare tribhuja kI do bhujoM ke pAdyopAnta-yahI sAbita karanAthA For Private and Personal Use Only

Page #28
(23) Ti. (1) yaha zaktA usa sUrata meM bhI saccI mAlUma detI hai navaka kona jo eka tribhuja kI do bhujoM se banA hai vahI ho jo dusare tribhuja kI do bhuja se banA hai jaikhAki tribhuja pha a sa aura ja a ba meM hai (5 vIM mAdhya dekho) yA jabaki tribhujoM meM vyAdhAra ubhayaniSTa ho jaisA ki tribhuja pha ba sa aura jasaba meM hai ( 5vIM mAdhya dekho ) yA jabaki tribhujoM meM eka bhuja ubhayaniSTa ho Ti0 (2) isa sAdhya ke subUta meM grAcchAdana kI kriyA ko kAma meM lAye haiM aura pAThavIM svayaM siddhi ke biloma ko mAna liyA hai -grAcchAdana kriyA se barAbarI daryAfa karane ke liye isa svayaM siddhi ke mAna lene kI z2arUrata hai ki hara zakla ko dharAtala para bagaira usakI sUrata aura bola tabdIla kiye hue eka jagaha se haTAkara dUsarI jagaha para rakha sakte haiM aura dharAtala meM usako lauTa sakta haiM isa bAta kA mAna lenA bhI z2arUra hai ki agara eka sIdhI rekhA ke do binduyoM ke darmiyAna kA hissA dUsarI sIdhI rekhA ke darmiyAna ke hisse para par3atA hai to usa sIdhI rekhA ke bAkI hismoM kI dizAaiM bhI eka dUsarI para par3atI haiM Ti0 (3) hara tribhuna meM chaha rAzi hotI haiM yAnI tIna bhuja aura tInakona aura (sivAya do qhAsa sUratoM ke) jaba ina chaha rAzoM meM se koI tInadI hoM to bAkI tIna daryAta hosaktI haiM aura tribhuja mAlUma ho saktA hai isaliye agara do tribhujoM meM eka tribhuja kI tIna rAzi jinase tribhuja mAlUma ho saktA hai dUsare tribhuja kI unhIM tIna rAzoM ke alaga barAvara hoM to yaha sAbita hotA hai ki tribhuja bhI grApasa meM barAbara hoMge i tIna rAzoM ko chaha sUrateM ho saktI haiM aura vaha yaha haiM. 1 tIna kone 2 tauna bhuja 3 do bhuja aura unase banA huA kona 8 do bhuja aura unameM se eka bhuja ke sAmane kA kona5 do kona aura unake bIca kI bhuja 6 do kona aura unameM se eka kona ke sAmane kI bhuja pahilI sUrata una do sUratoM meM se hai jinameM tribhuja nahIM daryAfa hoktAhai kyoMki tribhuja kI bhuja bargara kone ke ghaTane bar3hane ke ghaTa bar3ha saktI hai dUsarI mUrata isa adhyAya kI AThavoM sAdhya meM sAbita huI hai tIsarI sUrata isa sAdhya meM sAbita huI hai| cauthI sUrata meM bhI tribhuja ThIka 2 nahIM mAlUma ho saktA hai kyoMki yaha mumakina hai ki eka tribhuja kI do bhuja dUsare tribhuja kI do bhujoM ke vyalaga2 barAbara hoM aura eka bhaja ke sAmane kA kona bhI barAbara ho dUsare tribhuja ke eka kona ke jo pahalI bhuja ke barAbara bhuja ke sAmane hai lekina tribhuja vyApasa meM barAbara na hoM For Private and Personal Use Only

Page #29
(27) masalan pharja karo ki adasa eka samadivAhu trimuja hai jisakI ada aura asa maja Apasa meM barAbara haiM sada ko kimI ba bindu taka bahAyo aura aba milAyo aba yaha z2Ahira hai ki aba sa graura aba da tribhujoM meM 1 aba aura asa bhaja to barAbara haiM aba aura adabhajoM ke aura ba kona jo barAbara bhujo asa aura ada ke sAmane hai donoM tribhujoM meM ubhayaniSTa hai lekina vibhaja yApasa meM barAbara nahIM haiM ___pAMcavIM aura chaTI sarateM isa adhyAya kI chabbIsavauM sAdhya meM sAvita abhyAsa (5) agara do varga kSetra kI eka bhuja dUsare varga kSetra kI eka bhuja ke bharAvara ho to vaha donoM barga kSetra saba taraha se vyApasa meM barAbara hoge (6) sama tribAhu tribhuja ke kisI kona ko do barAbara hissoM meM bAMTatI huI rekhA usa kona ke sAmane kI bhuja ko bhI do barAbara hissoM meM bAMTe. gI aura unake sAtha samakona banAvegI (7) agara do sIdhau rekhA eka dUsarI ko barAbara hissoM meM kATatI hoM aura eka TUmarI ke sAtha samakona banAtI hoM to unameM se hara eka rekhA kA hara vinda TUsarI rekhA ke siroM se barAbara dUrI para hogA (8) aba sa da caturmaja kI aba aura ada bhuja barAbara haiM aura asa karNa ba a da kona ko do barAbara hissoM meM bAMTatA hai sAbita karo ki basa aura da sa bhana barAbara haiM aura a sa karNa basa da kona ko do barAbara hissoM meM bAMTatA hai sAdhya 5 prameyopapAdya sA. satra samadvibAhu tribhuja ke AdhAra ke Upara ke kona Apasa meM barAbara hote haiM aura agara barAbara bhujA baDhAyI jAye to AdhAra ke nIce ke kona bhI Apasa meM barAbara hoMge vi0 satra phaz2a karo ki abasa samahibAhu tribhuja hai jisakI aba bhuja asa bhuja ke barAbara hai aura yaha bho farja karo ki aba aura asa barAbara ba bhuja da aura ya binduoM taka bar3hAyI gayI haiM to aba sa kona barAbara hogA asaba kona ke aura da ba sa kona barAbara hogA ya sa ba kona ke garijAda a For Private and Personal Use Only

Page #30
(28) caM0- ba da meM koI pha bindu mAnalI aura bar3I rekhA aya meM se aja barAbara apha ke kATo sA.. aura phasa aura jaba ko milA do upa0-cUMki aja barAbara apha ke banAyI gayI hai aura aba barAbara hai asa ke isaliye phaasa tribhuja kI do bhuja phaa aura asa alagara jaaba tibhuja kI do bhujoM ja a ora aba ke barAbara haiM aura ina bhujoM ke darmiyAna kA phaaja kAna donoM tribhujoM meM ubhayaniSTa hai isaliye phasa AdhAra barAbara hai jaba AdhAra ke auraphaasa tribhuja barAbara hai jaba tribhuja ke ora bAkI kona ina tribhujoM ke jinake sAmane ke bhuja barAbara haiM alaga2 barAbara haiM yAnI asaka kona barAbara hai abaja kona ke aura aphasa kona barAbara hai ajaba kona ke sA. cUMki kula apha barAbara hai kula aja ke aura unake hisse aora apta Apasa meM barAbara haiM __isaliye bAkI himsA bapha barAbara hai bAkI hisse sa ja sA03 aura pha sa barAbara ja ba ke sAbita ho cukA hai aba cUki do bhujabapha aura pha sa alagara barAbara haiM saja aura jaba bhujoM ke aurabakasakonasa jaba kona ke barAbara sAbita ho cukA hai isaliye bapha sa ora sa ja ba vibhuja Apasa meM barAbara haiM aura unake bAkI kona jinake sAmane kI bhuja barAbara haiM alagara barAbara haiM yAnI pha ba sa kona barAbara hai ja sa bakona ke aura basa pha kona barAbara hai sa ba ja kona ke aura cUki yaha sAbita ho cukA hai ki kula a ba ja kona barAbara hai kula asa pha kAna ke aura unake hisse sa ba ja aura basa fa Apasa meM barAbara haiM For Private and Personal Use Only

Page #31
(28) isaliye bAqI kona a ba sa barAbara he bAqI kona a saba ke kha0 3 aura yaha kona a ba sa samahibAhu tribhuja ba sa AdhAra ke Upara ke haiM aura yaha bhI sAbita ho cukA hai ki pha ba sa aura ja saba kona Apasa meM barAbara hai aura yaha kona AdhAra ke nIce ke haiM phala - isaliye samahibAhu tribhuja ke AdyopAnta - yahI sAbita karamA thA anumAna -samacivAhu tribhuja ke satra kona Apala meM barAbara hote haiM Ti0 ( 1 ) isa sAdhya ko hama isa taraha bhI sAbita karasakte haiM agara hama aba sa tribhuja ko lauTa kara gharAtala meM isa prakAra rakva ki abiMdu kI jagaha na badalo jAya aura aba bhuSa asa bhuna para ho-caMki a kona donoM tribhujoM meM zAmila hai a sa bhuja a ba bhuja para par3egI aura cUMki a ba aura a sa vyApasa meM barAbara haiM sa bindu ba bindu para par3egA aura ba bindu sa bindu para par3egA aura a sa ba kona a ba sa kona ko pUrA pUrA eka legA aura ba sa ja kona saba pha kona ko aura isaliye a sa ba kona barAbara hogA a ba sa koma ke auaura basaja kona barAbara hogA saba pha kona ke abhyAsa (1) vighamakona samacaturbhuja ke grAmane sAmane ke kona Apasa meM barAbara hote haiM (10) agara eka hI AdhAra para do bama divAha vibhuja hoM aura vyA dhAra ke sAmane ke konoM ke darmiyAna eka rekhA khIMcI jAya to vaha rekhA yoMhI yA bar3ha kara vyAdhAra ko do barAbara hissoM meM bAMTegI aura vyAghAra ke sAtha samakona vanAvegI (11) pAMcavIM sAdhya ko varga ra harUpha rakkhe sAbita karo sAdhya 6 prameyopapAdya agara kisI tribhuja ke dI kona Apasa meM barAbara sA0 sUtra hoM to una konoM ke sAmane kI bhuja bhI Apasa meM barAbara hoMgI 0 sUtra farz2a karo ki a va sa eka tribhuja hai aura usake vi0 a ba sa aura a sa ba kona Apasa meM barAbara haiM For Private and Personal Use Only

Page #32
(30) to asa aura aba bhuja bho Apasa meM barAbara hoMgI upa0 agara a sa aura a va Apasa meM barAvara nahIM to unameM se eka dUsarI se baDI hogI farz2a karo ki aba bar3I hai a sa se aba meM se ba da barAbara a sa ke kATalI caura sa da milAo da sA0 3 a0 1 aba cUki da ba ba aura a sa ba tribhujoM meM da ba barAbara hai a sa ke aura ba sa donoM meM ubhayaniSTa hai yAnI eka vibhuja kI daba aura ba sa bhaja alagara dUsare vibhuja kI a sa aura sa ba do bhujoM ke barAbara haiM aura da ba sa kona barAbara hai a sa ba kona ke faz2a isaliye dasa AdhAra barAbara hai a ba AdhAra ke aura da ba sa vibhuja barAbara hai a sa babhuja ke sA0 4 yAnI koTA tribhuja barAbara hai bar3e vibhuja ke ora yaha vAta sAfa jhUTha hai sva0 2 isaliye a ba aura a sa nAbarAbara nahIM haiM yAnI a sabarAbara hai aba ke phala isaliye agara kisI tribhuja ke do kona AdyopAnta - yahI sAbita karanA thA anumAna - samAnakona tribhuja kI saba bhuMjA vyApasa meM barAbara hotI hai Ti0 (1) yAda rakhanA cAhiye ki aba meM se choTI rekhA ke barAbara hissA ba kona kI tarafa se kATanA cAhiye varana: cauthI sAdhya se isa sAdhya kA sAbita karanA aura mumakina hogA (Ta0 (2) eka sAdhya dUsaro sAdhya ko viloma usa mUrata meM hotI hai jaba ki isa mAdhya meM jo bAta kalpita vyartha kI jagaha para ho vaha pahilI sAdhya meM phala kI jagaha para ho aura jo bAta dUsarI sAdhya meM phala kI jagaha para ho vaha pahilI sAdhya meM kalpita artha kI jagaha para ho yaha sAdhA pAMcavIM mAdhya ke pahile hisse kA viloma hai yAnI isa bAdhya meM jo bAta kalpita grartha kI jagaha para hai usa hisse meM phala kI jagaha para hai aura jo bAta isameM phala kI jagaha para hai usameM kalpita artha kI jagaha para hai jaisA ki ina donoM sAdhyoM ko isa taraha para bayAna karane se sAfa z2Ahira honAyagA sAdhya 5 nagara do bhujA barAbara haiM to unake sAmane ke kona barAbara hai| sAcca 6 agara do kona barAbara haiM to unake sAmane ke bhuja barAbara For Private and Personal Use Only

Page #33
(31) isa bAta kA jAnanA bhI jarUra hai ki kisI mAdhya kI sacAI usake viloma kI sacAI ko kAyama nahIM karatI hai mumakina hai ki asalI sAdhya sahI ho lekina unakA viloma galata ho Ti0 (3) yaha mAdhya yatireka yukta se sAbita kI gayI hai jaba hama kisI sAdhya ke phala yAnI natIje ko sahau na mAna kara usake viparIta ko sahI mAnate haiM yAra umase grAkhira ko eka aisA natIjA nikalatA hai jo sApha bhUTha hai yA sAdhya meM jo bAta mAz2a kI gayI hai usake viruddha hai to hama ka. hate haiM ki sAdhya ke phala kA viparIta jisako hamane sahI mAnA thA galata hai aura imaliye sAdhya kA phala sahI hai aise subUta ko vyatireka yukta kaha te haiM yatireka yukta kI banikhata anvaya yukti kI loga akasara kama kadara karate haiM kyoMki yatiraka yukta meM yaha bAta to alabattA jAhira hojAtIhai ki sAdhya imArI mahI hai lekina usase yaha bAta ki sAdhya kyoM aura kisa bajaha se sahI hai nahIM mAlama hosaktI / vyatireka yakti ko ukUledasa ne mAdhyoM ke biloma ke sAbita karane meM aksara kAma meM lAyA hai aura anvaya yakti se usane bilomoM ke sAvita karane meM bahuta kama kAma liyA hai Ti. (8) isa mAdhyakI z2arUrata dUsare adhyAya kI cauthI sAdhya taka nahIM par3atI hai agara isako hama kahIM dUmarI jagaha para uThA kara rakhadeM to kucha kharAbI nahIM paidA hogI masalana agara hama isako chaThAravIM sAdhA ke vAda rakakheM to vaha isa taraha sAbita ho sakatI hai faz2a karo ki aba sa kona asa ba kona ke barAbara hai to asa bhuja bhI aba bhuja ke barAbara hogA aura yaha bhuna aApasa meM barAbara na hoto eka unameM se bar3I hogI phaz2a karoki aba baDI asa se to asaba kona var3A hogA aba sa kona se mA0 18) lekina yaha nA mumakina hai kyoMki a sa ba aura aba sa kona bamujiba phaz2a ke grApasa meM barAbara haiM isaliye ava aura asa nAbarAbara nahIM haiM yAnI aba barAbara hai asa ke __agara ima sAdhya ko chabbIsavauM sAdhya ke bAda likheM to isa taraha nAbita kareMge ba asa kona ko ada rekhA se jo basa AdhArase da bindu para milatI hai do barAbara hissoM meM bAMTo isa sUrata meM do trisuna a ba da vyaaura asada paidA hoMge aura chabbImavauM sAdhA ke hukama se aApasa meM sava taraha barAbara hoMge aura aba bhuna asa suja ke barAbara hogI Ti. (5) kaThI sAdhA grAcchAdana kriyA se bhI jaise ki pAMcauM sAdhA (Ti0 sA0 5 dekho ) sAbita kI gayI hai sAbita hosaktI hai abhyAsa (12) agara eka lamadvibAhu tribhuja ke aAdhAra ke Upara ke kona aba For Private and Personal Use Only

Page #34
(32) aura asaba rekhA ba da aura sa da se do barAbara hissoM meM bAMTe jAyaM vo sAbita karo ki basa da samadibAhu tribhuja hai (13) ba a sa tribhuja kA ba kona a kona se dUnA hai agara bada rekhA ba kona ko do barAbara hissoM meM bAMTa kara asamaja se da vinda para mile vo sAbita karo ki ba da barAbara hai ada ke (14) pahale agrAya ko pAMcavoM sAdhA meM agara phasa aura ba ja mindu ipara mileM to phaha barAbara jaha ke hogI (15. pahale yadhyAya kI pAMcavIM sAdhA meM gragara phasa graura ba ja binda ha para mileM to aha rakhA baasa ko na kodo barAbara hissoM meM bAMTegI savAlAta itihAna sAdhya 1 se 6 taka (1) pahalI sAdhA meM nirdiSTa grAra karNoya btaayo| (2) parimita sIdhI rekhA se kyA matalaba hai aura usakA biloma kyA hai (3) agara pahalau sAdhA meM aba ke dUsarI ora eka aura mama trivA. hu tribhuja banAyA jAve to donoM trinoM se mila kara konasI zakala paidA hovegI (4) dUsarI sAdhA kI kitanI mUrateM ho sakatI haiM (1) jaba diyA huyA binda na dI huI rekhA meM ho aura na usake bar3he hue hise meM ho (2) jaba vaha rekhA ke bhItara ho yA usake bane hue hisse meM ho (3) jaba vaha rekhA ke sire para ho (5) eka rekhA meM se jo donoM ora aparimita hai eka rekhA kI la. mbAI ke barAbara kaise kATa sakate haiM / (6) kyAna karo ki 3 avAyopakrama meM jo parakAra kA qhAsa aura parimita kAma rakkhA gayA hai isakI vajaha se dUsarI aura tIsarI sAdhA ko kyoM z2arUrata haI kyA yaha jarUra hai ki dUsarI sAdhA meM sirpha samatri. bAhu tribhuja banAyA jAve kyA hama isa jagaha samadivAha tribhuja banA sakate haiM (7) cauthI pAkala ke kalpita artha aura phala meM kitane kitane hisse hai unako vayAna karo (8) cauthau sAdhA ko kisa sIti se siddhi kiyA hai aura umarIti meM konasA svayaMsiddha kAma meM lAyA gayA hai (E) hara tribhuja meM kitane hisse hote hai (jabAva ) tIna sajA paura tIna kone (10) eka tribhuja ko dUsare tribhuja ke barAbara sAbita karane meM kama se kama kitane hima eka vibhuja ke dUsare tribhuja ke barAbara hone cAhiye ( javAba ) sAdhAraNa rIti se koI tIna sivAya tIna konoM ke, isakA muqhta pATha, chabbIsa, cAra sAdhya meM huyA hai For Private and Personal Use Only

Page #35
(33) (11) ina do sIdhI rekhAyoM ke jinake donoM bindu zAmila hai kauma kI khAsiyata cauthI mAdhya meM bayAna huI hai (bhavAva ) ve eka dUsare ko eka letI hai (12) 5, 6 mAdhyoM meM kyA sambandha (13) eka mAdhya dUsarI sAdhya ko pratiloma kaba hotI hai (14) ukta dasa ne viloma sAthyoM ko kima rIti se mihi kiyA hai (15) kyA kisI sAdhya kI sacAI usake biloma ko bhI sthApana karatI hai aura yadi nahIM karatI hai to udAharamA do / (16) yatireka yukti se kyA matalaba hai aura vyatireka yukti para anvaya yukti meM antara batAyo (17) chaTo mAdhya ko kaunamI jhaMTha bAta mAna kAra sAbita kiyA hai (18) chaTo sAdhya ko anvaya yukti siddhi karo sAdhya 7prameyopapAdya.. sA0 satra agara eka hI AdhAra para aura usake eka hI tarafa dI vibhuja ho to mumakina nahIM hai ki unake vaha bhuja jinake - sirai AdhAra ke eka sire para hoM Apasa meM barAbara hoM aura vaha bhuja bhI jinake sire AdhAra ke dUsare mire para ho Apasa meM barAbara hoM bi. satra agara yaha mumakina ho to farz2a karo ki eka hI AdhAra aba para aura usake eka hI tarafa aise do tribhuja asa va aura adaba haiM ki unakI sa a aura da abhuja jinake sire AdhAra ke asire para haiM Apasa meM barAbara haiM aura sa ba aura daba bhaja bhI jinake sire AdhAra ke ba sire para haiM Apasa meM barAbara hai aM0-sada milAo--isa zakla kI tIna sUrateM haiM pahalI sUrata yaha hai ki hara vibhuja kA zIrSa dUsare ma, tribhuja ke bAhara ho upa0- cUMki adabarAbara asa ke faz2a kI gaI haiisaliye a sa da kona barAbara hai adasa kona ke mA05 lekina asada kona basa da kona se bar3A hai kha.. For Private and Personal Use Only

Page #36
(34) isaliye adasa kona bhI basa da kona se bar3A hai isavAste badasa kona ba sa da kona se aurabho z2iyAdA bar3A hai phira cUMki ba sa barAbara ba da ke faz2a kI gaI hai isaliye badasa kona barAbara hai ba sa da kona ke mA05 lekina yaha sAbita ho cukA hai ki ba da sa kona ba sa da kona se bar3A hai isaliye badasa kona ba sa da kona se bar3A aura usake barAbara bhI hai aura yaha bAta nAmumakina hai dUsarI sarata yaha hai ki adaba vibhuja kA zoSa da vibhuja asa ba tribhuja ke andara hai aM0- asa aura ada ko ya aura pha binduoM taka bar3hAdI upa0- cUMki asa da tribhuja meM asabhuja barAbara hai adabhuja ke isaliye sa da AdhAra ke nIce ke ya sa da aura pha da sa kona Apasa meM barAbara haiM sA0 5 lekina yasa da kona basada kona se bar3A hai kha. isaliye phadasa kona bhI basada kona se bar3A hai isavAsta ba da sa kona basa dakonase aura bhI z2iyAdA bar3A hai phira cUMki ba sa barAbara ba da ke pharja kI gaI hai isaliye ba dasa kona ba sa da kona ke barAbara hai lekina yaha bAta sAbita hocako hai ki ba dasa kona ba sa da kona se bar3A hai isaliye ba da sa kona ba sa da kona se bar3A aura usake barAbara bhI hai aura yaha bAta nAmamakina hai tIsarI surata jisameM adabavibhuja kAdazopa sa asa ba vibhajJa kI bhujA para hai isa sUrata meM sAfa jAhira hai ki ba da aura basa Apasa meM barAbara nahIM ho sakI hai. For Private and Personal Use Only

Page #37
Achar (35) phala isaliye agara eka hI AdhAra para aura usakI eka ho tarafa do vibhana AdyopAnta yahI sAbita karanA thA Ti. (1) isa mAdhya kA kAma sipha pahile nadhyAya kI aAvI sAdhya ke mAbita karane meM par3atA hai so grAThavIM sAdhya kA saMbata dUsare taura para bhI ho sakatA hai aura usa sabUta meM isa sAdhya kI kucha jarUrata nahIM par3atI hai Ti. (2) ukta dasa ne isa mAdhya ke sAbita karane meM sAdhya ke natIje ke khilApha ko sahI mAna kara usase aAkhira ko aisau do bAteM nikAlI hai jo eka dUsarI ke viruddha haiM yAnI eka kona dUmare kona se bar3A aura usake barAbara bhI hai isa kisma ke subUta kA istemAla ukta dama ne sirpha isI sAdhya meM kiyA hai aura kimI dUsarI jagaha para nahIM kiyA hai Ti0 (3. yAda rakhanA cAhiye ki eka hI AdhAra para usake eka hItarapha aise do tribhuna homatI hai ki unakI vaha suja jinake sira grAdhAra ke eka sire para hoM Apasa meM barAbara hoM magara vaha suja jinake ghire AdhAra ke dUsare sire para hoM nAvarAbara hoM abhyAsa (16) sAbita karo ki do vRtta apane kendroM ko milAte hue rekhA eka yora sirpha eka vindu para aura do se z2iyAdA vindu yo para eka dUsare ko nahIM kATa sakta hai sAdhya 8 prameyopapAdya sA0 satra agara eka tribhuja kI do bhuja dUsare vibhuja kI do bha ja ke alaga alaga barAbarahoM aura unake AdhAra bhI Apasa meM barAbara hoM to kona jo eka vibhuja kI do bhujoM se banatA hai barAbara hogA dUsare vibhuja ke usa kona ke jo una bhujoM kI barAbara vAlI bhujoM se banatA hai vi0 sUtra farz2a karo ki aba sa vibhuja kI do bhuja aba aura asa vibhuja da ya pha kI daya aura dapha bhujoM ke alaga alaga barAbara hai yAnI aba barAbara da ya ke aura asa barAbara dapha ke hai aura basa AdhAra bhI / ya fa AdhAra ke barAbara hai to ba asa kIna barAbara hogA yadapha kona ke K For Private and Personal Use Only

Page #38
(36) upa0 kyoMki agara aba sa vibhuja daya fa tribhuja para isa taraha rakkhA jAya ki ba bindu ya binda para aura basa rekhA yafa rekhA para ho to cUMki basa barAbara hai ya fa ke ( phaz2a ) sa biMdu pha biMdu para par3egA aura jaba basa AdhAra ya pha adhAra para pUrA 2 par3atA hai to baa aura sa a bhuja ya da aura phada bhajoM para par3egA kyoMki agara basa AdhAra ya pha AdhAra para par3e lekina ba a aura muna ya da aura pha da bhujoM para na par3eM balaki mukhalipha jagahoM para ya ja aura phaja kI taraha par3eM to eka hI AdhAra para aura usake eka hI tarapha aise do vibhuna hoMge ki jinakI vaha bhuja jinake sire AdhAra ke eka sire para haiM Apasa meM barAbara haiM aura unakI vaha bhuja bhI jinake sire AdhAra ke dUsare sire para haiM Apasa meM barAbara hai| lekina yaha bAta nAmumakina hai sA. 7 isaliye agara basa AdhAra ya pha AdhAra para par3atA hai to vaa aura sa ja bhuja bhI yada aura pha da bhajoM para par3egI ... aura isaliye ba a sa kona aura ya da pha kona eka dUsare ko pUrA2 haka leMge aura isaliye vaha Apasa meM barAbara hai sva. 8 phala isaliye agara eka vibhuja kIdo bhuja dUsare tribhuja kI do ajoM ke adyopAnta yahI sAbita karanA thA anamAna isase yaha sAbita ho maktA hai ki barAbara bhujoM ke sAmane ke kona bhI nApasa meM barAbara haiM yAno ba koga barAbara ya kona ke aura ma kona barAbara hai pha kona ke aura donoM tribhuja bhI grApasa meM barAbara hai Ti. (1) isa sAdhya ko bagara madada mAtavauM sAdhya ke isa taraha mAbita kara sakta hai farja karo ki aba sa nimuna aura da ya pha tribhuna isa taura se rahAve gaye haiM ki basa aAdhAra yapha bAdhAra para hai aura libhajoM ke pI a aura da eka dUsare ke sAmane hai For Private and Personal Use Only

Page #39
(37) da amilAyo isakI tIna marate haiM pahalI mUrata yaha hai ki da agrAdhAra ya pha ko da aura pha ke bhUmi yAna kATatA hai cUMki a ya da tribhuja meM a ya bhuja da ya bhuja ke barAbara hai , isaliye ya da a kona ya ada kona ke barAbara hai sA05 // aura caMki apha da tribhuja meM apha bhuja da pha muja ke ka barAbara hai isaliye pha akona pha adakona ke barAbarahai nA.5 / lekina sAbita ho cukA hai ki ya da a.kona ya ada kona aM. ke barAbara hai imaliye kula ya da phakona kujaya apha kona ke barAbara hai sva0 2 lekina yasapha kona ba asa kona hai isaliye basa kona bada pha kAna ke barAbara hai dasaro sarata yaha hai ki da agrAdhAra ya phako na kATe caMki ayada tribhuja meM aya bhuja da ya maja ke barAbara hai isaliye yada a kona yaada kAna ke barAbara hai sA.5 __ aura ki apha da tribhaja meM aphasana da pha bhaja ke barAbara hai isaliye pha da akona phaada kona ke barA sA05 lekina sAbita hocukA hai ki kula ya da akona kula ya ada kona ke barAbara hai aura isake hisse pha da na yora pha ada yApasa meM barAbara haiM ilaliye bAkI hissA ya da pha barAbara hai bAkI hissA ya apha ke sva03 lekina ya apha kona ba asa kona hai isaliye ba asa kona ya da phakona ke barAbara hai tIsarI marata yaha hai ki da a aAdhAra yapha ke kisI eka mire para hokara jAtA hai caMki a ya da tribhuja meM da ya barAbara hai a ya ke isaliye ya aphe kona barAbara hai ya da pha kona ke mA05 ya -ka lekina ya apha kona ba asa kona hai isaliye ba asa kona barAbara hai ya da pha kona ke / Ti. (2) yaha mAdhya pahale adhyAya kI cauthI sAdhya kA viloma hai jaba kimI prameyopapAya sAdhya meM kaI bAteM pharja kI huI hoM aura unakA eka natIjA ho agara koI dUsarI sAdhya aisI banAI jAve ki pahalI mAya kI pharz2a ko huI bAtoM meM se eka bAta hama sAdhya kA natIjA ho aura pahalau sAdhya kA natIjA maya bAkI faz2a kI huI bAtoM ke ima mAdhya meM phana kI huI bAteM hoM to aisI do sAdhyoM ko bhI eka dUsarI kA biloma kahate haiM aura isI sUrata meM aAThavauM aura cauthI sAdhya eka dUsarI kA biloma haiM jaisA ki ina mAdhyoM ko isa taraha para kyAna karane se sApha mAlUma hotA hai For Private and Personal Use Only

Page #40
(38) agara do bhuja barAbara haiM sAdhya 85 to AdhAra barAbara hai aura aAdhAroM ke sAmane ke kona varAvara haiM agara do suja barAbara hai. to aAdhAra ke sAmane ke kona varAbara hai sAdhya yora AdhAra barAbara hai pATavauM sAdhya kA dUsarI kisma kA viloma yAnI agara eka tribhuja ke tIna kona dUsare tribhuja ke tIna konoM ke alaga alaga barAbara ho to barAbara konoM ke sAmane ke suja bhI grAyala meM barAvara hoMge sahI nahIM hai abhyAsa (17) agara samadvibAhu tribhuja ke zIrya se eka rekhA grAdhAra ke do barAvara hisse karatI huI khIMcau nAya to vaha zIrgha ke bhI do barAbara hisse karegI (18) viSamakona samacaturbhuja ke karNa jina konoM se hokara gujarate haiM unake dora barAbara hisse karate haiM ___(1) a ba sa aura ada va do tribhuja aba rekhA ke eka hI tarafa hai aura unakI asa aura ba da bhuja barAbara hai aura ada aura basa bhuja bhI barAvara haiM aura ada aura ba sa eka dUsarI ko ya bindu para kATatI haiM to sAbita karo ki a ya va samadibAhu tribhuja hai sAdhya 6 vastUpapAdya sA.satra- diye hue saralakona ke do barAbara hisse karo vi0 satra- phaja karo ki ba a sa diyA huA a sarala kona hai usake do barAbara hisse karane haiM aMkana-- aba meM koI da bindu lo aura baDI rekhA asa meM se aya barAbara ada ke kATalI sA03 aura da ya milAdI avA01 daya para ase dUra da pha sa samatribAhu vibhaja banAo sA. 1 aura apha milAo avA0 1 to apha rekhA ba asa kona ke do barAbara hisse karegI upa0-cUMki aya barAbara ada ke banAI gaI hai For Private and Personal Use Only

Page #41
(38) aura maka do vibhaja da apha aura ya apha meM ubhayaniSTa hai yAnI do suja da aaura apha alagara barAbara haiM ya a aura apha do bhujoM ke bhIra dapha AdhAra ya pha AdhAra ke barAbara hai isaliye da apha kona barAbara hai ya apha kona ke isaliye diye hue varasa sarala kona ke apha rekhA se do barA. vara hisse hogaye aura isI kona ke do barAbara hisse karane kI janavarata thI Ti. (1) a se dUra mamavivAhu tribhuja banAne kI kaida isaliye kI gaI hai ki vyagara aisA na ho aura samatribAha tribhuja da ya ke usa tarapha banAyA jAve jisa tarafa da a ya tribhuja hai to eka sarata meM mumakina hogA ki pha bindu abindu para par3e aura usa marata meM apharekhA na khica sakegI yaha bhI yAda rakhanA cAhiye ki pha vinTu ba asa kona ke andara hogA kyoMki pha bindu ke ba a sa kona ke bAhara hone yA a ba yA asa rekhAoM para hone se yaha phala nikalegA ki samAvibAha trisujapha da ya ke AdhAra da ya para kA kona eka hI hAlata meM va da ya kona yA sa ya da kona me choTA hogA aura usase bar3A yA usake barAbara hogA aura yaha bAta nAsamakina hai Ti. (2) isa sAdhya ke lagAtAra istemAla karane se eka kona ke 4, 8, 16 vagareraH barAbara hisse ho sakate haiM lekina hara kona ke tIna varAbara hisse karane meM bar3e 2 lAyaka rekhAgaNita jAnane vAloM kA parizrama nighaphala rahA abhyAsa (20) navauM sAdhya ko bagaira madada AThavauM sAdhya ke sAvita karo sAdhya 10 vastupapAdya sA0satra- dI huI paramita sIdhI rekhA ke do barAbara hisse karo vi0 satra- faz2a karo ki aba dohuI paramita sIdhI rekhA hai usake do barAbara hisse karane haiM / aM0- aba para asa vasamavibAhu tribhuja banAo sA0 1 aura asaba kona ke sa da rekhA se jo aba ko da biMdu para kATatI hai do barAbara hisse karo mA08 For Private and Personal Use Only

Page #42
to aba ke da biMdu para do barAbara hisse ho jAyaMga upa0-- cUMki asa barAbara hai basa ke aura sa da do vibhuja asada aura ba sa da meM ubhayaniSTa hai yAnI do bhuja asa aura sa da alaga 2 barAbara haiM basa aura sada do bhujoM ke aura asada kona ba sa da kona ke barAbara hai isa liye ada adhAra barAbara hai ba da AdhAra ke sA0 4 isaliye aba rekhA ke da bindu para dI barAbara hisse hogaye aura isI rekhA ke do barAbara hisse karane kI z2arUrata thI Ti. isa mAdhya ke lagAtAra kAma meM lAne se eka paramita sIdhI rekhA ke cAra grATa solaha ityAdi barAbara hisse ho sakta haiM abhyAsa (21) sAbita karo ki dasavoM sAdhya meM sa da rekhA a va rekhA ke sAtha samakona banAtI hai (22) dI haI paramita sIdhI rekhA ko itanA bar3hAyo ki bar3A havyA hissA usa rekhA kA jo dI huI rekhA aura bar3he hue hisse se bane tihAI ho sAdhya 11 vastUpapAya sA0 satra-diye hue bindu se jo eka do huI sodho rekhA meM hai eka aisI sIdhI rekhA khIMco jo dI huI rekhA ke sAtha samakona banAve vi0 satra-- phaz2a karo ki basa dI huI sIdhI rekhA aura usameM a diyA huA jindu hai abindu se eka aisI socI rekhA khIMcanI hai - jo basa ke sAtha sama kona banAve aM0- basa meM koI da bindu lelo aura aya barAbara ada ke banAo yada papha ya sama tribAhu tribhuja banAo sA. 1 aura pha amilAo sA. For Private and Personal Use Only

Page #43
(41) to apha sIdhI rekhA jo abindu se khoMcI gayI hai basa rekhA ke sAtha abindu para samakona banAvego upa0-cUMki aba barAbara ada ke banAI gaI hai aura apha do vibhuja da apha aura ya apha meM ubhayaniSTa hai yAnI daaaura apha do bhuja alaga2 barAbara hai ya a aura apha do bhujoM ke aura da pha AdhAra barAbara hai ya pha AdhAra ke pa0 24 isaliye da apha kona barAbara hai ya apha kona ke sA08 aura yaha Asanna kona haiM lekina jaba eka sIdhI rekhA dUsarI sodhI rekhA para khar3I hokara aise Asanna kona banAva jo eka dUsare ke barAbara hoM to una konoM meM se haraeka kona ko samakona kahate haiM pa0 10 isaliye da apha aura ya apha konoM meM se haraeka samakona hai isaliye diye hue a bindu se jo dI huI basa sIdhI rekhA maiM hai apha sIdhI rekhA jo basa ke sAtha samakona banAtI hai khiMcagayo- aura isI rekhA ke khIMcane kI z2arUrata thI anamAna-- isa sAdhya kI madada se sAbita hosaktA hai ki do sodhI rekhA ubhayaniSTa hissA nahIM rakha saktoM agara mumakina ho to faz2a karo ki abasa ora aba da do sIdhI rekhAoM meM aba hissA ubhayaniSTa hai va binda se baya aisI sIdhI rekhA khIMco jo aba rekhA ke sAtha samakona banAtI ho sA0 11 cUki aba sa sodhI rekhA faz2a ko gayo hai isaliye sa ba ya kona barAbara hai ya ba a kona ke cUMki abada bhI sIdhI rekhA phaz2a ko gayI hai isaliye dabaya kona barAbara hai ya ba a kona ke For Private and Personal Use Only

Page #44
isaliye daba ya kona sa va ya kona ke barAbara hai sva. 1 yAnI choTA kona barAbara bar3e kona ke hai aura yaha nAmumakina hai sva. isaliye do sIdho rekhA ubhayamiSTa hissA nahIM rakhatauM yahI sAbita karanA thaa| Ti0 (1) yaha anumAna ukale dasa meM jo yUnAnI javAba meM likhI hai nahIM hai isako simasana sAhaba ne gyArahavauM sAdhya ke sAtha lagAyA hai magara isa para bar3A bhArI aitarAja ho sakA hai kyoMki hama nahIM jAnate ki baya laMba kisa. taraha khIMcA jAyagA agara hama usake khIMcane ke liye gyArahavIM sAdhya kI madada leve to z2arUra hai ki hama ba a ko bar3hAveM aura jaba hama ba a ko bar3hAeMge to yaha bAta mAna lenA pharja hogA ki yaha sirpha eka taraha va saktI hai kyoMki bagara isa bAta ke mAnalene ke hama nahIM jAna sakne ki sirpha ekahI laMba ba yakhiMcegA aura jaba hamane aba kA sirpha ekahI taraha bAhanA mAnaliyA to hamane unma dAve ko jisako hama sAbita karanA cAhiye mAnaliyA agara mimasana sAhaba kA anumAna terahavIM sAdhya ke bAda Ave to vaha ima taraha sAbita ho saktA hai agara samakina ho to faz2a kaho ki abasa cyora abada do sIdhI rekhAyoM meM aba hissA ubhayanira hai ba biMdu se koI ba ya rekhA khIMco to aba ya aura bayasa kona mila kara barAvara dI samakona ke hoMge (sA. 13) aura aba ya aura ya ba da kona bhI milakara barAbara do samakona ke hoMge (sA. 13) isaliye abaya aura yabasa kona barAbara hoMge aba ya auraya ba da konoM ke ( sa01) isaliye yabasa kona ya ba da kona ke barAbara hogA (sva.3) yAnI kula apane eka Tukar3e ke barAbara hogA aura yaha nAmumakina hai (kha ) isaliye do sIdhI rekhA ubhayanie hissA nahIM rakhatI agara simalana sAhaba ko isakA qhayAla karanA hI thA ki do sIdhI rekhA ubhaya nira hissA rakhatI hai yA nahIM to unako cAhiye thA ki ise pahale hI qhayAla karate kyoM ki pAMcavIM sAdhya meM agara do sIdhI rekhA ava taka eka hI hoM aura ba bindu se judo hoM to ba sa AdhAra ke nIce ba bindu para do choTe bar3e koga paidA hoMge aura unameM se hara eka basa ja kona ke barAbara hogA logoM ko yaha bhI rAya hai ki pahalI sAdhya hI meM cupa cApa mAna liyA gayA hai ki asa aura basa rekhA sa bindu para jahAM vaha milatI haiM ubhayanira hissA nahIM rakhatI simasana sAhaba ne isa natIje kA bayAna gyArahavauM sAdhya se pahale kahIM nahIM kiyA hai agara hama isa anumAna ko nikAla kara dasavo svayaM siddhi For Private and Personal Use Only

Page #45
(43) maiM yaha bAta jiyAdA karadeM ki agara eka sIdhI rekhA ke koI do biMdu dUsa rau sIdhI rekhA ke do biMduyoM para par3e to para una ho binduoM ke andara aura bAhara ho jAyage donoM sIdhI rekhA eka dUsarI par3egI to saba jhagar3e tamAma Ti0 (2) gyArahavIM sAdhya navIM sAdhya kI eka khAsa sUrata hai donoM vAdhyoM meM afa aisI rekhA khIMcI gayI hai o va aura satra ke sAtha a biMdu para barAbara kona banAtI hai navIM sAdhya meM baa rekhA aura ma a rekhA ke liye koI qada nahIM hai gyArahavIM mAdhya meM yaha kada hai ki batra aura saa rekhA ekahI sIdha meM hoM navIM aura gyArahavIM sAdhyoM ke dAve ekahI dAve meM iva taraha bayAna hote haiM ki usa bindu se jahAM do dI huI khIdhI rekhA milatI haiM eka aisI sIdhI rekhA khIMco jo dI huI rekhAyoM ke sAtha barAbara kona banAve Ti0 (3) do binduyoM ke darmiyAna kI dUrI vaha mIdhI rekhA hai jo una bindu yoM ko milAtI hai aura eka bindu ko eka sIdhI rekhA se dUrI ha choTI se choTI sIdhI rekhA hai jo usa bindu se usa rekhA taka khIMcI jAgha abhyAsa (23) eka aisA bindu daryAkRta karo jo diye hue tIna binduoMoM se jo eka hI sIdhI rekhA meM nahIM haiM barAbara dUrI para hI (24) dI huI sIdhI rekhA meM eka aisA bindu daryAfa karo ki jisakI dUrI do diye hue bindu yoM se barAbara ho aura yaha bhI batAo ki kisa hAlata meM aisA bindu daryAfa na ho sakegA sAdhya 12 vastUpapAdya sA0 satra dI huI aparamita sIdhI rekhA para diye huye bindu se jo usa rekhA ke bAhara hai eka lamba DAlo vi0 sUtrafarz2a karo ki aba dI huI aparamita sIdhI rekhA hai jisako donoM tarafa cAheM jitanA bar3hA sakte haiM aura sa diyA huA bindu usake bAhara hai sabindu se sIdhI rekhA aba para eka laMba DAlanA hai aM0- aba kI dUsarI tarapha koI da bindu le lo For Private and Personal Use Only sa A gra pha ya

Page #46
(44) aura sa kendra se sa da dUrI para ya phaja vRtta khoMcI jo aba se fa aura ja para mile avA0 3 phaja ke ha biMdu para do barAbara hisse karo sA. 10 aura sa ha milAI avA. 1 to saha jo sa bindu se khIMcI gaI hai do huI aba rekhA para lamba hogI sa pha aura sa ja milAo avA. 1 upa0-cUki phaha barAbara ha ja ke banAI gaI hai aura ha sa do vibhuja phaha sa aura ja ha sa meM ubhayaniSTa haiM yAnI do bhuja phaha aura ha sa do bhujoM jaha aura ha sa ke alaga 2 barAbara haiM aura sa pha AdhAra barAbara hai sa ja AdhAra ke pa0 15, isaliye phaha sa kona barAbara hai jahasa kona ke sA08 aura yaha Asanna kona haiM lekina jaba eka sIdhI rekhA dUsarI sIdhI rekhA para khar3I hokara Asanna kona barAbara banA to una konoM meM se haraeka kona samakona hotA hai aura khar3I sIdhI rekhA ko dUsarI sIdhI rekhA para lamba kahate haiM isaliye sa ha rekhA aba para lamba hai pa. 10 isaliye sa biMdu se jo dI huI aba rekhA ke bAhara hai saha rekhA lamba aba rekhA para khiMcagaI - aura isI lamba ke khoMcane kI z2arUrata thI Ti0 (1) isa sAdhya meM isa bAta ko mAna liyA hai ki vRtta aba rekha ko do bindayoM para kATegA kyoMki jaba hama khayAla karate haiM ki hatta kI paridhi kA eka eka hissA aba rekhA ke donoM tarafa hai aura paridhi eka taraha kI lagAtAra rekhA hai to yaha jAhira bAta mAlama detI hai ki paridhi do bAra aba sIdhI rekhA ko kATatI huI guz2aragI dI huI rekhA meM apa. rimita hone kI kaida rakkhI gaI hai kyoMki agara yaha kaida na hotI to yaha samakina thA ki khAma hAlatoM meM paridhi aba rekhA ko kisI jagaddha para na kATatI yA sirpha eka hI jagaha para kATatI For Private and Personal Use Only

Page #47
(jha) e Ti0 (2) ukta dasa ne samakona banAtI huI rekhA aura lamba rUpa rekhAyoM meM yaha pharka rakkhA hai ki jaba rekhA kisI dUsarI rekhA ke eka bindu se gyArahavIM mAdhya ke anusAra khIMcI gaI hai usako ukta dala ne samakona banAtI huI rekhA kahA hai aura jaba rekhA kinI bindu se jo dUsarI rekhA ke bAhara hai bArahavIM mAdhya ke anusAra usa rekhA para DAlI gaI hai unako ukta dasa ne lamba kahA hai lekina isa samaya ke likhane vAle isa faqa kA kucha bhI qhayAla nahIM karate aura hara eka ko dUsarI kI jagaha istemAla karate haiM abhyAsa (25) gara kisI tribhuja ke zIrSa se vyAdhAra para lakha DAlA jAve aura vaha lamba AdhAra ko do barAbara hissoM meM bAMTe to vaha tribhuja samaddivAhu hogA (26) do diye hue binduyoM se jo dI huI rekhA ke Amane sAmane kI tarphI' meM hai aisI do rekhA khIMco ki vaha dI huI rekhA se aise bindu ghara mileM ki unase bane hue kone ke dI huI rekhA se do barAbara hisse hoM paura yaha bhI bayAna karo ki kisa hAlata meM ina rekhAoMoM kA khIMcanA nAmumakina hogA sAdhya 13 prameyopapAdya sA0 sUtra - jo kona eka sIdhI rekhA dUsarI sIdhI rekhA ke sAtha usakI eka tarafa banAtI hai vaha yA to do samakona hote haiM yA donoM milakara do samakona ke barAbara hote haiM vi0 sUtra farz2a karo ki aba sIdhI Shi rekhA sadasodhI rekhA ke sAtha usake eka rafa saba a aura aba dakona banAtI hai to yaha kona yA to do samakona hoMge milakara do samakona ke barAbara hoMge kyoMki agara sa ba a kona a ba da kona ke barAbara hai to unameM se haraeka samakona hai " va da rekhA khIMco upa0 to sa ba ya aura ya ba da kona do samakona haiM For Private and Personal Use Only ya zra da agara sa ba a kona aba da kona ke barAbara nahIM hai aM0 ba bindu se sa da ke sAtha samakona banAtI huI baya sa sA0 11 pa0 10

Page #48
(46) cUMki savaya kona barAbara hai sa ba a aura aba ya do konoM ve ina do gharoM meM se hara eka meM ya ba da kona milAzrI isaliye sabaSa aura ya ba da kona barAbara hai sa ba a aura yava aura yavadatonoM konoM ke phira caMki da ba a kona davaya aura ya ba akonoM ke barAbara aura dUna donoM barAbaroM meM se hara eka meM avasa kona milAo isaliye da ba a aura aba sa kona milakara barAbara haiM da baya aura cAya aura aba yatInoM konoM ke sva02 lekina sAbita ho cukA hai ki sa ba ya aura ya ba da kona bhI inhIM tIna konoM ke barAbara haiM __ aura jo cIz2a eka hI cIz2a ke barAbara hotI haiM vaha Apasa meM barAbara hotI haiM isaliye saba ya auraya bada kona milakara daba aaura abasa kona ke barAbara haiM kha01 lekina sa ba ya aura yabada dI samakona haiM isaliye daba aura aba sa kona milakara do samakona ke barAbara haiM phala isaliye jo kona eka sIdhI rekhA dUsarI sIdhI rekhA ke sAtha AdyopAnta- yaho sAbita karanA thA anumAna 1 saba kona jo kaI sIdhI rekhA eka sIdhI rekhA ke eka vinTa para usake eka hI tarapha banAtI hai mila kara do samakona ke barAbara hote haiM anumAna 2 agara do mobI rekhA eka dUsarI ko kisI bindu para kATeM to usa binda ke cAroM kona minakara barAbara hoge cAra samakona ke anumAna 3 saba kAna jo kaI sIdhI rekhAyoM ke eka bindu para milane se baneMge mila kara cAra samakona ke barara hoge Ti. (1) terahavIM sAdhya ke dAva meM isa ibArata kA ki emake sAtha kona vanAtI honA jarUra hai kyoMki agara yaha ibArata na ho to sAdhya kI eka yaha bhI marata hogI ki eka rekhA dasarI rekhA ke sire para khaDI ho ra usa marata meM sirpha eka kona banegA Ti. (2) agara do kona milakara barAbara do samakona ke hoM to unameM se haraeka ko dUsare kA pUraka kahate hai aura agara do kona mila kara barA. vara eka samakona ke hoM to unameM se haraeka dUsare kA koTi hogA For Private and Personal Use Only

Page #49
(80) abhyAsa (27) agara basa kona kI eka bhuja ba a zIrSa kI tarafa da taka bar3hAyI jAya aura aya aura apha rekhA va asa aura saada konoM ke dora barAbara hisse kareM to sAbita karo ki yatra pha mamakona hai (28) kisI kona ke pUraka aura usI kona ke koTi ke darmiyAna kA farka samakona hotA hai sAdhya 14 prameyopapAdya sA0 sUtra agara kisI sIdhI rekhA ke eka bindu para do sIdhI rekhA usakI Amane sAmane kI tarafoM se Akara Asanna kona barAbara do samakona ke banAyeM to yaha donoM sIdhI rekhA eka hI sIdhI rekhA meM hoMgI vi0 sUtra faz2a karo ki va sIdhI rekhA ke va vindu para saba aura daba do sIdhI rekhA a ba rekhA kI Amane sAmane kI taraphoM se Akara saba ora a ba da Asannakona barAbara do samakona ke banato haiM to saba ora da ba eka hI sIdhI rekhA meM hoMga upa0- agara da ba aura basa eka hI bIdhI rekhA meM nahIM to farz2a karo ki yaba aura basa ekahI sodhI rekhA meM haiM cUMki aba rekhA sabaya rekhA se ba biMdu para milatI hai isaliye saba aura aba ya zrAsanna kona milakara do samakona ke barAbara haiM sA0 13 6 lekina saba a aura aba da kona bhI milakara do samonA ke barAbara haiM (bamUjina faz2a ) C isaliye saba a aura abada kona sabaa aura akSaya konoM ke barAbara haiM sva0 1, 19 ina donoM barAbaroM meM se saba a kona nikAla DAlo. isaliye bAkI a ba da kona barAbara hai bAkI a ba ya koma ke va. 20 For Private and Personal Use Only sa va ya da

Page #50
(48) yAnI kula apane eka Tukar3e ke barAbara hai aura yaha bAta nAmumakina hai isaliye yava aura sa ba eka hI sIdhI rekhA meM nahIM haiM aura isI taraha sAbita ho saktA hai ki sivAya bada ke koI aura sodhI rekhA bhI basa ke sAtha milakara eka sIdhI rekhA nahIM hosaktI isaliye bada hI basa ke sA milakara eka sIdhI rekhA huI phala-isaliye kisI sodhI rekhA ke eka biMdu para AdyopAnta yahI sAbita karanA thA Ti. (1) yaha sAdhya terahavauM sAdhya kA viloma hai isako yatirekayakti se sAbita kiyA hai isa sAdhya meM saba aura daba rekhAoM ke aba rekhA kI grAmane sAmane kI tarafoM se Akara milane kI kaida naho to samakina hai ki jo kona do sIdhI rekhA kisI tIsarI sIdhI rekhA ke sAtha banAveM vaha do samakona ke barAbara hoveM lekina donoM rekhA eka hI sIdhI rekhA meM nahIM jaisAki isa tasvIra meM sa ba aura ba da sIdhI rekhA aba zra sIdhI rekhA ke sAtha aise do ko aba aura aba da banAveM ki vaha mila kara do samakona kI barAbara hoM lekina / sa ba aura ba da sIdhI rekhA ekaho sodhA rekhA meM nahoM bara- Ti. (2) vidyArthI ko gaura karane se mAlUma hogA ki sa ba a aura aba ya konoM ko sa ba a aura aba da konoM ke barAbara mAbita karane meM pahilI aura gyArahavIM svayaMsiddhi donoM kA hukama lagAnA z2arUra hai Ti. (3)TauDahanTara sAhaba ne gyArahavIM svayaM siddhi ko isataraha sAbita kiyA hai aura isa subUta para ula dama ke usala kI rU se koI aitarAja nahIM ho sakA hai phaz2a karo ki aba rekhA sa a da rekhA ke sAtha a bindu para samakona banAtI hai aura ya pha rekhA ja ya ha rekhA ke sAtha ya bindu para samakona banAtI hai to ba a sa aura pha ya ja kona aApasameM barAbara hoMge __ koI a sa lakhAI le lo aura ada aura ya ha aura ya ja ina sabako asa ke barAbara banAo ha ya ja rekhA ko da a sa rekhA ya sadasa para isa taraha rakkho ki ha vinTu da bindu para ho aura ha ja rekhA kI dizA dasa rekhA kI dizA para ho aura va aura pha biMdu da sa rekhA kI eka For Private and Personal Use Only

Page #51
(48) ho tarafa meM hoM to ja biMdu sa para par3egA aura ya biMdu abiMdu para aura ya pha bhI apha para par3egI agara ya pha rekhA aba rekhA para na par3e magara kisI aura jagaha para aka kI taraha ho to ha ya pha kona dazaka kona ke barAbara hogA aura pha ya ja kona ka a sa kona ke barAbara hogA lekina haya pha kona aura pha ya ja kona babhUjiba phaz2a ke grApasa meM barAbara hai isaliye da aka aura ka asa kona ApasameM barAbara hai lekina da aba aura ba asa kona bhau bamUjida phaz2a ke grApasameM barAbara haiM aura sa aba kona sa a ka kona se bar3A hai isaliye da aba kona sa a ka kona se bar3A hai aura isaliye da aka kona sa a ka kona se aura bhI z2iyAdA bar3A hai lekina yaha sAbita ho cukA hai ki da aka kona sa aka kona ke barAbara hai isaliye da aka kona sa a ka kona ke barAbara aura usase bar3A bhI hai aura yaha mAfa jhUTa bAta hai imaliye ya pha rekhA aba rekhA para par3atI hai aura isaliye pha ya ja aura ba a sa kona yApasameM eka dUsare ko pUrA 8ka lete haiM aura isaliye Apasa meM barAvara haiM sAdhya 15 prameyopapAdya sA0 satra- agara do sIdhI rekhA Apasa meM eka dUsarI ko kATeM to sanmakha kona ApasameM barAbara hoMge vi0 satra- faz2a karo ki aba aura sa da do sIdhI rekhA ya biMdu para eka dUsarI ko kATatI haiM to ayasa kona barAbara hogA dayaba kona zrA ke aura ayada kona barAbara hogA sayaba kona ke upa0 cUMki aya rekhA sada rekhA ke sAtha ya biMdu para sayaa paura a ya da Asanna kona banAtI hai yaha donoM kona milake do samakIna ke barAbara haiM sA0 13 phira cUMki da ya rekhA aba rekhA ke sAtha ya biMdu para ba yada paura daya a Asanna kona banAtI hai yaha donoM kona milakara do samakona ke barAbara haiM sA0 13 lekina yaha sAbita ho cukA hai ki sayaa aura ayada kona malakara do samakAna ke barAbara haiM For Private and Personal Use Only

Page #52
(50) isaliye sayaa aura ayada kona bayada aura ayada konoM ke barAbara haiM ina barAbaroM meM se ayada kona nikAla DAlA isaliye bAko sayaa kona barAbara hai bAkI bayada konake sva03 aura isI taraha sAbita hosaktA hai ki sa ya ba kona ayada kIna ke barAbara hai phala isaliye agara do sIdhI rekhA eka dUsarI ko kisI bindu para kA AdyopAnta yahI sAbita karanA thA Ti. (1) Upara kA subUta isa taraha likhane se saMkSepa hosaktA hai ki sanmukha ke kona Apasa meM barAbara haiM kyoMki donoM konoM meM se hara eka kA pUraka eka hI kona hai / Ti. (2) anumAna jo ukta dama ne isa mAdhya ke nIce likhe hai hamane unako isa kitAba meM mAkUla vajahoM ke sababa terahavIM sAdhya ke nIce rakkhA hai Ti. (3) ukjI dasa ne isa sAdhya ke viloma ko ki " agara cAra sIdhI rekhA kisI bindu para mila kara cAra kona aise banAve ki unameM se grAmane sAmane ke do do kona aApama meM barAbara hoM to unameM se do do rekhA eka eka saudhau rekhA meM hoMgI" nahIM sAbita kiyA hai vaha isa taraha sAbita hosaktA hai pharja karo ki aya, sa ya, ba ya aura da ya cAra sIdhI rekhA (pandrahavIM sAdhya kI tasvIra dekho)ya biMdu para milakara aise cAra kona banAtI hai ki unameM se Amane sAmane ke do do kona barAbara haiM yAnI a ya sa aura baya da kona Apasa meM barAbara haiM aura sa ya ba aura a ya da kona grApasa meM barAvara hai to aya aura ba ya rekhA eka sIdhI rekhA meM hoMgI aura sa ya aura da ya rekhA eka sIdhI rekhA meM hoMgI caMki a ya sa kona barAbara hai ba ya da kona ke aura sa ya ba kona barAbara hai a ya da kona ke imaliye aya sa aura sa ya ba kona mila kara ba yada aura da ya a konoM ke barAbara haiM (va.) lekina yaha cAroM kone milAkara cAra samakona ke barAbara hai ( anu0 3 sA0 13 ) isaliye a ya sa aura sa ya ba kona mila kara do samakona ke barAbara haiM aura isaliye a ya aura ba ya ekahI sIdhI rekhA meM haiM ( mA0 14) aura isI taraha yaha bhI sA. bita ho saktA hai ki sa ya aura ya da ekahI sIdhI rekhA meM hai| savAlAta itihAna zakala 7 se 15 taka (1) sAtavauM zakala kI tIsarI sarata khIMco aura bayAna karo ki sucUta ko kyoM z2arUrata nahIM hai For Private and Personal Use Only

Page #53
(51) (2) pAThavauM zakala ko anvI sAdhana se siddhi karo tAki sAtavIM sAdhya kI z2arUrata na rahe (3) kyA nauvoM sAdhya meM yaha z2arUra nahIM hai ki samatribAhu tribhuja a se dUra banAyA jAve (4) batAo ki pahilI sAdhya meM kisa taraha rekhA ke do barAbara hisa kara sakate hai (5) sAbita karo ki gyArahavIM zakala navauM zakala kI eka qhAsa sUrata hai (6) do qhata mustakIma (sIdhI rekhA) hissA zAmila nahIM rakhate kyA yaha anumAna pahile bhau kisI sAdhya meM mAna liyA gayA hai (7) kina maratoM meM ve sIdhI rekhA jo tribhaja ke chanta: konoM ke do barAbara hisse karate haiM tribhuja ke kInoM ke sAmane ke bhujoM yA bhuja ko bhI do barAbara bhAgoM meM bAMTate haiM (javAva) sirpha eka sujA yAmI grAdhAra ko jaba samadibAhu tribhuja hotA hai aura kula bhujoM ko jaba samitrabAhu tribhuja hotA hai (8) kyA 12 vI sAdhya meM aparimita rekhAdI huI hone kI prataz2arUra hai () 13 vIM zakala meM kaunasI vastapapAya sAdhyA kI jarUrata par3I hai kyA kisI prameyo papAdA sAdhya kI bhI jarUrata par3I hai (javAba) nahIM khi svayaM miDDiyoM ko (10) agara do rekhA eka dUsare ko kATeM to ve kitane kone banAveMgI (11) 14 vauM za ka la meM kauna se tIna khata eka binTu meM hokara guz2arate hai (12) 14 vauM sAdhya ke dAve meM kaunasI zarta kI z2arUrata hai| (13) 15 vI sAdhya kA biloma bayAna karo aura sAbita karo (14) 13, 14, 15, sAdhyoM kA kyA majamUna hai (javAba ) kona jo eka bindu para banate haiM . sAdhya 16 prameyopapAya sA0 satva-- agara kisI tribhuja kI eka bhuja bar3hAI jAya to vahiH kona apane sAmane ke haraeka antaH kona se bar3A hogA vi0 satra- phaz2a karo ki aba sa tribhuja kI ba sa bhuja kisI da bindu taka bar3hAI gayI hai to asa da bahiH kona apane sAmane ke hara /\M eka sa aba aura aba sa antaH konase bar3A hogA / aM. asa ke ya bindu para do barAbara hi. va sa mase karo sA. 10 For Private and Personal Use Only

Page #54
aura baya milAzrI avA. 1 ba ya ko kisI pha binda taka bar3hAo zravA0 2 aura ya pha barAbara baya ke kATalo sA03 aura sa pha milAo avA0 1 upa0-- cUMki ya sa barAbara a ya ke aura ya pha barAbara ba ya ke banAyI gayI hai yAnI abaya aura saphaya do vibhujoM meM aya aura baya do bhuja sa ya aura ya pha do bhujoM ke alagara barAbara haiN| aura a ya ba kona sa ya pha kona ke barAbara hai sA. 15 isaliye aba AdhAra saphaAdhAra ke barAbara hai aura abaya vibhuja sa pha ya vibhaja ke barAbara hai aura eka tribhuja ke bAkI kona alaga 2 TUsare vibhuja ke bAkI konoM ke barAbara haiM yAnI vaha kona Apasa meM barAbara haiM jinake sAmane kI bhuja barAbara haiM sA04 isaliye baaya kona barAbara hai phasaya kona ke lekina asada kona phasaya kona se bar3A hai sva. 8 isaliye asada kona baasa kona se bar3A hai isI taraha agara asa bhuja ja bindu taka baDhAyI jAya aura basa ke do barAbara hisse kiye jAya to yaha sAbita ho sakatA hai ki basaja kona abasa kona se bar3A hai lekina basaja kona asada kona ke barAbara hai isaliye asada kona asa ba kona se bar3A hai phala- isaliye agara kisI tribhuja kI eka bhuja bar3hAyI jAya to vahiH kona AdyopAnta yahI sAbita karanA thA Ti. (1) tAlibaima ko cAhiye ki abhyAma ke liye dUsare hisse ke subUta ko jisakI tarafa izArA kiyA hai likha DAle jisase isa sAdhya kI sacAI acchI taraha unake jI meM mamAgAve For Private and Personal Use Only

Page #55
(Ta0 (2) isa sAdhya aura Age kI bAjI2 sAdhyoM ke sAvita karane meM isa svayaMsiddhi ko mAna liyA hai ki agara do barAbara cIz2oM meM se eka kisI tIsarI cIna se bar3I ho to dUsarI bhI usase bar3I hogI abhyAsa (28) ba sapha tribhuja ke tInoM anta: konoM kA yoga (16 vauM sAdhya dekho) tribhuja a ba sa ke tInoM antaH konoM ke yoga ke barAbara hai (30) kisI sIdhI rekhA para eka biMdu se eka se z2iyAdA lamba nahIM gira sakta hai (31) agara kisI biMdu se eka sIdhI rekhA jo eka dI huI mIdhI rekhA ke sAtha eka adhika kona aura eka nyana kona banAve khIMcI jAya aura usI biMdu se usI rekhA para eka lamba girAyA jAya to sAbita karo ki lakha nyUna kona kI tarafa giregA (32) eka biMdu se kisI maudhI rekhA taka do se z2iyAdA barAbara rekhA nahIM khica saktI haiM sAdhya 17 prameyopapAdya mA0 satva vibhuja ke hara do kona milakara do samakona se choTe hote haiM vi0 satra farz2a karo ki abasa eka tribhuja hai to usake hara do kona milakara do samakona se kama hoMge aM0 kisI basa bhuja ko da taka bar3hAo upa0 cUMki asada kona aba sa tribhuja kA bahiH kona hai isaliye asada kona apane sAmane ke a ba sa antaH kona se bar3A hai sA0 16 ina donoM barAbaroM meM se hara eka meM asa ba kona milAzrI isaliye asada aura a sa ba kona milakara abasa aura asa ba konoM se bar3e haiM basa For Private and Personal Use Only

Page #56
(54, lekina asada aura a sa ba kona milakara do samakona ke barAbara haiM sA0 13 isaliye aba sa kona aura asaba kona milakara do samakona se kama hai isI taraha yaha bhI sAbita hosatA hai ki basa aura asa ba kona bhI milakara do samakona se kama hai __ aura vasa aura asaba kona bhI milakara do samakona se kama haiM phala isaliye tribhaja ke hara do kona AdyopAnta yaho sAbita karanA thA Ti. (1) yaha sAdhya pichalI sAdhya kA sirpha eka anumAna mAlUma detI hai z2AhirA svaghaMsiDi 12 kI jisakA yaha viloma hai TIkA ke liye rakkhI gaI hai yaha aura solahavIM donoM sAdhya isa adhyAya kI battIsavoM sAdhya meM zAmila hai Ti0 (2) sattarahavIM sAdhya tribhuja kI bagaira kisI bhujA a ke bahAne ke isa taraha sAbita ho sakatI hai ba sa meM koI / viMdu da lo aura ada milAyo ba Ta sa caMki a da sa kona a ba sa kona se aura a da ba kona a sa ba kona bar3A hai (sA. 16) isaliye adaba aura a da sa kona mila kara aba sa aura a sa ba konoM se bace hai lekina a da ba aura a da sa kona mila kara do samako na ke barAbara haiM (sA0 13) imaliye a sa ba aura a ba sa kona milakara do samakona se kama hai isI taraha yaha bhI mAbita homaktA hai ki ba asa aura a sa ba kona mila kara do mamakona se kama hai aura va asa aura a ba sa kona mI milakara do samakona se kama hai abhyAsa (33) tribhuja ke tInoM upantaH kona mila kara tIna samakona se choTe hote haiM (34) tribhuja ke hara dI bahiHkona milakara do samakona se dyaura tInoM bahiH kona milakara tIna samakona se z2iyAdA hote haiM For Private and Personal Use Only

Page #57
(55) sAdhya 18 prameyopapAdya sA0 satra-- hara vibhuja meM bar3I bhuja ke sAmane kA kona bar3A hotA hai vi0 sUtra- pharja karo ki a va sa eka tribhuja hai aura usa ko asa bhuja aba bhuja se bar3I hai to aba sa kona a sa ba kona se bar3A hogA aM0- cUMki asa bhuja aba bhuja se bar3I hai usameM se ada barAbara aba ke kATalo (sA0 3) / aura ba da milAo avA0 1 basa upa0- cUMki adaba kona da ba sa vibhuja kA bahiH kona hai isaliye adaba kona apane sAmane ke ba sa da antaH kona se bar3A hai sA0 16 lekina adaba kona barAbara hai aba da kona ke sA0 5 isaliye abada kona bar3A hai basa a kona se isaliye abasa kona aura bhI z2iyAdA bar3A hai basa a kona se phala-isaliye vibhuja kI bar3I bhuja ke sAmane kA kona AdyopAnta yahI sAbita karanA thA anumAna- vighamabAhu tribhuja ke kona nAbarAbara hote haiM abhyAsa (32) avasada caturbhuja kI ada bhuna saba bhujoM se bar3I hai aura basa bhuja sabase choTI hai to sAbita karo ki aba sa kona ada sa kona se aura basa da kona baada kona se bar3A hai (36) tribhuja ke usa bhuja para jo bAkI do bhujoM meM se kisI se choTI nahIM hai jo lamba sAmane ke kona se DAlA jAtA hai vaha tribhuja ke bhItara par3atA hai For Private and Personal Use Only

Page #58
farja sAdhya 18 prameyopapAdya sA0 satra hara tribhuja meM bar3e kona ke sAmane kI bhuja baDI hotI hai vi0 sUtra-- farz2a karo ki abasa eka tribhuja a hai jisakA abasa kona asaba kona se bar3A hai | to asa bhuja aba bhuja se bar3I hogI upa- agara asa bhuja aba bhuja se bar3I nahIM hai to vaha usake barAbara yA usase choTI hai agara asa barAbara hai aba ke to abasa kona bhI barAbara hai asaba kona ke sA. 5 lekina yaha kona Apasa meM barAbara nahIM hai isaliye asa bhI aba ke barAbara nahIM hai agara asa choTI hai aba se to avasa kona bhI choTA hai asaba kona se sA0 18 lekina abasa kona asaba kona se choTA nahIM hai faz2a isaliye asa bhI aba se choTI nahIM hai| aura yaha sAbita hocukA hai ki asa barAbara nahIM hai aba ke isaliye asa bar3I hai aba se phala-isaliye hara tribhuja meM bar3e kona ke sAmane kI bhaja AdyopAnta yahI sAbita karanA thA Ti. (1) yaha sAdhya aThArahavIM sAdhya kA viloma hai zora chaTI sAdhya ke mAtha vahI sambandha rakhatI hai jo aThArahavIM sAdhya pAMcavIM sAdhya ke sAtha rakhatI hai yaha sambandha ina sAyoM meM se do do ko milAkara isa taraha bayAna karane se mAlUma hogA " tribhuja kA eka kona dUmare kona ke barAbara For Private and Personal Use Only

Page #59
(sA. 5) yA usase bar3A yA choTA (sA. 18) hogA jaisA ki pahile kona ke sAmane kI bhuja dUsare kona ke sAmane kI bhuja ke barAbara yA usase bar3I yA choTI ho" aura " tribhuja kI eka bhuja dUsarI suja ke barAbara (sAI) yA usase bar3I yA choTI (sA.16) hogI jaisA ki pahilI bhuja ke sAmane kA kona dUsarI bhuja ke sAmane ke kona ke barAbara yA usase bar3A yA choTA ho ina cAroM sAdhyoM ke grAesa ke sambandha ko hama isa taraha para bhI bayAna karake jAhira karate haiM sAdhya 5 agara aba suja=asa tribhuja to sa kona =ba kona | sAdhya 6 agara sa kona = ba kona to aba bhuja- asabhuja sAdhya 18 agara aba bhuja , asa bhuja to sa kona , ba kona (sAdhya 16 agara sa kona > ba kona to aba bhuja , asa suna do do sAdhya jo koSa, rekhAyoM ke andara hai eka dusarI kA biloma haiM kyoMki jo bAta eka meM kalpita artha kI jagaha para hai vaha dasarI meM phala kI kI jagaha para hai Ti0 (2) sAdhya 16 yatireka yukti se sAbita kI gaI hai abhyAsa (37) ad rekhA aba sa tribhuja ke a kona ke do barAbara hisse karatI hai aura usakI ba sa bhuja se da biMda para milatI hai sAbita karo ki ba a bar3I hai ba da se aura sa a bar3I hai sa da se __ (38) agara bargakSetra ke kisI a kona se eka rekhA usake sAmane kI bhujoM meM se eka ko kATatI huI aura dUsarI ke bane hue hisse se pha biMdu para milatI huI khIMcI jAya to apha usa varga kSetra ke karNa se bar3I hogI (38) jitanI sIdhI rekhA kisI bindu se eka dI huI rekhA taka khIMcI jAya unameM se lamba saba se choTI hogI aura jo rekhA lamba ke najadIka hogI vaha dUra kI rekhA se choTI hogI sAdhya20 prameyopapAdya sA0 satra- tribhuja kI hara do bhuja milakara tIsarI se bar3I hotI haiM For Private and Personal Use Only

Page #60
(58) vi0 sUtra farz2a karo ki abasa eka vibhuja hai to usakI hara do bhuja milakara tIsarI se bar3I hoMgI yAnI aba aura asa milakara basa se aura aba aura va sa milakara asa se aura sa a milakara aba se bar3I hoMgI aM0 va a ko kisI da biMndu taka bar3hAo a da barAbara a sa ke banAo aura dasa milAo basa aura For Private and Personal Use Only da sa upa0 cUMki ada barAbara a sa ke banAI gayI hai isaliye a sa da kona barAbara hai aT sa kona ke sA05 lekina sad kona a sa da kona se bar3A hai. kha0 Ta 4 avA0 2 sA0 3 avA0 1 isa lile va sa da kona a T sa kona se bhI bar3A hai cUMki da ba sa vibhuja meM basa da kona bar3A hai ba da sa kona se aura bar3e kona ke sAmane kI bhuja bar3I hotI hai sA0 18 isaliye ba da bar3I va sa se lekina va da barAbara hai va aura a sa ke kyoMki ada a barAbara hai asa ke isaliye va a aura asa milakara bar3I haiM basa isI taraha yaha bhI sAbita hotA hai ki aba aura basa milakara ca sa se aura va sa aura sa a milakara aba bar3I hai se phala isaliye tribhuja kI hara do bhuja milakara AdyopAnta yahI sAbita karanA yA

Page #61
(58) Ti. (1) yAda rakkho ki jina do bhujoM ko tIsarIse bar3I a sAvita karanA cAhate ho una do bhujoM meM se kisI eka bhuja ko usa tarapha bahAne se jidhara vaha donoM bhuja milatI / haiM aura bar3e hue hisse ko dUsarI ke barAbara banAne se yaha sAdhya sAbita hogI Ti. (2) yaha sAdhya isa taraha bhI sAbita ho sakatI hai va asa kona ke aya rekhA se do barAbara hisse karo (sA. 6) ava ba ya akona ya a sa kona se bar3A hai (sA. 16) le kina ya a sa kova ya aba kona ke barAbara banAyA gayA hai isaliye ba ya akona ya aba kona se bar3A hai aura isaliye aba bar3I hai baya se (mA016) isI taraha sAbita hosaktA hai ki asa bar3I hai ya sa se isaliye ba a aura asa mila kara basa se bar3I hai Ti0 (3) isa sAdhya kA yaha anumAna ho sakA hai ki do binduoM ke miyAna sIdhI rekhA sabase choTI dUrI hai kyoMki abindu basa rekhA se kaisA hI naz2adIka kyoM na ho ba sa hamepAha ba a aura sa a se choTI hai Ti. (4) isa mAdhya kI madada se yaha AsAnI se sAbita hosaktA hai ki tribhuja kI kisI do sunoM ke darmiyAna kA pharka tIsarI bhuja se choTA hotA hai kyoMki jisa sUrata meM ba a aura asa mila kara ba sa se bar3I haiM agara ina donoM bA barAbara meM se asa nikAla lI jAve to ba a bar3I hogI usa faka se jo ba sa aura a sa ke darmiyAna hai abhyAsa (40) tribhuja kI tInoM bhuna mila kara harabhuja ke dUne se bar3I hotI haiM (41) agara kisI bindu se tribhuja ke tInoM konoM taka rekhA khIMcI mAMya to yaha tInoM rekhA mila kara tribhuja kI tInoM bhujoM ke yoga ke Adhe se bar3I hoMgI (42) caturbhaja ko cAroM bhuja milakara donoM kaNoM ke yoga se bar3I hotI hai (43) tribhuja kI do suna milakara usa sIdhI rekhA ke jo tIsarI bhuja ke bIcoM bIca ke bindu se usa bhuja ke sAmane ke kona taka khIMcI jAya dUne se bar3I hoMgI (44) agara kisI bindu se caturbhuja ke cAroM konoM taka cAra sIdhI rekhA khoMcI jAyaM to vaha cAroM mila kara caturbhuja kI cAroM bhujoM ke prAdhe se bar3I hoMgI (45) hara caturbhuja ke kaNoM kA yoga una cAra rekhAoM ke yoga se choTA hotA hai jo kimI biMdu se caturbhuja ke cAroM konoM taka khIMcI jAya paranta usa biMdu para karNa eka dUsare ko na kATeM For Private and Personal Use Only

Page #62
(60) (46) dI huI sIdhI rekhA meM eka aisA biMdu daryAfa karo ki jisakI dUriyAM do biMduoM se jo dI huI rekhA ke eka hI tarafa meM hai milakara usa rekhA ke aura biMdukhoM meM se hara eka kI dUriyoM se kama hoM sAdhya 21 prameyopapAdya sA0 sUtra agara kisI vibhuja kI eka bhuja ke siroM se do sIdhI rekhA eka biMdu taka jo usa tribhuja ke andara hai khauMcI jAMya to yaha donoM sIdhI rekhA milakara tribhuja kI bAqI bhujoM se choTI hoMgI lekina una rekhAoM ke darmiyAna kA kona una bhujoM ke damiyAna ke kona se bar3A hogA vi0 sUtra farz2a karo ki abasa eka tribhuja hai aura usakI basa bhuja ke ba aura sa siroM se da biMdu taka jo usa tribhuja ke andara hai bada aura iral rekhA khIMcI gaI haiM sada va Yao sa to bada aura sa da milakara vibhuja kI aba aura asa bhujoM se choTI hoMgI lekina unake darmiyAna kA ba da sa kona tribhuja ke baasa kona se bar3A hogA zraM 0 ba da ko bar3hAo ki vaha a sa se ya biMdu para mile upa0 cUMki tribhuja kI do bhuja milakara tIsarI se bar3I hotI # For Private and Personal Use Only sA0 20 isaliye aba ya tribhuja kI do bhuja va a aura a ya milakara ba ya bhuja se bar3I haiM ina nAbarAbaroM meM se hara eka meM ya sa z2iyAdA karo to ba a aura asa milakara bar3I huI ba ya aura ya sa se aura cUMki sa ya da tribhuja kI saya aura yada do bhuja

Page #63
( 61 ) Acharya Shri Kailassagarsuri Gyanmandir milakara bar3I haiM sa da bhuja se sA0 20 aura ina nAbarAvaroM meM se haraeka meM da va jiyAdA karadI to sa ya aura ya va milakara bar3I huIM sa da aura daba se lekina yaha sAbita hocukA hai ki sa pra aura pra va milakara bar3I haiM sa ya aura ya va se isaliye va pra aura pra sa milakara aura bhI jiyAdA bar3I haiM va da aura dasa se phira cUMki tribhuja kA bahi: kona apane sAmane ke antaH kona se bar3A hotA hai sA0 26 isaliye sa da ya tribhuja kA ba da sa bahi: kona bar3A hai sa ya da antaH kona se isI dalIla se pra va ya tribhuja kA sayada bahi: kona bar3A hai va pra sa antaH kona se isaliye va dasa kona aura bhI z2iyAdA bar3A hai va prasa kona se isa vAste agara kisI tribhuja kI eka bhuja ke siroM se AyopAnta yahI sAbita karanA thA Ti0 isa sAdhya meM agara tribhuja kI bhuja ke siroM se sIdhI rekhA khIMcI jAne kI kaida ho to mumakina hosaktA hai ki do sIdhI rekhA jo umra bhuja ke kisI aura do binduyoM se khIMcI jAyaM tribhuja kI bAkI do mukha se bar3I yA unakI barAbara hoM lekina donoM rekhA milakara una bhujoM ke TUne se hamezA kama raheMgI agara bhaja jisake siroM se rekhA khIMcI jAyaM samatribAhu tribhuja kI bhuja ho yA aise samadvibAhu tribhuja kA bAdhAra ho ki jisakI hara bhujA vyAdhAra se bar3I ho to bhuja ke siroM se rekhA khIM jAne kI qaida kI kucha z2arUrata nahIM hai donoM sIdhI rekhA milakara khAta vaha bhuja ke siroM se yA usa bhuja ke kisI aura do biMduyoM se khIMcI gayI haiM hamezA samatribAhu tribhuja kI bAkI bhujoM yA samadvibAhu tribhuja kau suna se choTI hogI For Private and Personal Use Only

Page #64
Fw 2 sAdhya 22 vastUpapAdya sA. mAtra eka tribhuja banAo jisakI bhuja alaga alaga barAbara hoM dI huI aisI tIna sIdhI rekhAoM ke ki unameM se hara eka do milakara tIsarI se bar3I haiM vi0 sUtra pharja karo ki prAva aura sa aisI tIna dI huI sIdhI rekhA haiM ki unameM se haraeka do milakara tIsarI se bar3I hai yAnI naara va milakara bar3I hai sa se aura a aura sa milakara bar3I haiM va se aura va aura sa milakara bar3I hai ase aisA tribhuja banAnA hai ki usakI tInoM bhuja alaga alaga barAbara hoM na, ba ora sa ke aMka-daya aisI sIdhI rekhA khIMco ki / vaha i para parimiti ho lekina ya kI tarafa cAheM jitanI bar3ha sake dapha barAbara bha ke aura phaja barAbara va ke aura jaha barAbara sa ke banAnI sA03 pha keMdra se phada dUrI para da kala vRtta khauMcI avA0 3 aura ja keMdra se jaha dUrI para ha kala vRtta khoMco avA03 ka bindu se jahAM donoM hatta Apasa meM eka dUsare ko kATate haiM kapha aura ka ja rekhA pha aura ja binduoM taka khoMco to ka phaja tribhuja kI bhuja a, ba aura sa sIdhI rekhAoM ke alaga 2 barAbara hoMgI upa. caMki da ka la vRtta kA pha keMdra hai For Private and Personal Use Only

Page #65
( 63 ) isaliye pha ka barAbara hai pha da ke pari0 15 lekina pha da barAbara a ke banAyI gayI hai isalile pha ka barAbara a ke hai sva0 1 phira cUki ha ka la vRtta kA ja keMdra hai| isaliye ja ka barAbara hai jaha ke pari0 15 lekina ja ha barAbara sa ke banAyI gayI hai isaliye ja ka barAbara sa ke hai aura phaja barAbara va ke banAyI gayI hai isaliye kapha, phaja aura jaka tIna sIdhI rekhA alaga 2 barAbara haiM a, ba aura sa ke aura isaliye ka phaja tribhaja kI kapha, phaja aura jaka tInoM bhuja alaga alaga barAbara haiM dI huI tIna ava aura sa sIdhI rekhAoM ke aura aise hI tribhuja ke banAne kI z2arUrata thI Ti. 1 dI huI tIna sIdhI rekhAtroM meM se haraeka do kA milakara tImarI se bar3I honA isaliye z2arUra hai kyoMki bagaira isa zarta ke sAdhya kA hala honA nAmumakina hai / Ti. 2 bAz2a loga ulI dasa para yaha aitarAz2a karate haiM ki hattoM kA jo isa sAdhya ke hala karane ke liye khIMce gaye haiM Apasa meM kaTanA sAbita nahoM kiyA hai lekina isa pate para ki da pha, phaja aura ja ha sIdhI rekhAyoM meM se haraeka do milakara tIsarI se bar3I haiM khayAla karane se sApha jAhira hai ki utta grApasa meM eka dUsare ko kATeMge kyoMki isa kitAba kA ma. hune vAlA jo jarA bhI alI rakhatA hogA phaurana samaka jAvegA ki vRtta jo pha keMdra se pha da dUrI para khIMcA hai pha ha sIdhI rekhA ko pha aura ha viMduoM ke darmiyAna kATegA kyoMki pha ha bar3I hai pha da se aura vRkta jo ja keMdra se ja ha dUrI para khIMcA hai da ja sIdhI rekhA ko da aura ja viMduoM ke darmiyAna kATegA kyoMki da ja bar3I hai ja ha se aura yaha vRtta z2akara Apasa meM kaTeMge kyoMki yAda aura ja ha milakara phaja se bar3I haiM For Private and Personal Use Only

Page #66
( 64 ) Ti. 3 isa adhyAya kI pahalI sAdhya isa sAdhya kI eka khAsa sUrata hai kyoMki isa sAdhya meM agara a, ba aura sa Apasa meM barAbara hoM to yaha sAdhya aura pahalI sAdhya ekahI ho jAyaMgI yaha bhI jAhira hai ki phaja aAdhAra ko dUsarI tarapha eka aura aisA tribhuja bana sakatA hai ki jisakI bhuja dI huI tIna sIdhI rekhAyoM ke barAbara hoM abhyAsa (47) diye hue tribhuja ke barAbara tribhuja banAyo (ya) diye hue Rjabhuja kSetra ke barAbara Rjabhuja kSetra banAyo sAdhya 23 bastUpapAdya sA. sUtra dI huI sIdhI rekhA ke diye hue bindu para diye hue sarala kona ke barAbara kona banAo vi0 sUtra farz2a karo ki ava dI huI sIdhI rekhA hai aura usameM adiyA huA bindu hai ora da sa ya diyA huA saralakona hai aba sIdhI rekhA ke prabindu para kona banAnA hai jo da sa ya kona ke barAbara ho da--- ya pha __ aM sada aura sa ya meM da aura ya bindu lo da ya milAo avA0 1 ava para aphaja eka aisA tribhuja banAo ki usakI bhaja tIna sIdhI rekhAoM sada, da ya aura sa ya ke barAbara isataraha se hoM ki prapha barAbara ho sa da aura pha ja barAbara daya ke aura jaa barAbara ya sa ke sA. 22 to phaja kona barAbara dasa ya kona ke hogA upa. cUMki phama aura aja alaga 2 barAbara haiM dasa aura sa ya ke aura phaja AdhAra barAbara hai daya AdhAra ke For Private and Personal Use Only

Page #67
( 65 ) isaliye phacpraja kona barAbara hai da sa ya kona ke sA08 isaliye dI huI aba sIdhI rekhA ke pra bindu para pha aa ja kona diye hue dasa ya saralakona ke barAbara bana gayA -- aura isI kona ke banAne kI z2arUrata thI abhyAsa (8) agara kisI tribhuja ke do kona milakara tIsare kona ke barAbara hoM to usa tribhuja ke do samadivAhu tribhuja vana sakte haiM (16) agara basa tribhuja ke a aura ba kona milakara sa koma ke barAbara hoM to aba usa sIdhI rekhA se jo sa kona se aba ke bIcoM bIca ke bindu taka khIMcI jAya dUnI hogI. (50) eka tribhuja kA grAdhAra aura AdhAra para kA eka kona aura usakI bhujoM kA yoga mAlUma hai to usa tribhuja ko banAya (51) eka tribhuja ke bhuja aura una bhujoM ke bIca kA kona mAlUma usa tribhuja ko banAyo (52) eka tribhuja ke bhuja aura una bhujoM meM se eka ke sAmane kA kona mAlUma hai umra tribhuja ko banAya (53) eka tribhuja kA vyAdhAra aura AdhAra para kA eka kona vyara usakI bhujoM kA yoga yA pharka mAlUma hai to usa tribhuja ko banAo (54) do bindu diye hue haiM jinameM se eka bindu eka dI huI rekhA meM hai usa dI huI rekhA meM eka aura aisA bindu daryAkRta karo ki diye hue binduyoM se unakI dUriyoM kA jor3a yA pharka eka dI huI lambAI ke barAvara ho aura yaha bhI sAbita karo ki hara hAlata meM aise do do bindu daryAkRta ho sakte haiM sAdhya 24 prameyopapAdya sA0 sUtra agara eka tribhuja kI do bhuja dUsare tribhuja kI do bhujoM ke alaga 2 barAbara hoM lekina kona jo eka tribhuja kI ina do bhujoM se banA hai bar3A ho dUsare tribhuja ke usa kona se jo dUna bhujoM kI barAbara bhujoM se banA hai to usa tribhuja kA jisakA kona bar3A hai AdhAra bar3A hogA dUsare tribhuja ke AdhAra se vi0 sUtra pharz2a karo ki pra va sa aura da ya pha aise do tribhaja haiM ki unakI a va aura pra sa bhuja alaga 2 barAbara For Private and Personal Use Only

Page #68
haiM da ya aura da pha bhujoM ke yAnI aba barAbara hai dava ke aura asa barAbara hai da pha ke lekina basa kona bar3A hai ya da pha kona se ___ to basa AdhAra bar3A hogA ya pha AdhAra se aM0 pharja karo ki da ya aura dapha meM da ya bar3A nahIM hai dapha se daya ke 6 biMdu para aura usake usa tarapha jidhara dapha hai ya da ja kona barAbara va asa kona ke banAo sA0 23 daja barAbara da pha yA asa ke banAo sA. 3 aura ya ja aura ja pha milAzrI avAH / upa. cUMki daya barAbara hai aba ke aura jabarAbara asa ke yAnI tribhuja da ya ja kI do majadaya aura daja vibhaja avasa kI aba aura asa do bhujoM ke alaga 2 barAbara haiM aura yadaja kona asa kona ke barAbara banAyA gayA hai isaliye ya ja AdhAra barAbara hai basa AdhAra ke sA05 aura cUMki da phaja tribhuja meM daja barAbara hai da pha ke isaliye da phaja kona barAbara hai daja pha kona ke sA05 lekina dajapha kona bar3A hai yajapha kona se kha. isaliye daphaja kona bhI bar3A hai yajapha kona se aura isaliye ya phaja kona aura bhI z2iyAdA bar3A hai For Private and Personal Use Only

Page #69
( 6 ) Acharya Shri Kailassagarsuri Gyanmandir ya ja ka kona se aura cUMki yaphaja tribhuja meM ya pha ja kona dar3A hai ya japha kona se aura bar3e kauna se sAmane kI bhuja bar3I hotI hai sA0 18 isaliye ya ja bhuja bar3I hai ya pha bhuja se lekina ya ja barAbara va sa ke sAbita ho cukI hai isaliye basa bar3I hai ya pha se phala isaliye agara eka tribhuja kI do bhuja dUsare tribhuja kI do ajoM ke AdyopAnta yahI sAbita karanA yA Ti. 1 isa mAdhya meM ukta dama ne isa bAta ko vagaire sAbita kiye mAna liyA hai ki da ha choTI hai da pha se yAnI pha biMdu ya ja rekhA ke nIce hai isako hama isa taraha sAbita kara sakte haiM cUM ki da ha ja kona tribhuja da vaha kA vahi:kona hai isaliye da ha ja kona bar3A daya ja grantaHkona se ( mA0 16 ) aura cUMki da ya ja tribhuja meM da ja bar3I hai da ya se bAusa ke barAbara hai isaliye da ya ja kona bar3A hai da ja ya kona se yA usake barAbara hai (sA0 18, 5) lekina yaha sAbita hocukA hai ki da ha ja kona da ya ja kona se bar3A hai isaliye da ha ja kona da ja ha kona se bar3A hai isa vAste da ja bar3I hai da ha se ( mA0 16 ) lekina da ja barAbara hai da pha ke isaliye dapha bar3I hai da ha se yAnI pha biMdu ya ja rekhA ke nIce hai Ti. 0 2 isa mAdhya meM yaha zarta ki da ya bhuja da pha bhula se bar3I nahIM hai simasana sAhaba ne z2iyAdA kI hai agara yaha pUrva naho to sAdhya kI tIna mUrateM hotI haiM yAnI pha biMdu tha ja rekhA meM ho yA usase Upara yA nIce ho agara pha biMdu ya ja rekhA meM ho to usa sUrata meM sApha jAhira hai ki yapha choTI hogI ya ja se aura agara pha biMdu ya ja rekhA ke Upara hai to da pha aura ya pha milakara da ja aura ya ja se choTI hoMgI (sA0 21 ) aura cUMki da pha aura da ja vyApasa meM barAbara haiM isaliye ya phachoTI hogI ya ja se Ti0 3 yaha sAdhya isa taraha bhI sAvita hosaktI hai daya pha tribhuja ko a ba sa tribhuja para isa taraha rakkhA ki da ya For Private and Personal Use Only

Page #70
( 68 ) kona nuja a ba bhuja ko pUrA 5 Dhaka leve to cUMki ya da pha kona basa se choTA hai da pha bhuja ba a aura sa a bhujoM ke darmiyAna par3egI aura pha biMdu yA to vasa para yA usa se Upara yA nIce na par3egA pahalI sUrata agara pha biMdu ba sa vyAdhAra para par3atA hai to basa bar3I hai ba pha se isaliye ba sa bar3I hai yapha se va dUsarI surata yagara pha biMdu ba sa vyAdhAra ke Upara par3atA hai to asa aaurava milakara bar3I haiM a pha baura va pha se (sA021) aura a pha aura a sa vyApasa meM barAbara haiM isaliye va sa bar3I hai bapha se isaliye ba sa bar3I hai yapha se pha For Private and Personal Use Only Wo Ming pha tIsarI sUrata vyagara pha biMdu ba sa vyAdhAra se nIce par3atA hai phurz2a karo ki apha aura va sa eka dUsarI ko ja biMdu para kATatI haiM to cUMki a ja gaura ja sa milakara bar3I haiM asa se (sA0 20 ) aura phaja aura ja va milakara bar3I haiM bapha se isaliye a pha aura va sa milakara bar3I haiM a sa aura ba pha se lekina apha barAbara hai a sa ke isaliye va sa bar3I hai ba pha se isaliye basa bar3I hai yapha se sa pha sa sAdhya 25 prameyopapAdya sA0 sUtra agara eka tribhuja kI do bhuja dUsare tribhuja kI do bhujoM ke alaga 2 barAbara hoM lekina eka tribhuja kA AdhAra dUsare tribhuja ke AdhAra se bar3A ho to jisa tribhuja kA AdhAra bar3A hai usakI bhujoM se banA huA kona dUsare tribhuja ke usa kona se jo una bhujoM kI barAbara bhujoM se banA hai bar3A hogA vi0 mUtra pharz2a karo ki va sa aura daya pha aise do tribhuja haiM ki unakI prava pha aura pra sa do bhuja alaga barAbara haiM da ya va aura da pha do bhajoM ke yAnI pra va barAbara hai da ya ke aura sa ya ja Ta

Page #71
(68 ) asa barAbara hai da pha ke lekina basa AdhAra bar3Ahai ya pha AdhAra se to va asa kona bar3A hogA ya da pha kona se upa. kyoMki agara vAsa kona ya da pha kona se bar3A nahIM hai to ba sa kona yA to usake barAbara hai yA usase choTA hai agara va asa kona ya da pha kona ke barAbara hai to basa AdhAra bhI yapha AdhAra ke barAbara honA cAhiye sA04 lekina ba sa AdhAra ya pha AdhAra ke barAbara nahIM hai (pharja) isaliye va asa kona ya da pha kona ke barAbara nahIM hai agara va asa kona yada pha kona se choTA hai| to vasa AdhAra ko bhI yapha AdhAra se choTA honA cAhiye sA0 24. lekina vasa AdhAra ya pha AdhAra se choTA nahIM hai pharja isaliye ba asa kona ya da phakona se choTA nahIM hai aura yaha sAbita hocukA hai ki ba asa kona ya da pha konna ke barAbara nahIM hai __ isaliye ba a sa kona ya da pha kona se bar3Ahai phala isaliye agara eka tribhuja kI do bhuja dUsare tribhuja ka do bha joM ke AdyopAMta-yahI sAbita karanA thA Ti. 1 yaha sAdhya isa taraha bhI sAbita a hosatI hai asa para a sa ja aisA tribhuja ba. / nAyo ki usakI ja a, asa aura sa ja ha sa ya bhuja alaga 2 da ya pha tribhuja kI ya da, da For Private and Personal Use Only

Page #72
( 70 ) T pha aura pha ya bhujoM ke barAbara hoM ( sA0 22 ) aura ja ba milAyo ___ caMki ba sa bar3I hai ya pha se ( farja ) vAnI ja sa se isaliye baja sa kona bar3A hai ja ba sa kona se (sAH 18) ja biMdu para ba ja ha kona jaba ha kona ke barAbara banAyo (sA0 23) aura aha milAo aba caki a ba ha aura ajaha tribhujoM meM aba barAbara hai a ja ke aura aha donoM meM ubhayaniSTha hai aura ba ha aAdhAra barAbara hai ja hayAdhAra ko ( sA0 6 ) isaliye ba a ha kona barAbara hai ja aha kona ke (sA08) lekina ja aha kona bar3A hai ja asa kona se bAnI bar3A hai ya da pha kona se isaliye ba a ha kona bar3A hai ya da pha kona se isaliye va asa jona aura bhI z2iyAdA bar3A hai ya da pha kona se Ti. 2 isa sAdhya ke sAbita karane kA tIsarA tarIkA yaha hai / da ya pha tribhuja ko a ba sa tribhuja para isa taraha rakakhA ki va viduba biMdu para aura ya pha kI dizA ba sa kI dizA para ho aura ya da pha aura ba asa kona grAmane sAmane hoM to caMki ya pha choTI hai ba sa se topha viMda basa para ba aura sa biMduoM ke darmiyAna par3egA- da amilAo isako cAra sUrateM haiM pahalI sarata yaha hai ki da agrAdhAra ba sa ko pha ghara kATe caMki ba a da kona aura ba da a kona barAbara ha 1/pha kyoMki a ba aura ba da barAbara haiM aura ba a sa kona / aTa kona se bar3A hai isaliye va asa kona ba da pha yAnI ya da pha kona se bar3A hai dasarI sarata yaha hai ki da arekhA ba sa aAdhAra ko / pha aura sa ke darmiyAna kATe cUMki ba da akoga ba da pha kona se bar3A hai (va.) aura ba da a aura ba a da kona barAbara haiM kyoMki ba a aura ba da arAvara haiM isaliye ba a da kona ba da pha kona se bar3A hai isaliye va asa kona ba da pha yAnI ya da pha kona se aura bhI z2iyAdA bar3A hai tIsarI sUrata yaha ki da aAdhAra ba sa ko pha aura ba ka darmiyAna kATe da pha ko ja taka bahAyA /pha / For Private and Personal Use Only

Page #73
( 71 ) ki da ja bar3I hai da pha se aura da pha varAvara asa imaliye da ja bar3I hai a sa se yAnI aja se aura bhI va z2iyAdA bar3I hai isaliye da a ja kona a da ja kona se bar3A hai (mA 18) / aura ba a da aura ba da akona barAbara haiM kyoMki va da aura aba barAbara haiM liye ba a sa kona ba da pha bAnI ya da pha kona se bar3A hai ( sva04) cauthI sUrata yaha vida a aAdhAra basa ko na kATe asa ko ja takA pAyo ___ ki da ja choTI hai da pha se aura da pha barAbara hai sA028 ___ imaliye da ja choTI hai a sa se yAnI a ja se aura vam bhI jiyAdA choTI hai inaliye ja ada kona ja da akona se choTA hai aura ba ada aura ba da a kona varAvara haiM kyoMki ba da aura ba a varAvara haiM inaliye va asa kona bada pha kona se yAnI ya da phakona se bar3A hai (sva05) Ti03 yaha sAdhya caubIsauM sAdhya kA biloma hai aura grAThavIM sAdhya ke nAtha vahI ilAkA rakhatI hai jo caubIsavIM sAdhya caudhI sAdhya ke sAtha rAbatI hai ina cAra lAdhyoM ke Apasa kA ilAkA tumako isa taraha bayAna karane se mAlama hogA agara aba-daya sAya to basa-yapha aura asa-dapha aura a konada kona agara aba-daya aura asa-dapha to a kona - dona sAdhya 8 aura basa-yapha For Private and Personal Use Only

Page #74
( 72 ) agara aba-daya to va sa (yapha sAdhya 24 aura asa= dapha lekina a kona rada kona - nayara aba-daya - - sAdhya 25 aura asa= dapha to a kona (da kona -- lekina basa yapha ina cAra mAdhyoM meM se do do ko milAkara isa taraha bayAna karate haiM " agara eka tribhuja kI do bhuja dUsare tribhuja kI do bhugoM ke alaga alaga barAbara hoM to eka tribhuja kA aAdhAra dUsare tribhuja ke prAdhAra se bar3A yA choTA hogA ( sA0 24) yA usake barAbara hogA ( sA0 4 ) jaisAki pahale nibhuja ke AdhAra ke sAmane kA kona bar3A yA choTA hai dUsare trija ke AdhAra ke sAmane ke kona se yA usake barAbara hai" " aura gragara tribhuja kI do maja dUsare tribhuja kI do bhujoM ke alaga alaga barAbara hoM to eka tribhuja kI do bhujoM se banA huA kona dUsare tribhuja kI sujoM se bane hue kona se bar3A yA choTA hogA ( sA0 25 ) yA unake barAbara hogA (sA08) jaisA ki pahale tribhuja kA grAdhAra bar3A yA choTA hai dRmare tribhuja ke grAdhAra se yA usake barAvara hai" sAdhya 26 prameyopapAdya sA0 sUtra agara eka tribhuja ke do kona dUsare tribhuja ke do konoM ke alaga alaga barAbara hoM aura eka tribhuja kI eka bhuja dUsare tribhuja kI eka bhuja ke barAbara ho aura yaha barAbara bhuja cAhe barAbara konoM ke darmiyAna kI hoM yA unake sAmane kI hoM to eka tribhuja kI bAkI bhuja alaga alaga dUsare tribhuja kI bAkI bhujoMke barAbara hoMgI aura eka tribhuja kA tIsarA kona dUsare tribhuja ke tIsare kona ke barAbara hogA vi0 sUtra farz2a karo ki abasa aura dayapha aise do tribhuja haiM ki unake kona pravasa aura asava alaga alaga For Private and Personal Use Only

Page #75
barAbara haiM dayapha aura daphaya konoM ke yAnI abasa kona barAbara hai daya pha kona ke aura asaba kona barAbara hai da phaya kona ke aura eka eka bhuja bhI ina konoM kI Apasa meM barAbara hai pahale faz2a karo ki basa aura yapha bhuja jo ina tribhujoM ke barAbara konoM ke darmiyAna meM haiM Apasa meM barAbara haiM / ___ to eka tribhuja kI bAkI bhuja alaga agala barAbara hoMgI dUsare tribhuja kI bAkI bhujoM ke yAnI aba baraNayara hogI daya ke aura asa barAvara hogI dapha ke aura basa tIsarA kona bhI badaka sosare kona ke barAvara hogA upa0 kyoMki agara aba bhuja da ya bhuja ke barAbara nahIM hai to eka ina donoM meM z2arUra dUsarI se bar3I hai agara mumakina ho to farz2a karo ki aba bar3I hai daya se baja barAbara yada ke banAo sA03 aura saja milAo avA0 1 caMki jabasa aura dayapha do tribhujoM meM jaba barAbara hai daya ke aura basa barAbara hai yapha ke yAnI jaba aura vasa do bhuja alaga alaga barAbara haiM daya aura yapha do bhujoM ke aura jabasa kona barAbara hai dayapha kona ke isaliye jasa AdhAra barAbara hai dapha AdhAra ke aura jabasa tribhuja barA hai dayapha tribhuja ke aura eka tribhuja ke bAkI kona alaga a, barAbara haiM dUsare tribhuja ke bAkI konoM ke yAnI vaha kona Apasa meM barAbara hai jinake sAmane kI bhuja barAvara haiM sA04 4u For Private and Personal Use Only

Page #76
( 74 ) isaliye jasaba kona barAbara hai daphaya kona ke lekina asaba kona barAbara hai daphaya kona ke pharja isaliye jasaba kona barAbara hai prasava kona ke sva0 1 yAnI choTA kona bar3e kona ke barAbara hai aura yaha bAta nAmumakina hai sva. isaliye aba nAbarAbara nahIM hai daya ke yAnI aba barAbara hai dayA ke aba avasa aura dayapha tribhujoM meM cUMki aba barAbara hai daya ke aura vasa barAbara hai yapha ke aura avasa kona barAbara hai dayapha kona ke farz2a isaliye asa AdhAra barAbara hai dapha AdhAra ke aura tIsarA kona basa barAbara hai tIsare kona yada pha ke dUsarI sUrata yaha farz2a karo ki bhuja jo barAbara kono ke sAmane haiM Apasa meM barAbara haiM yAnI aba barAbara hai da ya ke ___ to isa sUrata meM bhI eka tribhuja kI bAkI bha ja alaga alaga dUsare tribhuja kI bAkI bhujoM ke barAbara hoMgI yAnI vasa barAbara yapha ke Ira asa barAbara dapha ke hogI aura tIsarA kona vaasa tIsare kona yadapha ke barAbara hogA upa. kyoMki agara basa barAbara yapha ke nahIM hai to ina donoM meM se eka z2arUra dUsarI se bar3I hai farz2a karo ki vasa bar3I hai yapha se a.. baha barAbara yapha ke banAo aura aha milAo avA03 - / avA03 / For Private and Personal Use Only

Page #77
( 75 ) vaha aura dayapha tribhujoM meM aba barAbara hai vaha kona cUMki daya ke aura baha barAbara hai yapha ke aura barAbara hai dayapha kona ke isaliye =praha AdhAra barAbara hai dapha AdhAra ke aura pravaha vibha uja barAbara hai da ya pha vibhuja ke aura eka vibhaja ke bAqI kona alaga alaga barAbara haiM dUsare tribhuja ke bAkI konoM ke yAnI vaha kona Apasa meM barAbara haiM jinake sAmane ke bhuja barAbara haiM sA0 4 farz2a isaliye = haba kona barAbara hai daphaya kona ke lekina daphaya kona barAbara hai pra sa ba kona ke isaliye aha ba kona barAbara hai asa ba kona ke yAnI ahasa vibha uja kA ahaba bahi: kona apane sAmane ke asaba antaH kona ke barAbara hai aura yaha nAmumakina hai sA0 13 kha0 1 isaliye basa nAbarAbara nahIM hai ya pha ke yAnI basa barAbara hai yapha ke aba abasa aura dayapha bibhujoM meM cUM ki aba barAbara hai daya ke aura basa barAbara hai ya pha aura abasa kona barAbara hai kona ke daya pha isaliye asa AdhAra barAbara hai dapha AdhAra ke aura tIsarA basa kona barAbara hai tIsare yada pha kona ke sA0 4 phala isavAste agara eka vibhuja ke do kona dUsare vibhuja ke do konoM ke Ayonta - yahI sAbita karanA thA Ti0 1 isa sAdhA ko vyAcakAdana kriyA se isa taraha sAbita kara sakte haiM ( pahalI sUrata) agara da ya pha tribhuja a ba sa vibhuja para isa taraha rakkhA jAya ki ya biMdu ba biMdu para ho aura ya pha bhuja basa bhuja para For Private and Personal Use Only

Page #78
to caMki ya pha barAbara basa ke hai pha biMdu sa biMdu para par3egA aura caMki pha yada kona sa ba aM kona ke barAbara hai isaliye ya da bhuna ba a para par3egI aura isaliye da biMdu yA to bapa para par3egA yA usakI sIdha meM par3egA phira cUMki ya pha da kona barAbara hai basa a kona ke isa liye pha da bhuja sa apara par3a gIgraura isaliye da biMdu yA to sa a para par3egA yA usakI sIdha meM par3egA lekina sAbita hocukA hai ki da viMdu yA toba a para par3egA yA usakI sIdha meM par3egA isaliye daviMdua biMdu para jo ba a aura sa a donoM meM ubhayaniya hai par3egA isaliye ya da aura ba aApasa meM eka dUsarI ko pUrA 2 kaleMgI aura isaliye grApasa meM barAbara hoMgI aura pha da aura sa a eka dUsarI ko pUrA 2 chakaleMgI aura isaliye Apasa meM barAbara hoMgI aura ya da pha aura ba a sa kona eka dUsare ko pUrA 2 8kaleMge aura isaliye aApasa meM barAbara hoge (dasarI sUrata) agara da ya pha tribhuja aba sa tribhaja para isa taraha rakkhA jAya ki da biMdu a biMdu para aura da ya bhuja aba bhuja para ho to caMki da ya barAbara a ba ke hai isaliye ya biMdu ba bidu para par3egA aura cUMki kona da ya pha barAbara hai kona aba sa ke isaliye bhuja ya pha bhuja basa para par3egI aura viMdu pha bhI biMdu sa para par3egA kyoMki agara bhuja ya pha bhuja ba sa para ho lekina pha viMdu sa biMdu para na par3e to pharja karoki ki pha viMdu ha biMdu kI jagaha para ba aura sa ke darmiyAna par3atA hai a ha milAyo (avA0 1) cUMki a haba kona barAbara hai da pha ya kona ke aura da pha ya kona barAbara hai a sa ba kona ke isaliye aha ba kona barAvara hai a sa ba kona ke yAnI bahiHkona apane sAsane ke antaHkona ke barAbara hai aura yaha nAmumakina hai (sA0 16 ) isalithe pha biMdu ha biMdu para yAnI ba aura sa ke darmiyAna nahIM par3atA hai isI taraha yaha bhI sAbita hosaktA hai ki pha biMdu ba sa bhaja ke bAda hue hisse para bhI nahIM par3a sakatA hai isaliye pha ThIka sa para par3egA aura imaliye basa barAbara hai ya pha ke isaliye asa AdhAra varAbara hai da pha AdhAra ke aura ba asa kona ya da pha kona ke barAbara hai . Ti. 2 caughI sAdhya ke tIsare Thippana meM bayAna huAhai ki hara tribhuja meM chaH rAzi hotI haiM aura agara ina chaH rAziyoM meM se koI tIna dI huI hoM to sivAya pahalI aura cauthI sUrata ke aura sUratoM meM bAkI tIna rA For Private and Personal Use Only

Page #79
ja zeM daryAphata homatI hai aura tribhuja mAlUma hosaktA hai cauthI sUrata meM agara eka khAsa zarta lagAdI jAve to do tribhuja jinameM se eka tribhuja kI do bhuja barAbaravara hoM dUsare tribhuja kI do bhujoM ke aura una bhujoM meM se do barAbara bhujoM ke sAmane ke kona barAbara hoM Apasa meM barAbara hoMge isa kada ke mAtha usa sUrata ko isa taraha bayAna karate haiM "agara eka tribhuja kI do bhuja dUsare tribhuja kI do sunoM ke vyalaga 2 barAbara hoM aura una bhujoM meM se do barAvara sujoM ke sAmane ke kona Apasa meM barAbara hoM aura yaha zarta bhI ho ki dUmarI do barAbara bhujoM ke sAmane ke kona donoM adhika kona hoM yA nya nakona hoM yA unameM se eka samakona ho to eka tribhuja kI tomarI bhuja dusare tribhuja kI tIsarI bhuja ke barAbara hogI aura raka vibhuja ke bAkI kona alaga Trasare visuja ke bAkI konoM ke barAbara hoMge" u dama ne isa sUrata ko chor3a diyA hai vaha isa taraha sAbita hokhatI hai ___ pharja karo ka a ba sa aura da ya pha tribhujoM meM aba barAvara hai da ya ke aura ba sa bharAra hai yapha ke aura ba a sa aura ya da pha konajo do basa aura ya pha barAbara bhujoM ke sAmane haiM yA- a da pasa meM barAbara haiM aura a sa ba aura da phaya / koga jo dUsarI do aba aura da ya barAbara bhujoM /ke sAmane hai yA to donoM adhika kauna haiM yA nyanakona haiM yA unameM se eka sasakona hai to asa barAvara da pha ke hogI aura a ba sa kona da ya pha kona ke aura a sa ba kona da pha ya kona ke barAbara hogA agara asa barAvara da pha ke na ho to aja barAbara da pha ke bagAyo aura ba ja milAyo cUMki a ba ja aura da ya pha tribhujoM meM ba a barabara hai ya da ke aura a ja barAbara da pha ke hai aura ba a ja kona ya da pha kona ke barAbara hai isaliye ba ja barAbara hai ya pha ke aura a ja ba kona barAbara hai daphaya kona ke ( sA0 4) lekina ba sa varAvara hai yapha ke (phaja ) isaliye baja barAbara hai ba sa ke (sva0 1) imaliye ba sa ja kona barAbara hai ba jasa kona ke (sA. 5) pahale pharja karo ki asa ba aura da pha ya donoM nyU na kona haiM to a ja ba kona bhI nyU nakona hai aura isaliye ba ja sa adhikakona hai ( sA0 13) isaliye ba sa ja kona bhI adhika kona hai aura yaha hamAre faz2a ke khilApha hai (dUsarI sarata) pharja karo ki a sa ba aura da pha ya donoM adhikakoga For Private and Personal Use Only

Page #80
( 78 ) haiM to ajaba konajodaphaya kona ke barAbara sApita hocukA hai adhika kona hai aura isaliye ba ja sa nyU nakona hai (sA. 13) aura isaliye basa ja kona bhI nyU nakona hai aura yaha hamAre phUla ke khilApha hai (tIsarI sUrata) farz2a karo ki a sa ba aura da pha ya konoM meM se koI eka samakona hai ___ agara a sa ba samakona hai to ba ja sa bhI samakona hai isaliye basa ja aura ba ja sa kona milakara do samakona ke barAbara haiM aura yaha nAmumakina hai ( sA0 17) agara da pha ya samakona hai to ajaba bhI samakona hai aura isaliye ba ja sabhIsamakona hai aura isaliye basaja bhI samakona hai isaliye ba sa ja aura ba ja sa kona milakara do samakona ke barAbara haiM aura yaha nAmumakina sA017 ___ isalile asa nAbarAbara da pha ke nahIM hai yAnI asa barAbara da pha ke hai isaliye aba sa tribhuja barAbara hai da ya pha tribhuna ke aura eka 'tribhuja ke bAkI kona alama 2 dUsare tribhuja ke bAkI konoM ke barAbara hai yAnI a ba sa kona da ya pha kona ke aura asaba kona da pha ya koMna ke barAbara hai abhyAsa (55) tribhuja kI kisI do bhuja se bane hue kona ke eka rekhAdo barAbara hisse karatI hai agara usa rekhA ke kisI bindu se una bhujoM para lamba girAveM to vaha Apasa meM barAbara hoMge (56) tIna sIdhI rekhA dI huI haiM unameM se kisI eka meM aisA bindu dAphata karo ki usase jo bAkI rekhAyoM para lamba girAye jAyaM grAphsa meM barAbara hoM aura yaha bhI batAyo ki kisa hAlata meM yaha sAdhya nAmumakina hai (57) tIna diye hue bindu haiM eka aisI sIdhI rekhA khA~co ki vaha una binduoM meM se kisI eka meM hokara gujare aura usa para bAkI do binduoM se no lamba girAye jAyaM grApasa meM barAbara hoM aura yaha bhI batAyo ki kisa hAlata meM yaha sAdhya nAmumakina hai| (58) aba sa tribhuja ke a kona ke eka rekhA do barAbara hisse karatI hai ba se bada lamba usa rekhA para girAyA gayA hai aura ba da baekara asa se yA a sa ke bahe hue hisse se ya bindu para milatI hai to sAbita karo ki ba da barAbara hai da ya ke sA04 For Private and Personal Use Only

Page #81
(5) a ba aura asa koI do sIdhI rekhA abindu para milatI haiM kisI da bindu se eka aisI sIdhI rekhA una donoM rekhAoM se ya aura pha binduvyoM para milatI huI khIMco ki 'a ya barAbara ho apha ke (60) do samakona tribhuja aise haiM ki jinake karNa grApasa meM barAbara haiM aura eka tribhuja kI eka bhaja dasare virAja kI eka bhaja ke barAbara hai to sAbita karo ki donoM tribhuja saba taraha vApasa meM barAbara hai savAlAta itihAna sA6 se 26 taka (1) solahavauM sAdhya ke sAbita karane kA rahA dasa ne konasI svayaMmiti ko mAna liyA hai (2) Rjubhuja kSetra ke vahi: kona aura santa: kona kI tArIfa karo (3) rekhAgaNita kI satrahavIM sAdhya kA viloma bayAna karo (4) 18 vIM aura 16 vIM sAdhya kA kalpitArtha aura phala batAyo (5) kaunasI zakala se yaha natIjA nikAla sakta haiM ki do binduoM ke bIca kI sIdhI rekhA saba se choTI dUrI hai (javAba ) sAdhya 20 se kyoMki abindu ba sa rekhA se kaisA hI najadIka kyoM naho basa hamezA ba a aura ma sa se choTA hI hotA hai (6) kyA 21 vauM sAdhya meM yaha zarta z2arUra hai ki tribhuja ke aAdhAra ka siroM se sIdhI rekhA khIMcI jAya (7) 22 vauM sAdhya ke dAve meM tIna sIsI rekhAoM meM se haraeka do kA milakara tIsarI se bar3A honA kyoM jarUtI hai sAbita karo ki isa zarta ke pUrA hone se donoM vRtta jarUra eka dUsare ko kATate haiM (8) kina kina hAlatoM meM 22 vI sAdhya ke banAne meM vRtta eka dUsare ko na kATeMge (1) 22 vauM sAdhya ke dAve meM agara do kA jor3a tIsarI rekhA ke barAbara hotA to kyA vRtta mila jAte to sAro ki ve eka dUsare ko na kATate (10) "aisI tIna sIdhI rekhAoM se eka tribhuja banAo ki jinameMse haraeka do milakara tIsare se bar3e haiM" kyA konoM ke liye bhI aisI prata z2arUrI hai (11) kyA aisA tribhuja banA sakta haiM jisake bhujoM kI lambAI kA makhkhancha 1, 2, 3 hai yA jisake bhujoM kI lambAI kA sambandha 1, 2, 3 hai (12) kyA aisA tribhuja banA sakta haiM jisake konoM kA sambandha 1,2,3 hai apane javAba ke sahI yA galata hone kA sabUta do (13) caubIsavI sAdhya ke amala meM isa zarta kI ki da ya bhuja da pha For Private and Personal Use Only

Page #82
(80) bhuja se bar3I nahIM hai kyoM z2arUrata hai (14) "agara do tribhujoM meM se eka nimuna kI koI tIna mikadAreM dUsare tribhuja kI unhI tIna mikadAroM ke alaga alaga barAbara hoM to li. bhuja hara sUrata meM yApasa meM barAbara hoMge" kyA yaha prakala hara sUrata meM sahI hai ina saba sUratoM kA bayAna karo ki jinameM tribhujoM kI barAbarI kI ukta dasa ne pahale adhyAya meM jikra kiyA hai kaunasI marata ukta dama ne nahIM bayAna kI hai (javAba ) TippaNI nambara 2 mAdhA 26 dekho (15) 26 vI mAdhA kI dUsarI sUrata kA viloma bayAna karo kaunamau hAlatoM meM vaha sahI hai isako sAbita karo paribhASA ekAntara kona una konoM ko kahate haiM jo do sIdhI rekhA kisI tIsarI sIdhI rekhA se usa ava/ ke do binduoM para milakara usa para do kona yAmane sAmane kI taraphoM meM banAtI hai jaise isa tasvIra meM kona aba sa aura ba sa da ekAntara kona haiM sAdhya 27 prameyopapAdya sA0 mata agara eka sIdhI rekhA kisI aura do sIdhI rekhAoM para gira kara ekAntara kona eka dUsare ke barAbara banAveM to vaha donoM sIdhI rekhA samAnAntara hoMgI vi0 matra farz2a karo ki yapha sIdhI rekhA aba aura sa da do sIdhI rekhAoM para gira kara ayapha aura yaphada ekAntara kona eka dUsare ke barAbara banAtI hai to aba samAnAntara hogI sadake va ya/ a upa. agara ava samAnAntara sa da ke da ma naho to aba aura sada bar3hakara kisI tarapha cAhe ba aura da kI tarafa yA aaura sa kI tarafa kahauM mila jAyaMgI agara mumakina ho to faz2a karo ki aba aura sad bar3ha kara va aura da kI tarapha ja bindu para mila jAyaMgI nAtA ha For Private and Personal Use Only

Page #83
( 81 ) to jaya pha eka tribhuja hai cUMki ja ya pha tribhuja kI jaya eka bhuja a bindu taka bar3hI hai isaliye bahiH kona aya pha apane sAmane ke antaHkona ya phaja se bar3A hai sA0 16 lekina a ya pha kona ya phaja kona ke bagabara hai(faz2a) isaliye aya pha kona bar3A hai ya phaja kona se aura usake barAbara bhI hai aura yaha nAmumakina hai| isaliye aba aura sa da bar3hakara ba aura da kI tarapha nahIM mila saktoM __ aura isI taraha yaha bhI sAbita hosaktA hai ki aba aura sada bar3hakara a aura sa kI tarafa nahIM mila saktI haiM __ lekina vaha sIdhI rekhA jo eka dharAtala meM hoM aura donoM tarafa kitanI hI dUra taka bar3hane se kahIM na mile eka dUsarI kI samAnAntara hotI haiN| isaliye aba samAnAntara hai sa da kii| phala- isaliye agara eka sIdhI rekhA kisI aura do sIdhI rekhAoM para AdyopAnta-yahI sAbita karanA thA Ti. isa sAdhya kI tasvIra meM bahasa karane kI garaja se ya baja aura pha da ja dehI rekhAoM ko sIdhI rekhA aura ya pha da ja ba ko vibhuja khayAla karanA cAhiye abhyAsa (61) agara ya ja ha pha sIdhI rekhA a ba aura sa da do sIdhI rekhAoM ko jo ekahI dharAnala meM hai ja aura ha binduoM para kATe aura ajaya aura pha ha da kona barAbara nAve to aba aura sa da samAnAntara hoMgI (62) agara ya ja ha pha sIdhI rekhA aba aura sa da do sIdhI rekhAoM ko jorakahIdharAtala meM haiM ja aura ha binduoM para kATe aura ya ja ba aura da ha pha kona milakara do samakona ke barAbara hoM to aba aura sada samAnAntara hoMgI For Private and Personal Use Only

Page #84
( 82 ) (63) jo rekhA kisI aura rekhAoM ke sAtha samakona banAtI hai to vaha rekhA pApasa meM samAnAntara hoMgI (64) hara samadivAhu tribhuja ke zIrSa bahiHkona ke do barAbara hisse karane vAlI rekhA AdhAra ke samAnAntara hotI hai ___ sAdhya 28 prameyopapAdya sA0 sUtra agara eka sIdhIrekhA kisI aura do sIdhI rekhAoM para girakara apanI eka tarafa meM bahiHkona aura usake sAmane kA antaHkona barAbara banAve yA apanI eka tarafa do antaHkadona samakona ke barAbara banAve to vaha donoM sIdhI rekhA samAnAntara hoMgI saha vi0 sUtra pharja karo ki ya pha sIdhI rekhA aba aura sa da do sIdhI rekhAoM para girakara ya ja va bahiHkona usake sAmane ke jahada antaHkona ke barAbara apanI eka tarafa meM banAtI hai yA apanI eka tarapha ke ba ja ha aura jahada antaHkona do samakona ke barAvara banAtI hai to aba samAnAntara hogI sa da kI ba ya a upa. cUMki ya ja ba kona jahada kona ke / barAbara hai aura ya ja va kona Aja ha kona ke barAbara hai sA015 isaliye ajaha kona jahada kona barAbara hai sva. 1 aura yaha ekAntara kona haiM isaliye aba samAnAntara hai sa da kI sA0 27 phira cUMki ba ja ha aura jahada kona milakara do samakona ke barAbara haiM farz2a aura ajaha aura vajaha kona bhI milakara do samakona ke barAbara hai sA0 13 For Private and Personal Use Only

Page #85
( 83 ) isaliye ajaha aura vajaha kona milakara jahada aura vajaha konoM ke barAbara haiM kha0 1 ina barAbaroM meM se vajaha kona jo donoM meM ubhayaniSTa hai nikAla DAlA isaliye bAkI ajaha kona barAbara hai bAkI ja hada kona ke sva. 3 aura yaha ekAntara kona haiM isaliye aba sahAnAntara hai sada kI phala isaliye agara kadhI rekhA kisI do sIdhI rekhAoM para girakara AdyopAnta--yahI sAbita karanA thA Ti. isa sAdhya meM do sAdhya zAmila haiM sAdhya 26 prameyoSapAdya sA0 sUtra agara eka sIdhI rekhA dI sIdhI samAnAntara rekhAoM para gire to ekAntara kona Apasa meM barAbara aura usa kI eka tarafa meM bahi: kona aura usake sAmane kA antaH kona Apasa meM barAbara aura usakI eka tarafa meM do antaH kona milakara do samakona ke barAbara paidA hoMge vi0 sUtra farz2a karo ki yapha sIdhI rekhA aba aura sada do samAnAntara sIdhI rekhAoM para giratI hai to aja ha aura ja ha da ekAntara kona . Apasa meM barAbara hoMge aura ya pha ke eka tarafa da meM baja va bahiHkona aura usake sAmane kA jahada antaH kona mApasa meM barAbara hoMge aura ba ja ha aura ja hada do antaHkona milakara do samakona ke barAbara hoMge upa. kyoMki agara ajaha kona jahada kona ke barAbara For Private and Personal Use Only

Page #86
( 84 ) naho to unameM se eka z2urUra dUsare se bar3A hogA agara mumakina ho to farz2a karo ki ma ja 6 kona bar3A hai cUMki pra ja ha kona bar3A hai ja ha da kona se aura ina donoM nAbarAbaroM meM se haraeka meM ba ja ha kona milAyA isaliye pra ja 6 aura ba ja ha kona milakara bar3e haiM va ja ha aura ja ha da konoM se lekina pra ja ha aura va ja ha kona milakara do samako na ke barAbara haiM sA0 23 isaliye vajaha aura ja ha da kona milakara do sama kona se kama haiM lekina agara do sIdhI rekhAoM para eka sIdhI rekhA ke girane se usakI eka tarapha meM do antaHkona aise baneM ki vaha donoM mila kara do samakona se kama hoM to vaha donoM sIdhI rekhA lagAtAra bar3hAyI jAne se kahIM na kahIM usa tarapha meM jidhara vaha kona haiM jo milakara do samakona se kama haiM mila jAyagI sva0 22 isaliye pra va aura sa da lagAtAra bar3hAyI jAne se mila jAyagI lekina yaha kabhI nahIM milasaktI haiM kyoMki yaha samAnAntara haiM C. isaliye pra ja ha kona ja ha da kona ke nAbarAbara nahIM hai yAnI usake barAbara hai cUMki a ja ha kona ya ja ya kona ke barAbara sA 15 isaliye ya ja ba kona ja ha da kona ke barAbara hai 0 1 ina donoM barAbaroM meM va ja ha kona milAyA isaliye ya ja va aura ba ja ha kona milakara barAbara For Private and Personal Use Only

Page #87
-- barAbara hai vajaha aura jahada konoM ke sva. 2 __ lekina ya ja ba aura vajaha kona milakara do samakona ke barAbara haiM isaliye vajaha aura ja ha da kona milakara do samakona ke barAbara haiM phala isaliye agara eka sIdhI rekhA do samAnAntara sIdhI rekhAoM para gire to kone AdyopAnta-yahI sAbita karanA thA Ti. 1 bArahavIM svayaMnidha pahalI hI bAra isa mAdhya meM istemAla kI gayI hai Ti. 2 isa sAdhya ko pile phAra sAhava ne varga ra bArahavIM svasiddhi kI madada ke isa taraha sAbita kiyA hai agara aja ha kona ja ha da kona ke barAbara nahoto inameM se eka bar3A hogA dUsare se agara mumakina aho to pharja karo ki ca ja ha kona ja ha da kona se kI bar3A hai ha ja ke ja viMdu para aura usake usa tarapha meM jidhara aja ha kona hai ha ja ka koja ja ha da kona sa / ke barAbara banAyo aura ka ja ko la taka bagAyo ki ka ja ha aura ja ha da ekAntara kona Apasa meM barAbara haiM isaliye ka la samAnAntara hai sa da ko ( sA0 27) lekina aba bhI sa da kI samAnAntara hai ( pharja) isaliye aba aura ka la jo ekahI ja biMdu meM hokara gujaratI haiM donoM samAnAntara haiM sa da kI aura yaha nAmumakina hai (bArahavIM svayaMsiddha kA Tipa pana dekho) isaliye ajaha aura ja hada ekAntara kona yApama meM nAbarAbara nahIM haiM yAnI Apasa meM barAbara haiN| __ ki ya ja ba kona aja ha kona ke barAbara hai ( sA0 15) aura ajaha kona ja ha da kona ke barAbara mAbita hocukA hai isaliye e jaba bahiHkona barAbara hai ja ha da anta:kona ke (kha0 1) ___ caMki ya ja ba kona ja ha da kona ke barAbara hai aura ina donoM barAbaroM meM se haraeka meM ba ja ha kona milAyo isaliye ya ja ba aura ba ja ha kona milakara ba ja ha aura ja ha da kona ke barAbara haiM (sva02) lekina ya ja ba aura ba ja ha kona milakara do samakona ke barAbara haiM (sA0 13) isaliye ba ja ha aura ja ha da anta:kona bhI milakara do samakona ke barAvara haiM ( sva0 1) For Private and Personal Use Only

Page #88
Ti. 3 ima mAthya meM tIna mukhatalipha mAthe pAmila haiM unameM se pahalI sAdhya sattAIsavIM mAtha kA vilosa hai aura dUsarI aura tImArI sAdhyapravAI navauM sAdhya ke pahale aura dUsare hirahoM kA viloma hai abhyAsa (65 ) jo rekhA samadvibAhu tribhuja ke grAbAra kI samAnAntara hogI vaha bhujoM ke sAtha barAbara kona vanAvegI (66 ) a aura ba do rekhA alaga 2 sa aura da do rekhAyoM ko samAnA ntara haiM yAnI asamAnAntara sa kI gaura va samAnAntara da kI ho to sAvita karo ki jo bhakAva kA da ke sAtha hai barAbara hogA ugra bhayAna ke jo ba ko sa ke sAtha hai (0) agara eka tribhaja ke bhaja dUsare cimAja ke ajI ke alaga 2 gAna nAntara haiM to eka tribhuja ke kone dUsare vibhAga ke kohoM ke ujAgara karAkara hoMge (8) agara do kona Apasa meM barAbara hoM aura unakI ekaja Apasa meM samAnAntara hoM to eka kona kI garI bhaja gare kona kI TUnarI maja ko samAnAntara hogI (68 ) agara asada aura ba sa da lAsana konoM ke samaya aura kApha dekhA do do barAbara hise kareM aura ya pharekhA jo aba rekhA kI samAnAntara khIMcI jAba aura sa da ko jasiMdu para kATe to sAbita karo ki yaja barAvara heja pha o ( 70 ) eka sIdhI rekhA ke sire do samAnAntara sIdhI rekhAyoM para haiM utta rekhA ke bIcoM bIca ke biMdu se eka aisI sIdhI rekhA khIMcI. gadhI ki usake sire una do samAnAntara rekhAgoM para par3ate haiM to sAbita karo ki usa sIdhI rekhA ke bhI usa siMdu para do barAbara hisse hote haiM (71) adhara visI niMda se jo do samAnAntara rekhAoM se vAyara dUrI garahe do rekhA una sasAnAntara nalAoM ko kATatI haI khIcI jAvaM lo samAnAntara rekhAyoM ko hirama jo una rajA ko darmiyAna hoMge vyApala meM barAbara hoMge ( 2 ) agara yodhI rekhA jo eka tribhuja ke zIrSa bahiHkona ke do barA. vara hirahe karatI hai usa cimAja ke AdhAra ke samAnAntara bhI hai tosAbhita kAro zivaha tribhuja samavivAhu hai ( 73 ) a basa tribhuja ko ba a sa kova ke a da rekhA do barAbara hisa karatI jaura basa se da biMdu para milatI hai daya aura dapha samAnAntara haiM asamoracanA kI rAna aura basa se ya aura pha miMda parakhimAtI hai lAbita karIdaya aura dapha vApasa meM barAbara For Private and Personal Use Only

Page #89
( 87 ) ( 74 ) a va sa tribhuja kI ba sa bhuja da viMdu taka bar3hAyI gayI hai aura sa ya rekhA a sa ba kona ke aura saja rekhA asada kona ke do2 varAvara hise karatI haiM ya sa rekhA aba bhuja se ya biMdu para milatI hai aura ya ja samAnAMtara hai ba sa kI vyaura asa ko pha biMdu para kATatI hai sAbita karo ki ya pha aura pha ja aApasa meM barAbara haiM ( 75 ) usa samAnAMtara catubhuja ke bhujoM kA jor3a jo kisI samavivAha tribhuja ke eka bhuja ke kisI viMdu se bAkI do bhujoM ke samAnAntara rekhA khIMcane se banatA hai usa tribhuja ke bhuja se dUnA hotA hai sAdhya 30 prameyopapAdya sA. sUtra jo sIdhI rekhA kisI ekahI sIdhI rekhA kI samAnAMtara hotI hai vaha Apasa meM bhI samAnAMtara hotI haiM vi0 satra farz2a karo ki aba aura sa da meM se haraeka yapha kI samAnAMtara hai to aba samAnAMtara hogIsada kI 0. jahaka aisI sIdhI rekhA farz2a karo ki vaha aba, yapha aura sada ko kATe upa cuki jaha ka do samAnAMtara sIdhI rekhAoM prava aura yapha ko ja aura ha binduoM para kATatI hai isaliye ajaha aura jahapha ekAMtara kona barAbara haiM (sA028) aura cUMki jahaka rekhA yapha aura sa da do sIdhI samAnAMtara rekhAoM ko ha aura ka binduoM para kATatI hai isaliye ja haphabahiHkonaha ka da antaHkona ke barAbara hai(sA028 ora yaha sAbita hocukA hai ki prAjaka kona jahapha kona ke barAvara hai isaliye ajaka kona jaka da kona ke barAbara hai kha0 1 aura yaha ekAMtara kona hai -- - da For Private and Personal Use Only

Page #90
( 88 ) isaliye aba samAnAMtara hai sa da kI phala isaliye jo sIdhI rekhA kisI ekahI sIdhI rekhA kI AdyopAMta-yahI sAbita karanA thA Ti. isa sAdhya meM agara aba aura yapha meM se haraeka sada kI samAnAntara ho to isI taraha sAbita ho saktA hai ki aba aura ya pha Apasa meM samAnAntara hoMgI- ukta dasa ne jo sUrata sAvita kI hai vaha aisI sAfa jAhira hai ki subUta kI suhatAja nahIM hai kyoMki jaba aba aura sa darekhA yapha rekhA se jo unake darmiyAna meM hai nahIM milatI to aApasa meM bhI kahIM na mileMgI aura isaliye samAnAntara hoMgI abhyAsa (76) tIsauM sAdhya ke viloma ko bayAna karo aura mAbita karo sAvya 31 bastUpapAdya sA. sUtra diye hue bindu se eka aisI sIdhI rekhA khauMco ki vaha do huI sIdhI rekhA ke samAnAMtara hI vi0 sUtra farz2a karo ki adiyA huA bindu aura vasa dI huI sodhI rekhA hai ase eka aisI sIdhI rekhA khIMcanI hai ki vaha vasa kI samA nAMtara ho 0-vasa meM koI da bindu lo aura ada milAo ada sIdhI rekhA ke a bindu para daa ya ya a pha kona adasa kona ko barAbara aura ada kI ba sa sAmane kI tarafa meM banAo sA0 23 aura aya ko pha taka bar3hAo to yapha samAnAMtara hogI basa kI / upa. cUMki ada sIdhI rekhA yapha aura basa do sIgho rekhAoM se milatI aura unake sAtha yaprada aura adasa For Private and Personal Use Only

Page #91
ekAMtara kona eka dUsare ke barAbara banAtI hai / isaliye yapha samAnAMtara hogI basa kI . sA. 26 phala isaliye diye hue prabindu se apha sIdhI rekhA dI huI basa sIdhI rekhA kI samAnAMtara khiMca gayI ___ aura isI rekhA ke khauMcane kI z2arUrata thii| Ti. 1 isa sAdhya ke graMkana meM yaha ibArata "ada ke nAmane kI tarapha meM honI jarUra hai kyoMki agara ya ada kona ada rekhA kI usI tarapha meM banAyA jAya jidhara adasa kona hai to sAdhya kA hala honA nAmumakina hogA Ti. 2 isa sAdhya ke banAne meM teIsavIM sAdhya kI kucha z2arUrata na par3egI agara gyArahavIM aura bArahavIM mAthyoM kI madada lI jAya abhyAsa (77) kisI tribhuja ke aAdhAra para ke kone aura usa lamba kI lambAI jo aAdhAra para usake sAmane ke kone se DAlA jAtA hai mAlama hai usa ki bhuja ko banAyo (78) dI huI sa da rekhA meM eka aisA bindu ba ryAphata karo ki agara usa bindu se eka diye hue bindu ataka sIdhI rekhA khIMcI jAya to kona aba sa eka diye hue kona ke barAbara ho (GE) a basa samakona tribhuja ke aba karNa meM da binTu aisA daryA fata karo ki ba da barAbara ho usa lamba ke jo da se asa para girAyA jAve (80) aba sa eka mamadivAhu tribhuja hai usakI aba aura asa varA vara bhajoM meM da aura ya aise viMdu dAphata karo ki ba da, da ya aura yasa yApama meM barAbara hoM (81) mamadibAhu tribhuja ke basa aAdhAra ke sAtha samakona banAne vAlI rekhA aba bhuja ko da viMdu para aura sa a ke bAda hue hisse ko ya biMdu para kATato hai to sAvita karo ki a ya da mamadivAhu tribhuja hai (82) una tribhujoM meM jinakA ekahI zIrgha kona hai aura jinake grAdhAra ekahI viMdu meM hokara gujarate haiM vaha tribhuja mabase choTA hogA jisake AdhAra ke usa biMdu para do barAvara hisse hote haiM (83) abasa eka tribhuja hai usake ba sa aAdhAra ke samAnAntara eka daya rekhA aisI khIMco ki isake da aura ya sire tribhuja ke aba aura asa bhujoM para hoM aura vaha barAbara ho (1) ba da yA sa ya ke (2) vaha aura sa ya ke yoga ke (3) va da aura sa ya ke antara ke For Private and Personal Use Only

Page #92
(83) do diye hue viMduoM se jo do dI huI samAnAntara rekhAyoM meM hai aisI do rekhA soco jo dI huI samAnAntara rekhAyoM ke sAtha eka vighamanona samacaturbhuva banAne (85) aba aura sa da do dI huI rekhA hai unake darmiyAna eka aisI rekhA dI huI lambAI kI khIMco jo kisI tIsarI dI huI yapha rekhA kI khajAnAntara ho sAdhya 32 prameyopapAya sA0 sUtra agara kisI tribhujakI eka suja bar3hAI jAya to bahi kona apane sAmane ke do antaH konoM ko barAbara hogA aura tInoM antaH kona milakara do samakona ke barAbara hoMge zra ya vi0 sUna farz2a karo ki aba sa ekA tribhuja / hai usakI basa bhaja da bindu taka bar3hAI gayI hai to asada bahiHkona apane sAmane ke anasa aura va prasa do aMtaHkonoM ke barAbara hogA aura tribhuja ke avasa, vAsa aura asaba tInoM aMtaHkonamilakara do samakona ke barAbara hoMge aMsa bindu se saya rekhA va akI samAnAMtara khoMco (sA031) upa. cUMki aba samAnAMtara saya kI hai aura asa una para giratI hai isaliye asa ya aura vanasa ekAntara kona Apasa meM barAbara haiM __sA. 28 phira cUMki aba samAnAntara saya kI hai aura ba da una para giratI hai isaliye sayada bahiHkona apane sAmane ke avasa antaH kona ke barAbara hai sA. 28 lekina asaya kona va nasa jhona ke barAbara sAbita hocukA hai For Private and Personal Use Only

Page #93
( 1 ) isaliye kula asada bahiHkona apane sAmane ke vAsa aura abasa do antaHkonoM ke barAbara hai sva. 2 ina barAbaroM meM se haraeka meM prasava kona milAo isaliye asada aura asaba kona milakara sabanna, vaasa aura saba tInoM konoM ke barAbara haiM kha. 2 lekina prasAda aura asaba kona milakara do samakona ke barAbara haiM sA. 13 __isaliye sabasa, vanasa aura aba tInoM kona milakara do samakona ke barAbara hai sva0 1 phala isaliye agara kisI vibhuja kI eka bhuja-AdyopAnta yahI sAbita karanA yA Ti. isa sAdhya meM do mAdhya zAmila hai isa sAdhya kA dUsarA hissA yAnI tribhuja ke tInoM kona milakara do samakoNa ke barAbara hote haiM vagaira vAye tribhuja kI kisI bhuja ke isa taraha sAbita hosato haiM __ aviMdu se da a ya samAnAntara ba sa kI khIMco sA031) Tha zra ya caMki da a aura ba sa aApasa meM samAnAntara haiM aura aba / una para giratI hai isaliye aba sa kona barAbara hai ba ada ekAntara kona ke ( mA0 26 ) aura naMki ya a aura sa ba va sa vyApala meM samAnAntara haiM aura a sa una para giratI hai toba sa a kona barAbara hai sa a va ekAntara koca ke (sA0 26) lekina aba sa kona da aba kona ke barAbara lAvita ho cukA hai isaliye aba sa aura basa a kona milakAra barAbara haiM da aba aura sa a ya konoM ko (sva02) ina varAvaroM meM se haraeka meM ba a sa kona milAyA isaliye aba sa, ba sa a aura sa a va kona milakara varAvara haiM da ava, ba asa aura sa aya konoM ke ( sva0 2) lekina da a ba aura ba a sa aura sa a ya koga milakara do sasakona ke barAbara haiM (sA0 13 ) isaliye abasa, basa a aura sa a ba koga milakara do samakoga ke barAbara haiM ( sva02) anu0 hara Rjubhuja kSetra ke saba aMtaHkona aura cAra rUmakona For Private and Personal Use Only

Page #94
( 2 ) milakara barAbara haiM utane samakonoM ke jo ginatI meM kSetra kI bhujoM kI tAdAda se dUne hoM upa0 agara kisI prava sadaya Rjubhuja kSetra yA ke andara koI pha biMda liyA jAya aura usa biMdu se aba saba konoM taka sIdhI rekhA khauMcI jAyaM to jAhira hai ki vaha kSetra utane tribhujoM meM baTa jAyagA jitanI usameM bhuja haiM __ cUMki hara tribhuja ke tInoM kona milakara do samakona ke ba. rAbara haiM aura yahAM itane tribhuja haiM jitanI Rjubhuja kSetra kI bhuja haiM ___ isaliye ina tribhujoM ke saba kona barAbara haiM utane samakonoM ke jo ginatI meM kSetra kI bhujoM kI tAdAda se dUne hai lekina ina tribhujoM ke saba kona Rjubhuja kSetra ke saba aMta: konoM ke aura una konoM ke jo pha biMdu para hai barAbara hai ___ aura jo kona pha biMdu para jo ina tribhujoM kA ubhayaniSTa zIrSa hai bane hai vaha cAra samakona ke barAbara haiM (anu0 3 sA0 13) isaliye ina tribhujoM ke saba kona barAbara haiM Rjubhuja kSetra ke saba aMtaHkonoM aura cAra samakona ke lekina sAvita hocukA hai ki ina tribhujoM ke saba kona utane samakonoM ke bhI barAbara haiM jo ginatI meM Rjubhuja kSetra kI bhajoM kI tAdAda se dUne haiM isaliye Rjubhaja kSetra ke saba aMtaHkona aura cAra samakona milakara barAbara haiM utane samakona ke jo ginatI meM Rjubhuja kSetra kI bhujoM kI tAdAda se dune haiM Ti. 1 yaha anumAna isa taraha bhI sAvita hosaktA hai agara kimI aba sa da ya Rjubhuja kSetra ke kisI da kona se sAmane ke kInoM taka sIdhI rekhA khIMcI jAya to jAhira hai ki vaha kSetra utane tri. bhujoM meM baTa jAyagA jo ginatI meM usa kSetra kI bhujoM kI tAdAda se do For Private and Personal Use Only

Page #95
( 83 ) . caMki tribhuja ke tInoM kona milakara dosamakona ke barAbara haiM aura da yahAM itane tribhaja haiM ki unakI tAdAda uma kSetra kIbhajoM kI tAdAda ya sa se do kama hai isaliye tribhujoM ke sava kona milakara varAvara haiM utane / samakona ke jo ginatI meM kSetra kI bhujoM kI tAdAda ke dUne se a ba cAra kama haiM lekina ina tribhujoM ke saba kona milakara barAbara hai Rjubhuja kSetra ke maba anta:konoM ke isaliye Rjamaja kSetra ke saba granta:kona mila kara barAbara haiM utane samakona ke jo ginatI meM usa kSetra ko bhajoM ko tAdAda ke dUne se cAra kama haiM isaliye Rjubhuja kSetra ke saba chAnta:kona aura cAra mamakona milakara barAbara haiM utane samakonoM ke jo ginatI meM usa kSetra kI bhujoM kI tAdAda se dUne haiM Ti 2 isa anumAna kI madada se hara sama bahubhuja samAna kona kSetra ( jisakI saba bhuja aura saba kona Apasa meM samAna hoM ) ke kona kI kImata dAphata hosaktI hai agara usakI bhujoM kI tAdAda mAlUma ho / anu0 2 hara Rjubhaja kSetra ke saba bahiHkona jo usakI bhujoM ko eka dUsaro ke bAda ekaho tarapha meM bar3hAne se paidA hote haiM milakara cAra samakona ke barAbara hote haiM cUMki hara antaHkona masalan ava sa maya a- / pane pAsa ke prabada bahiHkona ke do samakona ke barAbara hai isaliye saba aMtaHkona maya apane pAsa ke bahiHkonoM ke barAbara haiM utane samakonoM ke jo ginatI meM Rjubhuja kSetra kI bhujoM kI tAdAda se dUne hai lekina yaha Upara ke anumAna se sAbita hai ki Rjubhaja kSetra ke saba aMtaHkona aura cAra samakona milakara barAbara haiM utane samakona ke jo ginatI meM usa kSetra kI bhajoM kI tAdAda se dUne haiM isaliye saba aMta:kona aura saba bahiHkona milakara barAbara haiM saba aMtaHkonoM aura cAra samakona ke kha. 1 dUna barAbaroM meM se aMtaHkonoM ko nikAla DAlA isaliye saba bahiHkona cAra samakona ke barAbara haiM sva. 3 Ti. 1 ima anumAna kI madada se hara samabahubhuja samAnakona kSetra kI bhujoM kI tAdAda mAlUma hosaktI hai agara usake eka kona kI kImata mAlama ho For Private and Personal Use Only

Page #96
(84 ) Tei0 2 yaha donoM anumAna limasana sAhaba ne z2iyAdA kiye haiM dUsare vya. numAna meM bayAna karanA cAhiye thA ki Rjubhuja ke bahiHkona se kyA murAda hai agara usa biMTu se jahAM Rjubhuja kSetra kI do bhuja milatI haiM una bhujoM meM se koI bhaja bar3hAyI jAya to kona jo usa bhaja ke vada hue hissa aura TrasarI bhaja se banegA Rjubhaja kSetra kA bahiHkona hogA do majoM meM se koI sI aja batAyI jAya ekahI bAta hai kyoki kona jo isa taraha baneMge donoM vyApama meM paMdrahavI sAdhya se barAbara hoMge usI dasa ne unhI Rjubhaja kSetra kA bayAna kiyA hai jinake saba konoM kA rukha grandara kI tarapha hai eka aura taraha kA Rjubhuja kSetra bhI aisA bana saktA hai ki usameM kona aphasa kA rukha bAhara kI tarapha hai lekina yaha kona kSetra apha sa da ya da ya kA anta:kona nahIM hai isa kona ke badale isa kSetra meM antaH kona vaha kona hai jo cAra samakona se vaqadara kona apha sa kama /pha hai aise antaHkona ko jo dosamakona se bar3A hai punayukta kona sa a kahate hai battIsavI' sAdhya kA pahalA anumAna to una kSetroM meM bhI jinameM eka yA kaI anta:kona punayukta haiM sAbita hosaktA hai jekina dUsarA anumAna aise kSetroM meM sAbita nahIM hotA ya da agara kisI Rjubhuja kSetra apha sa da ya kA anta:kona la ja viMTu pha para punaryukta ho to asa milAne aura usako ph| sa kI tarapha bahAne se sAbita hojAyagA ki kona / ma apha aura hasada aura ka da ya aura la ya a milakara cAra samakona ke bakadara kona ja pha sa z2iyAdA hai Ti0 3 vattImavI sAdhya se vyaura bhI kaI anumAna nikalate haiM aura vaha anumAna yaha haiM 3-agara tribhuja ke do konoM kI mikadAra mAlUma hai to tIsare konako bhI mikadAra mAlama hai kyoMki tribhaja ke tInoM kona milakara varAvara do samakona ke hote haiM 4-gragara tribhuja kA eka kona samakona hai to bAkI do kona milakara eka samakona ke barAbara haiM aura agara tribhuja ke do kona milakara tIsare kona ke barAbara haiM to tIsarA kona samakona hai 5----agara eka tribhuja ke do kona mila kara tIsare kona se choTe haiM to tIsarA kona vyadhika kona hai aura agara bar3e haiM to tIsarA kona nyUnakoSa hai ---samatribAhu tribhuja kA haraeka kona do samakona kI eka tihAI yAnI eka samakona kI do tihAI hai isa anumAna kI madada se samakona ke tIna varAbara hine hosatI haiM 7-ugragara samavivAhu tribhuja kA zIrghakona samakona hai to vAkI do konoM meM se haraeka grAdhA samakona hai For Private and Personal Use Only

Page #97
( lyU ) -agara kina tribhuja ke do kona dUsare tribhuja ke do konoM ke barAbara ha to usa tribhuja kA tIsarA kona bhI dUsare tribhuja ke tIsare kona ke barAbara hai &- - caturbhuja kSetra ke satra kona milakara cAra samakona ke barAbara haiM (yaha anumAna bhimasana mAhaba ke pahale anumAna kI eka khAsa sUrata hai lekina caki isakA kAma aksara jagaha para vyAyA hai isaliye yAda rakhane ke lAba) abhyAsa (8) agara magavADa tribhuja ke AdhAra ke siroM se usakI bhujoM para girAye jAyeM to una konoM meM se jo yaha laMba yAdhAra ke sAtha paidA karegA haraeka zIrghakona se vyAdhA hogA (80) kinI tribhuja ya ba sa kI bhujoM para bAhara kI tarapha basada, savaya aura va samatibAhu tribhuja banAye gaye haiM sAbita karo ki da, baba aura sapha rekhA vyApasa meM bAbara haiM (ya) samAnako samagraSThabhuja ke eka kona kI mikadAra batAyo 8) eka samabhuja samAnakona kSetra kA eka grantaH kona barAbara 1 khasakIna ko to batAo ki usa kSetra meM kitanI bhuja (60) do diye hue biMduvyoM se aisI sIdhI rekhA khIMco ki vaha eka sIdhI rekhA ke sAtha bikA mukAma diyA huA hai eka samavibAhu tribhuja banAve yaha bhI batAyI ki kisa hAlata meM samadvibAhu tribhuja na bana sakegA (11) yagara do sIdhI rekhA kisI samadvibAhu tribhuja ke vyAdhAra ke Upara ke konoM ke dora barAbara hisse kareM aura vaha rekhA bar3hakara kisI biMdu para eka dUsarI se mileM to sAbita karo ki kona jo una rekhAoM ke mi lane se paidA hogA samadvibAhu tribhuja ke bahi: kona ke barAbara hogA (12) samadivAhu tribhuja kA zIrSaka hai aura ba a bhuja biMdu da taka itanI bar3hAyI gaI hai ki da barAvara ba a ke hai aura sa da khIMcI gayI hai kiro ki basa da samakona hai (63) do sIdhI rekhA bada aura sada kisI tribhuja abasa ke yahi: kona ba gaura sa ke do barAbara hisse karatI hai aura biMdu da para milatI are karo ki kona va Tasa aura kona va asa kA gradhA milakara eka samakoNa hai (64) banAyo ki usakA zIrghakona usake bA dhAra para ke kauna se ko (65) lie basa kI suNa va biMdu ya para aura bhuga aba biMdu ja para do barAbara hilsoM meM banatI hai yaya biMdu pha taka itanI bar3hAyI ga kI hai ki yapha barAbara hai yaya ke aura saja hi taka itanI bar3hA pAyamAhuti For Private and Personal Use Only

Page #98
( 86 ) yI gayIhai ki ja ha barAbara hai sa ja ke tosAbita karo ki pha ba aura haba ekahI sIdhI rekhA meM haiM (6) eka aisA samadibAhu tribhuja banAyo ki usaka AdhAra para ke haraeka kona kI tihAI usake zIghakona ke prAdhe ke barAbara ho (7) aba aura asa aisI do mIdhI rekhA haiM jinakA mukAma diyA huA hai ina donoM rekhAoM meM aise do biMdu ma aura ka ryAphata karo ki agara ma aura ka milAye jAve to ama aura ma ka milakara eka dI haI sIdhI rekhA ke barAbara hoM aura unake bIca kA kona eka diye hae kona ke barAbara ho (8) samavivAhu tribhuja ke aAdhAra ke siroM se pradIrgha se dUra mista meM aisI do rekhA khIMcI gayI haiM ki unameM se haraeka grAdhAra ke sAtha romA kona banAtI hai ki vaha tribhuja ke barAbara konoM meM se haraeka kA tihAI hai aura yaha rekhA aura tribhuja ke bhuja bahakara grAyasa meM milate haiM to nA. vita karo ki tIna tribhuja jo AdhAra ke nIce paidA hoMge vaha sama vivAda (E) do sIdhI rekhA a ya ja aura sa ya da viMdu ya para eka dUsarI ko kATatI haiM aura sIdhI rekhA asa aura daba do tribhuja a sa ya aura ba ya da banAtI huI khIMcI gayI hai aura kona asa ya aura dava va rekhA sapha aura bapha se jo biMdu pha para milatI hai do do varAbara hissoM se baTate haiM mAbita karo ki kona ya a sa aura ya da ba milakara kona sa ka ba se dUne haiM (100) agara tribhuja ke kisI kona se usa kona ke sAmane kI bhuja ke vIcoM bIca ke biMdu taka rekhA khIMcI jAya to vaha rekhA usa bhuja ko Adhe ke barAbara yA usake vyAdhi se bar3I yA choTI hogI sutAvika inake ki kona jise rekhA khIMcI gayI hai samakona yA adhika kona yA nyUnakona hai (101) tribhuja kA koI kona samakona yA adhika kona yA nyanakona hogA mutAbika isake ki dhorekhA jo usa kona se usake mAmane ke bhuja ke bIcoM bIca ke biMdu taka khIMcI jAya usa bhuja ke prAdhe ke barAbara yA usake Adhe se ur3I yA choTI hogI ( 102) tribhuja aba sa ke kona ase usake sAmane ke bhuja para eka va girAyA gayA hai aura yaha laba usa maja yA usake bahara hisse se viMdada para milatA hai aura kona ba se usake sAmane ke bhuja para eka laMba girAyA gayA hai aura yaha laMba usa bhaja yA usake bAda hue hisse se biMdu ya para milatA hai todo sIdhI rekhA jo da aura ya biMduoM se prAdhAra a ba ke bIcoM bIca ke biMdu taka khIMcI jAyaMgI Apasa meM barAbara hoMgI For Private and Personal Use Only

Page #99
( 20 ) (103) kisI tribhuja ke AdhAra ke konoM se unakI sAmane kI bhujoM para laMba girAye gaye haiM aura yaha laMba una bhujoM yA unake bar3he hue hissoM se milate haiM to vaha mIdhI rekhA jo una biMduyoM ke darmiyAna jahAM laMba bhujoM yA unake bar3he hue hissoM se milate haiM usa laMba se jo grAdhAra ke bIcoMbIca ke bindu se usa rekhA para girAyA jAya do barAbara hissoM meM vAMgI * (104) agara aba sa aura a ba da do samakona tribhuja a ba ka para aura unake sa aura da zIrSa milAye jAMya to caturbhuja ke hara bhuja ke nAmane ke do do kona jo isa taraha paidA hoMge vyApala meM barAbara hoMge (105) pahale gradhyAya kI pahalI sAdhya meM vRtta eka dUsare ko sa aura ha binduoM para kATate haiM aura aba bar3hakara eka vRtta se bindu ka para milatI hai sAbita karo ki sa ha ka namatribAhu tribhuja hai (106) namadivAhu tribhuja ke AdhAra para ke konoM ko do barAbara hismoM meM bAMTanevAlI sIdhI rekhA tribhuja ke bhujoM se da dhaura ya binduoM para mi latI haiM sAbita karo ki da ya tribhuja ke vyAdhAra ke samAnAntara hai (107) aba aura a sa do dI huI sIdhI rekhA haiM a ba meM eka bindu sadiyA huA hai ma se aisI sIdhI rekhA khoMco ki vaha a sa se ka bindu para milakara amaka kona a ka ma kona se tigunA banAve (108) samakona tribhuja banAyo jisakI do bhuoM kA yoga aura karNa mAlama hai (206 ) samakona tribhuja banAo jisakI do bhujoM kA vyantara aura karNa mAlUma hai (110 ) samakona tribhuja banAo jisakA karma aura laMba jo samakona se karNa para girA hai mAlUma hai (111 ) samakoNa tribhuja banAyo jisakI tInoM bhujoM kA yoga aura jisakA eka kona mAlUma hai (112) samakona ke tIna barAbara hissa e karo ( 113) dI huI paramiti sIdhI rekhA ke tIna barAbara hisse karo ( 124 ) diye hue biMdu se do samAnAntara rekhAoM taka aisI do barAvara rekhA khIMco ki vaha eka dUsarI ke sAtha samakona banAtI hoM ( 115 ) tribhuja jisakI tInoM bhujoM kA yoga mAlUma hai aisA banAgrI ki usake kona diye hue tribhuja ke konoM ke barAbara hoM ( 116 ) tribhuja a ba sa ke bahi: kona ba sa da ko rekhA sa ya aura kona va asa kI rekhA atha do 2 barAbara hissoM meM bAMTatI haiM aura lA For Private and Personal Use Only

Page #100
(88 ) yaha donoM rekhA ya biMdu para milatI haiM sAvita karo ki kona a ya sa kona aba sa kA AdhA hai (117) agara kisI Rjubhuja kSetra ke jisameM bhujoM kA zumAra (na) hai bhuja donoM tarapha bar3hAye haiM to saba kona jo pahale aura tIsare bhuja aura dUsare aura cauthe bhuja aura tIsare aura pAMcave bhuja ityAdi aura akhIra aura pahale bhuja se baneMge mila kara 2 ( na-4 ) samakona ke varAbara hoMge sAdhya 33 prameyopapAya sA0 sUtra sIdhI rekhA jo do barAbara samAnAntara sIdhI rekhAoM ke eka eka tarapha ke siroM ko milAto haiM Apasa meM barAbara aura samAnAntara hotI haiM vi0 sUtra farz2a karo ki aba aura sada do barAbara aura samAnAntara sIdhI rekhA hai aura unake eka eka tarafa a ke siroM ko asa aura vada sIdhI rekhA milAtI haiM to asa aura vada Apasa meM barAbara aura samAnAntara hoMgI aM. vasa milAo a. 1 upa. cUMki ava samAnAntara sada kI hai aura vasa una para giratI hai __isaliye kona abasa barAbara hai ekAntara kona va sada sA0 28 aura cUMki aba barAbara hai sa da ke aura vasa do tribhuja abasa aura dasava meM ubhayaniSTa hai yAnI do bhuja prava aura usa alaga alaga barAbara haiM do bhujoM dasa aura saba ke aura kona avasa barAbara kona dasaba ke sAbita hocukA hai isaliye AdhAra asa barAbara hai AdhAra bada ke aura vibhaja avasa barAbara hai tribhuja da sa ba ke ora bAkI kona eka For Private and Personal Use Only

Page #101
( ce ) tribhuja ke alaga alaga barAbara haiM dUsare vibhaja ke bAkI konoM ke yAnI vaha kona Apasa meM barAbara haiM jinake sAmane ke bhuja barAbara haiM sA. 4 isaliye kona asaba barAbara hai kona sa va da ke aura cUMki sIdhI rekhA va sa do sIdhI rekhA prasa aura vada para gira kara unake sAtha barAbara ekAntara kona prasava aura savada banAtI hai isaliye asa samAnAMtara hai bada kI sA0 27 aura asa barAbara vada ke sAbita hocukI hai phala isaliye sIdhI rekhA jo do barAbara aura samAnAMtara sIdhI rekhAoM adyopAMta-yahI sAbita karanA thA anumAna caturbhUja kSetra jisakI grAmane sAmane kI bhuja varAvara aura mAnAMtara ho samAnAMtara caturbhuja hai / Ti. isa sAdhya meM yaha prata ki sIdhI rekhA eka eka tarapha ke siroM ko malAtI haiM jarUrI hai kyoMki agara yaha pAta naho to zabaha par3egA ki pAyA sIdhI rekhA asa aura ba da binduoM aaura sa ko aura ba aura da se milAtI haiM yA mIdhI rekhA ada aura basa binduoM a aura da ko paura ba aura sa ko milAtI haiM abhyAsa ( 118) agara koI sIdhI rekhA jo do asamAnAMtara barAbara rekhAoM 'ekahI tarapha ke siroM ko milAtI hai una rekhAoM ke sAtha apanI eka tarapha meM barAbara kona banAveM to sAbita karo ki una rekhAyoM ke dUsarI rapha ke siroM ko milAne vAlI rekhA pahalI rekhA ke samAnAntara hogI 116) tribhuja ke grAdhAra ke siroM se jo rekhA mAmane kI bhajoM taka cI jAyaM to vaha kisI sUrata meM eka dUsarI ko do barAbara hissoM meM kATeMgI sAdhya 34 prameyopapAdya sA. sUtra samAnAntara caturbhuja kI Amane sAmane kI bhaja For Private and Personal Use Only

Page #102
( 100 ) aura kona Apasa meM barAbara hote haiM aura karNa usako do barAbara hissoM meM bAMTatA hai na vi0 sUtra farz2a karo ki pra va dasa samAnAntara caturbhuja hai aura basa usakA karNa hai to prava barAbara hogI sada ke aura pra sa barAbara hogI va da ke aura kona cma bada barAbara hogA kona upra sa da ke aura kona va prasa barAbara hogA kona vadasa ke aura karNa va sa samAnAntara caturbhuja aba dasa ke do barAbara hisse karegA gra va upa0 cUMki pra va samAnAntara sa da kI hai aura basa una para giratI hai isaliye kona nma va sa barAbara hai ekAntara kona basa da For Private and Personal Use Only ke sA0 28 aura cUMki upra sa samAnAntara va da kI hai aura saba una para giratI hai isaliye kona prasava barAbara hai ekAntara kona saba da ke sA0 28 aba cUMki do tribhuja pravasa aura dasava meM eka tribhuja ke do kona pra va sa ora va sapra alaga alaga varAvara haiM dUsare tribhuja ke do konoM basada aura savada ke aura bhuja vasa donoM tribhujoM meM ubhayaniSTa hai isaliye bAkI bhuja ina tribhujoM kI alaga alaga barAbara haiM aura eka tribhuja kA tIsarA kona barAbara dUsare tribhuja ke tIsare kona ke yAnI bhuja pra va barAbara hai bhuja sa da ke aura bhuja prasa varAvara hai bhujabada ke aura kona va upra sa barAbara hai kona sadaba sA0 26

Page #103
phira caMki kona aba sa barAbara kona basada ke hai aura . kona sa ba da barAvara kona asatra ke hai __isalive kala kona avada barAbara hai kula kona bhAsada ___ aura kona va asa barAbara kona badasale sAbita hovakA isaliye samAnAntara caturbhaja kI Amane sAmane kI muja aura kona Apasa meM barAbara hote haiM aura karNa usake do barAbara hihaM karatA hai caki saba barAbara hai sa da ke aura vasa ubhayaniSTa hai yAnI do bhuja aba aura basa alaga alaga barAbara haiM do bhujoM dasa aura sava ke aura kona abasa barAbara kona va sada ke sAbita hotukA hai isaliye tribhuja avasa barAbara hai tribhuja dasava ke (sA0 4) isaliye basa karNa avadasa samAnAntara caturbhuja ke do barAbara hisse karatA hai| phala isaliye samAnAntara caturbhuja kI Amane sAmane kI bhaja aura kona AdyopAnta--yahI sAbita karanA thA Ti.1 agara isa sAdhya meM dUsarA karNa bhI khIMcA jAya to mAbita hosaktA hai ki vaha bhI samAnAntara catubha ja ke do barAbara hisse karegA aura donoM karNa eka dUsare ke do do barAbara hisse kareMge agara mamAnAntara caturbhaja kA eka kona samakona ho to usake saba kona samakona hoMge aura donoM karNa yApama meM barAbara hoMge aura agara samAnAntara catubhuja bargakSetra yA viSamakoNa samacatubhuja hai to usake karNa eka dUsare ke do barAbara hisse kareMge aura eka dUsare ke sAtha samakona banAyeMge tAlivailama ko cAhiye ki ina bAtoM ko sAbita karake yAda rakhe kyoMki yaha bar3e kAma kI bAteM haiM Ti. 2 isa sAvya meM tIna sAdhya pAmila haiM pahalI yaha ki "lamAnAntara For Private and Personal Use Only

Page #104
Achar ( 102 ) catubha ja kI grAmane sAmane kI bhuja barAbara hotI haiM" dUmI yaha ki " samAnAntara ttaturbhaja ke grAmane sAmane ke kona varAbara hote haiM " tIsare yaha ki " samAnAntara catubhuja kA hara karNa usake do barAbara himme karatA hai" ina tInI sAthyoM ke viloma yAnI " agara kisI catubhuja kSetrako grAmane sAmane kI bhuja yA kona yAyasa meM barAbara hoM yA caturbhaja kA hara karNa usake do barAbara hisse karatA ho to vaha caturbhuja kSetra samAnAntara caturbhuja hogA ullI dasa ne nahIM sAbita kiye haiM yaha biloma hara hAlata meM sahI haiM tAlibailama ko cAhiye ki inako sAbita kara yAda rakhe Ti0 3 agara kimI caturbhuja aba da sa meM jisake karNa ada aura basa haiM mIce likhI huI dama khAsiyatoM meM se koI do khAsiyateM pAyI jAveM to mAbita hosaktA hai ki vaha kSetra samAnAntara caturbhuja hogA 1 aba aura sa da kA Apasa meM samAnAMtara honA 2 asa aura ba da kA Apasa meM samAnAMtara honA 3 aba aura sa da kA Apasa meM barAbara honA 4 asa aura ba da kA Apasa meM barAbara honA 5 ba asa ora sa da va konoM kA Apasa meM barAbara honA 6 aba da aura da sa a konoM kA Apasa meM barAbara honA 7 basa kA ada ko do barAbara hissoM meM bAMTanA 8 ada kA basa ko do barAbara hissoM meM bAMTanA ra ada se catubhuja kSetra aba dasa ke dharAtala kA do barAbara hissoM meM bAMTanA 20 basa se catumuja kSetra aba dasa ke dharAtala kA do barA bara hissoM meM bAMTanA / jaba ina dasa qhAsiyatoM meM se tuma do do kI tIba loga to yaha paiMtAlIsa tIveM paidA hoMgI aba aura sa da kA Apasa meM samAnAntara honA asa aura ba da kA Apasa meM samAnAntara honA (aba aura sa da kA Apasa meM samAnAntara honA ba aura sa da kA Apasa meM barAbara honA For Private and Personal Use Only

Page #105
( 103 ) (aba aura sa da kA Apasa meM samAnAntara honA asa aura ba da kA Apasa meM barAbara honA (ava aura sa da kA Apasa meM samAnAntara honA ba asa aura sa da va konoM kA Apasa meM barAbara honA (aba aura sa da kA Apasa meM samAnAntara honA aba da aura da sa a konoM kA Apasa meM barAbara honA (aba aura sa da kA Apasa meM samAnAntara honA 6) basa kA ada ko do barAbara hissoM meM bAMTanA (ava aura sa da kA Apasa meM samAnAntara honA ada kA va sa ko do barAbara hissoM meM bAMTanA (ava aura sa da kA Apasa meM samAnAntara honA / ada se caturbhuja kSetra aba sa da ke dharAtala kA do barA bara hissoM meM bAMTanA ava aura sa da kA Apasa meM samAnAntara honA va sa se caturmuja kSetra ava sa da ke dharAtala kA dI barAbara hissoM meM bAMTanA asa aura va da kA Apasa meM samAnAntara honA ava aura sa da kA Apasa meM barAbara honA (asa aura vada kA Apasa meM samAnAntara honA asa aura va da kA Apasa meM barAbara honA (asa aura va da kA Apasa meM samAnAntara honA va asa aura sa da va konoM kA Apasa meM barAbara honA (asa aura va da kA Apasa meM samAnAntara honA avada aura da sa a konoM kA Apasa meM barAbara honA For Private and Personal Use Only

Page #106
(asa ora ba da kA Apasa meM samAnAntara honA ") va sa kA ada ko do barAbara hissoM meM bAMTanA (asa aura ba da kA Apasa meM samAnAntara honA ada kA basa ko do barAvara hissoM meM bAMTanA nisa aura bada kA Apasa meM samAnAMtara honA (ada se caturbhuja kSetra avasada ke dharAtala kA do ba rAbara hissoM meM bAMTanA ala aura bada kA Apasa meM samAnAMtara honA asa se catuja kSetra avasada ke dharAtala kA do ba. rAvara hissoM meM bAMTanA aba aura sa da kA Apasa meM barAbara honA asa aura ba da kA Apasa meM barAbara honA ava aura sa da kA Apasa meM barAbara honA va asa aura sadava konoM kA Apasa meM barAbara honA ava aura sada kA Apasa meM barAbara honA aSada aura dasa a konoM kA Apasa meM barAbara honA aba aura sada kA Apasa meM barAbara honA (basa kA ada ko do barAbara hissoM meM bAMTanA (bhava aura sa da kA Apasa meM barAbara honA prada kA vasa ko do barAbara hissoM meM bAMTanA prava aura sa da kA Apasa meM barAbara honA ada se catuja kSetra avasAda ke dharAtala kA do ba For Private and Personal Use Only

Page #107
( 105 ) rAbara hissoM meM bAMTanA (ava aura sa da kA Apasa meM barAbara honA / vasa se caturbhuja kSetra avasada ke dharAtala kA do va rAbara hissoM meM bAMTanA (asa aura vada kA Apasa meM barAbara honA asa aura da sa a konoM kA Apasa meM barAbara honA (asa aura vada kA Apasa meM barAbara honA "abada aura dasa konoM kA Apasa meM barAbara honA (asa aura bada kA Apasa meM barAbara honA vasa kA ada ko do barAbara hissoM meM bAMTanA aisa aura vada kA Apasa meM barAbara honA prada kA vasa ko do barAbara hissoM meM bAMTanA (asa aura vada kA Apasa meM barAbara honA (ada se caturbhuja kSetra abasada ke dharAtala kA do barA vara hissoM meM vAMTanA (asa aura bada kA Apasa meM barAbara honA vasa se caturbhuja avasada ke dharAtala kA do barAbara hissoM meM bAMTanA viprasa aura sadava konoM kA Apasa meM barAbara honA avada aura dasa konoM kA Apasa meM barAbara honA va asa aura sadava konoM kA Apasa meM barAbara honA (vasa kA ada ko do barAbara hissoM meM bAMTanA visa aura sadava konoM kA Apasa meM barAbara honava (ada kA vasa ko do barAvara hissoM meM bAMTanA For Private and Personal Use Only

Page #108
41 viasa aura sadaba konoM kA Apasa meM barAbara honA ada se caturbhaja avasada ke dharAtala kA do barAbara hissoM meM bAMTanA (vasa aura sadava konoM kA Apasa meM barAbara honA basa se caturbhuja abasa da ke dharAtala kA do barAbara hissoM meM bAMTanA (prabada aura dasa a konoM kA Apasa meM barAbara honA basa kA ada ko do barAbara hissoM meM bAMTanA prabada aura dasa konoM kA barAbara honA ada kA basa ko dI barAbara hissoM meM bAMTanA (abada aura dasanna konoM kA barAbara honA prada se caturbhuja avasada ke dharAtala kA do barAbara hissoM meM bAMTanA abada aura dasa a konoM kA barAbara honA vasa se caturbhuja abasada ke dharAtala kA do barAbara hissoM meM bAMTanA basa kA ada ko do barAbara hissoM meM bAMTanA / ada kA basa ko do barAbara hissoM meM bAMTanA (basa kA ada ko do barAbara hissoM meM bAMTanA 41 ada se caturbhuja avasada ke dharAtala kA do barAbara hissoM meM bAMTanA vasa kA ada ko do barAbara hissoM meM bAMTanA visa se caturbhuja avasada ke dharAtala kA do barAbara hissoM meM bAMTanA 2 For Private and Personal Use Only

Page #109
Shri Mahavir Jain Aradhana Kendra 43 44. 45 ( 107 ) ada kA basa ko do barAbara hissoM meM bAMTanA ada se caturbhuja avasada kA do barAbara hissoM meM bAMTanA ada kA basa ko do barAbara hissoM meM bAMTanA basa se caturbhuja asada ke dharAtala kA do barAbara hissoM meM bAMTanA da ha ada se caturbhuja avasada ke dharAtala kA do barAbara hissoM meM bAMTanA basa se caturbhuja avasada ke dharAtala kA do barAbara hissoM meM bAMTanA yagara ina paiMtAlIsa tatavoM meM se koI tataba do khAsiyatoM kI caturbha kSetra meM pAI jAya to sAbita hosaktA hai ki bAkI yATha khAsiyateM bhI caturbhuja kSetrameM hoMgI isaliye paiMtAlIsa tataboM se paiMtAlIsa sAdhya vana saktI haiM aura cUMki paiMtAlIsa sAdhyoM meM se hara eka ke phala meM bATa bAteM hoMgI imaliye haraeka sAdhya se grATa sAdhya jinake phala meM eka eka bAta ho banegI bAnI 45 sAdhyoM se 360 sAdhya paidA hoMgI yaha bhI yAda rakhanA cAhiye ki jo sAdhya tata 3, 10, 16, 20, 21, 22, 23, 24, 25, 26, 27, 28.26. 30, 35, 38, 42 aura 43 se paidA hoMgI hara hAlata meM vaha sahI na hoMgI tAlivailma ko cAhiye ki ina saba sAdhyoM ko tayAra karake sAbita kare Ti0 4 cauMtIsavIM sAdhya kI madada se hama haraeka parimita sIdhI rekhA ko jitane barAbara hissoM meM cAheM isa taraha bAMTa sakte haiM farz2a karo ki aba dI huI parimita sIdhI rekhA hai rekhA asa khIMco jo rekhA ava ke sAtha koI kona vanAve da a pha ja a aura isa rekhA meM se koI hissA na da lelo aura 'ada ke barAbara hisse da ya aura ya sa lagAtAra banAte jAo yahA~ taka ki yaha mava hisse utane hogaye hoM jitane histoM meM hama dI huI rekhA ko vAMTanA cAhate haiM saba ko milAyo aura ya ja aura da pha samAnAMtara saba kI khIMco (sA0 31 ) to sIdhI rekhA aba utane hissoM baTa jAyagI jitane hissoM meM hama cAhate haiM aura samAnAMtara aba kI khIMco For Private and Personal Use Only ha sA0 31

Page #110
( 108 ) cU~ki daha aura yaka aura aba Apasa meM samAnAntara haiM ( mA0 30 ) isaliye kona saya ka aura yada ha aura dapha yapasa meM barAbara haiM (sA0 26) gaura cUMki saka, yaha aura dapha vyapasa meM samAnAntara haiM (sA0 30 ) isaliye kona yasaka, daya ha aura adapha saba vyApasa meM varAbara haiM ( mA0 26 ) yora yasa, daya aura a da barAbara banAyI gaI haiM isaliye ya ka, daha aura apha vyApama meM barAbara haiM (sA0 26) cukiya ka barAvara ke ra jaba ke (sA0 34 ) isaliye jaba. barAbara hai pha ja phaja aura apha vyApasa meM barAbara haiM da ha abhyAsa Q ( 120 ) agara kimI catubhuja ke do bhuja samAnAMtara hoM aura bAkI do bhuja barAvara hoM lekina samAnAMtara nahIM to unake grAmane sAmane ke hara do kona milakara barAbara do samakona ke hoMge ( 121 ) gragara samAnAMtara caturbhuja ke grAmane sAmane ke konoM ko milAne vAlI rekhA una konoM ke do do barAbara hisse kare to usa samAnAMtara caturbhuja ke cAroM bhuja vyApama meM barAbara hoMge (122) diye hue biMdu se eka aisI rekhA khIMco ki usakA vaha hissA jo dI huI samAnAntara rekhAyoM ke bIca meM ho eka do huI laMbAI kAho (133) sIdhI rekhA jo kisI samAnAntara caturbhuja ke do grAsanna konoM ke do do barAbara hisse karatI hai samakona banAtI huI eka dUmerI ko TatI hai ( 124 ) samAnAntara caturbhuja ke Amane sAmane ke konoM ko do do varAvara hissoM meM bAMTane vAlI sIdhI rekhA yA to samAnAntara hotI haiM yA eka dUsarI ko eka letI haiM (125) agara kisI samAnAntara caturbhuja ke karNa vyApasa meM barAbara hoM to usake saba kona bhI Apasa meM barAbara hoMge (126) romA biMdu daryAkRta karo ki agara usase do dI huI rekhAoM para laMba girAye jAyeM to vaha laMtra do dI huI sIdhI rekhAyoM ke barAbara aura yaha bhI batAyI ki aise kitane biMdu daryAkRta hosake haiM 127 ) eka aisI sIdhI rekhA khIMco jo eka sIdhI rekhA ke barAbara ho aura dUsarI saudhI rekhA kI samAnAntara ho aura usake sire do dI huI mIbI rekhAoM para hoM vasaH 128) samAnAntara caturbhuja a pa sada ka aba, aura sada bhujoM vibhu isa taraha banAye gaye haiM ki basa para usa tarapha jicaturbhuja hai aura na aura sa da para sAmane kI tarapha meM ghara samAna lo sAbita karo ki a ba aura sa da para ke tribhujoMko zIrSa konoM kI TUri bAM usa vibhujake zIrSase jo vasa para banAyA gayA hai alaga 2 barAbara hai For Private and Personal Use Only

Page #111
(202) Acharya Shri Kailassagarsuri Gyanmandir samAnAMtara caturbhuja ke kaNa asa bada ke (126 ) agara kisI samAnAntara caturbhuja kA kona bar3hatA jAya lekina una bhujoM kI lambAI jinase vaha kona banA hai na bar3he to ka jouma kona ke zIrSa meM hokara guz2aratA hai kama hotA jAyagA ( 130 ) a, ba ra sa aise tIna biMdu eka sIdhI rekhA meM haiM ki aba barAbara basa ke hai sAbita karo ki lamba jo a gaura sa se kisI modhI rekhA para jo a gaura sa ke darmiyAna hokara nahIM guz2aratI hai girAye jAyeM donoM milakara hUne hoMge usa lamba ke jo ba se usa rekhA para girAyA jAya ( 131 ) agara samAnAntara caturbhuja ke konoM se kisI sIdhI rekhA para jo samAnAntara caturbhuna ke bAhara ho lamba girAye nAveM to do lamba jo grAmane sAmane ke konoM se gireMge milakara barAbara hoMge una do lamboM ke jo dUsare do grAmane sAmane ke konoM se gireMge (133) gregara ghar3abhuja kSetra meM vyAmane sAmane ke bhuja barAbara aura samA nAntara hoveM to tInoM sIdhI rekhA jo grAmane mAmane ke konoM ko milAveMgI ekahI biMdu para kaTeMgI ra (133) a ba aura asa do dI huI sIdhI rekhA haiM aura unake darmiyAna ya diyA huyAbindu hai ya se aimI sIdhI rekhA ja ya ha khIMco ki usakA hissA ja ha jo dI huI rekhAoM ke darmiyAna ho biMdu ya para do barAbara Tukar3oM meM baTe (134) diye hue samAnAntara caturbhuja ke andara eka aisA viSamakoNa samacaturbhuja banAyo ki usake eka kona kA zIrSa samAnAntara caturbhuja kI eka bhujA ke diye hue bindu para ho ( 135 ) a ba sa da eka samAnAntara caturbhuja hai aura ya gaura pha bhuja ada aura basa ke bIcoMbIca ke bindu hai sAbita karo ki baya aura da pha karNa asa ko tIna barAbara hissoM meM bAMTeMgI ( 136 ) samAnAntara caturbhuja ko usake eka bhuja ke diye hue bindu se eka sIdhI rekhA khIMcakara do barAbara hissoM meM bAMTo savAlAta imatihAna sAdhya 27 se sAdhya 34 taka ( 1 ) rekhAgaNita kI usa paribhASA aura svayaM mihni ko jo mIdhI samAnAtara rekhAoM se sambandha rakhatI haiM bayAna karo aura yaha bhI batAyI ki unakA kAma pahale gradhyAya kI kauna kaunasI sAdhyoM meM par3A hai (2) vyAsanakona, bahi:kona, grantaH kona vyaura ekAMtara kona kI tAraufa karo aura unako kAgaja para khIMcakara batAyo (3) sIdhI samAnAMtara rekhAoM aura una rekhAoM kI jo una para giratI haiM' khAmiyateM bayAna karo For Private and Personal Use Only

Page #112
( 110 } (4) sAbita karo ki maudhI samAnAMtara rekhAoM ke bIca kI dUrI, hameza: barAbara rahatI hai (5) agara do sIdhI rekhA samAnAMtara na hoM to sAbita karo ki pha una ekAMtara konoM kA jo aura sIdhI rekhA ina sIdhI rekhAoM para gira kara paidA kareMgI hamezA vahI eka kona hogA 1 (6) graTThAIsavIM sAdhya kA dUsarA hissA bagera sattAIsavIM sAdhya kI madada ke sAbita karo 64 (7) do sIdhI rekhA jo eka dUsarI ko kATatI haiM ekjhIsIzrI rekhA kI samAnAMtara nahIM hotI haiM" ko svayaMsiddha mAnakara rekhAgaNita kI bArahavIM svayaMsiddhi ko untIsavIM mAdhya kA eka natIjA karAra do (8) sAbita karo ki tIsavIM sAdhya kI jo sUrata ukta dana ne sAbita kI hai vaha isa kadara khApha jAhira hai ki mutrta kI muhatAja nahIM hai (6) ivAttIsavIM sAdhya ke aMkana (banAvaTa) meM yaha ibArata " ada ke dUsarI ? cora" honA kyA jarUra hai (10) tribhuja kI kisI bhujA ke binA bar3hAe sAbita karo kitrizuna ke tInoM kona milakara barAbara do samakona ke hote haiM (11) kisI tribhujAkAra kAgaz2a ke konoM ko isa taraha mor3o ki jisase najura ko yaha mAlUma hojAve ki tribhuja ke tInoM kona milakara barAbara do lamakona ke hote haiM ( 12 ) anumAna kI tArIpha karo battImavIM sAdhya ke donoM yanumAnoM kA dAvA likho aura pahale kA koI aura subUta do battIsavIM sAdhya se aura kauna kaunase anumAna nikala sakta haiM (13) punaryukta kona kI tArIpha karo - battIsavIM mAdhya kA konasA anumAna una sUratoM meM bhI jisameM eka yA kaI punaryukta kona grantaH kona hoM khAbita hotA hai (14) samabhuja Rjubhuja kSetra se kyA murAda hai jaba kisI samabhuja Rjubhuja kSetra ke eka kona kI mikadAra mAlUma ho to bhujoM kI tAdAda kisa taraha daryAkRta karate haiM aura bagara bhujoM kI tAdAda mAlUma ho to usake eka kona kI mikadAra kisa taraha daryAphata kara saktI haiM (15) ula samabhuja Rjubhuja kSetra ke bhujoM kI kI tAdAda batAyo jisakA bahi:koNa grapane grAsanna grantaHkona se TUnA hai (16) 33 va sAdhya meM yaha zarta ki sIdhI rekhA eka eka tarapha ke siroM ko milAtI haiM kyoM jarUra hai (17) agara do sIdhI rekhA kisI do aura sIdhI samAnAMtara rekhAoM ke mukhtalipha tarapha ke siroM ko milAve to batAo ki milAne vAlI rekhA kaba barAbara hoMgI aura kaba nAbarAbara hoMgI For Private and Personal Use Only

Page #113
(18) 34 vI sAdhya ke viloma kA dAvA linoM aura sAbita karo (16) agara kisI nasAnAMtara catuja kA eka kona samakona ho to usake mava kone sabhakoga hote haiM yora usake kase mI cyApasa meM barAbara hote haiM aura agara va samAnAMtara caturbhaja varga vA bidhamakona samacatuja ho to usake kaNa ekA dUmare ko do barAbara hissoM meM bAMTate haiM sAdhya 35 prameyopapAya sA0 sUtva samAnAMtara catubhuja jo ekAhI AdhAra para aura ekahI samAnAMtara rekhAoM ke darmiyAna meM hote haiM Apasa meM barAbara hote haiM vi0 sUtra pharja karI ki samAnAMtara caturbhuja avasada aura yavazapha ekAhI AdhAra vaza para aura brada ekahI samAnAMtara rekhAoM va sa ora apha ke / darmiyAna meM to samAnAMtara cata jama basada aura yabasapha aa. pasa meM barAbara hoMge upa0 agara samAnAMtara catuma ja avasada aura daba sapha kI majAda aura dapha jo AdhAra basa ke sAmane haiM eka hI viMTuMda para khatama ho to jAhira hai ki hara samAnAMtara catu: guja tribhuja basa kA dUnA hogA isaliye samAnAMtara caturbhuja avasada bAbara hogA samA nAtara catubhuja dabasa pha ke sva. 6 __ lekina agara samAnAMtara caturbhuja avasada aura sakasaka kI maja ada aura papha jo sAdhAravAsa ke sAmane eka ho / hAtamA kI For Private and Personal Use Only

Page #114
( 112 ) to cUMki atra sada samAnAMtara caturbhuja hai isaliye =prada barAbara hai basa ke aura isI vajaha se yapha barAbara hai basa ke sA0 34 isaliye ma da barAbara hai ya pha ke aura da ya ubhayaniSTa hai isaliye kula yA bAkI a ya barAbara hai kula yA bAkI da pha ke ru0 2 yA 3 sva 0 1 aura aba barAbara hai dasa ke aba tribhuja ya aba aura phadasa meM cUMki phada barAbara hai ya a ke aura dasa barAbara hai aba ke sA0 34 aura bahiHkona phada se barAbara hai apane sAmane ke ya prava antaHkona ke For Private and Personal Use Only sA0 28 isaliye tribhuja phadasa barAbara hai tribhuja yava ke caturbhuja prasapha meM se tribhuja phadasa nikAla DAlA aura usI caturbhuja meM se tribhuja ya prava nikAla DAlA to jo kSetra bAkI raheMge Apasa meM barAbara hoMge isaliye samAnAMtara caturbhuja basada barAbara hai samAnAM - kha0 3 tara caturbhuja ya ba sa pha ke phala isaliye samAnAMtara caturbhuja jo ekahI AdhAra para zrAbopAMta - yahI sAbita karanA thA Ti 1 isa mAdhya kA dAvA isa taraha bhI bayAna homaktA hai ki samA nAMtara caturdana jo ekahI vyAdhAra para hote haiM, aura jinakI u caI eka hI hai barAbara hote hai

Page #115
( 113 ) paribhASA-kimI lamAnAMtara catubha ja kI ucAI usa laMba kI laMbAI hai jo aAdhAra para usake sAmane ke bhuja ke kisI bindu se girAyA jAya Ti0 2 isameM aura isake grAge kI kaI sAdhyoM meM barAbara hone se yaha matalaba hai ki dharAtaloM ke sima kSetraphala barAbara hote haiM Ti. 3 dharAtala yAnI jamIna kI paimAyaza kI buniyAda isI sAdhya para hai ki roz2amarraha kI kAraravAI meM vyAyata kA rakabA yAnI kSetraphala usakI laMbAI ko caur3AI ke sAtha yAnI grAdhAra kI uMcAI ke sAtha guNA karane se daryAfata kiyA jAtA hai aura caMki isa sAdhya se mAbita hai ki ji ma samAnAMtara caturbhuja kA vyAdhAra aura usakI uMcAI yAnI samAnAMtara rekhAoM ke bIca ke dharAtala kI caur3AI kisI yAyata kA prAdhAra aura usakI uMcAI hai to usa samAnAMtara catubhuja kA rakabA uma yAyata ke rakabe ke barAbara hai isaliye hara mamAnAMtara caturbhuja kA rakabA usake AdhAra ko laMbAI aura usakI uMcAI ko grApasa me guNA dene se dayAphata hosaktA hai Ti.8 isa sAdhya kA viloma " yAnI samAnAMtara caturbhuja jo ekahI grAdhAra para aura usake ekahItara pha meM haiM aura jinake kSetraphala grApasa meM' barAbara haiM ekahI samAnAMtara rekhAyoM ke darmiyAna hoMge" ukta dasa ne nahIM bhAbita kiyA hai tAlibadala ma vyApa isakI sAbita kareM sAdhya 36 prameyopapAdya sA sUtra samAnAntara caturbhaja jo barAbara AdhAroM para aura ekahI samAnAntara rekhAoM ke darmiyAna hote haiM barAbara hote haiM vi. sUtra farz2a karo ki samAnAntara caturbhuja * avasada aura ya phaja ha barAbara AdhAra / va sapha na basa aura phaja para aura ekahI samAnAntara rekhAoM aha aura vaja ke darmiyAna haiM to samAnAntara caturbhuja ava sa da barAbara hogA samAnAMtara caturbhuja ya pha jaha ke aM0 va ya aura sa ha milAo upa cuki basa barAbara hai phaja ke da ya For Private and Personal Use Only

Page #116
( 114 ) aura pha ja barAbara hai yaha ke sA0 34 sva0 1 isaliye va sa barAbara hai yaha ke aura yaha donoM Apasa meM samAnAntara bhI haiM aura ina rekhAoM ke eka eka tarafa ke siroM ko sIdhI rekhA va ya aura saha milAtI haiM lekina jo sIdhI rekhA kisI do barAbara aura samAnAntara sIdhI rekhAoM ke eka eka tarapha ke siroM ko milAtI hoM vaha Apasa meM barAbara aura samAnAntara hotI haiM sA0 33 isaliye va ya aura saha Apasa meM barAbara aura samAnAM - tara haiM isaliye ya va sah samAnAMtara caturbhuja hai cUMki samAnAMtara caturbhuja pra ba sa da aura ya ba sa ha eka hI AdhAra ba sa para aura ekahI samAnAMtara rekhAoM vasa aura aura praha ke darmiyAna haiM isaliye samAnAMtara caturbhuja pra va sada aura yavasaha Apasa meM barAbara hai sA0 35 isI taraha yaha sAbita ho saktA hai ki samAnAMtara caturbhuja ya pha ja ha barAbara hai samAnAMtara caturbhuja ya ba sa ha ke isaliye samAnAMtara caturbhuja pra va sa da barAbara hai samAnAMtara caturbhuja ya pha ja ha ka phala isaliye samAnAMtara caturbhuja jo barAbara AdhAroM para eka hI samAnAMtara grAdyopAMta - yahI sAbita karanA thA tarapha Ti 1 isa sAdhya kA viloma " barAbara namAnAMtara caturbhuja ko barAbara bAdhAroM para jo ekahI sIdhI rekhA meM haiM aura una AdhAroM kI ekahI haiM ekahI samAnAMtara rekhAcyoM ke darmiyAna hoMge " sAbita karo di0 2 isa mAdhya aura tIna sAdhA kA viloma bhI yAnI" barAbara samAnAMtara caturbhuja jo ekahI mamAnAMtara rekhAoMke darmiyAna haiM yA toka For Private and Personal Use Only

Page #117
( 115 ) ho aAdhAra para yA barAbara AdhAroM para hoMge " sahI hai isako sAbita karo abhyAsa (137) agara kisI samalaMba caturbhuja kI do samAnAntara bhuga milakara kimI samAnAntara catubha ja ke aAdhAra kI dUnI hoM aura vaha samalaMba catumaMja aura samAnAMnara catubha ja ekahI samAnAntara rekhAyoM ke damiyAna hoM to yaha samalaMba caturbhuja aura samAnAntara catubhuja aApasa meM barAbara hoMge ( 138) agara kimI tribhuja aba sa ke bhujoM aba aura asa para samAnAntara caturbhuja pha ba aja aura ha asa ka banAye gaye haiM aura unake bhuja phaja aura ka ha jo tribhuja abasa kI bhujoM ke samAnAntara haiM viMdu na para eka dUbharI ko kATatI haiM yA bahakara nyAyala meM milatI haiM to yaha donoM samAnAntara caturbhaja milakara barAbara hoge samAnAntara caturbhuja ba da yasa ke jo tibhuja ke vyAdhAra basa para banAyA gayA hai aura jisakI ajaba da barAbara hai aura samAnAntara hai na a ke sAdhya 37 prameyopapAdya sA0 sUtra jo tribhuja ekahI AdhAra para aura ekahI samAnAMtara rekhAoMke darmiyAna hoM vaha Apasa meM barAbara hoMge ni0 sUtra farz2a karo ki abasa aura $_a_da_ dabasa ekahI AdhAra basa para aura ekahI / samAnAMtara rekhAoM prada aura vasa ke darmiyAna haiM to tribhuja avasa barAbara hogA tribhuja dabasa ke aMada ko donoM tarafa ya aura pha taka bar3hAyA sa se sa ya samAnAMtara ava kI aura va se va pha samAnAMtara sada kI khoMco sA0 31 upa0 to aba sa ya aura dasa bapha samAnAMtara caturbhujahai aura cUMki yaha samAnAMtara caturbhuja ekahI AdhAra basa para aura ekahI samAnAMtara rekhAoM ada aura basa ke darmiyAna hai isaliye samAnAMtara caturbhuja abasaya barAbara hai samAnAM bama For Private and Personal Use Only

Page #118
( 116 ) tara catubhuja dasava pha ke sA0 35 aura tribhuja avasa samAnAMtara caturbhuja abasaya kA AdhA hai aura tribhuja dabasa samAnAMtara caturbhuja dasa bapha kA AdhA hai sA0 34 lekina barAbara cIz2oM ke Adhe Apasa meM barAbara hote haiM sA0 7 isaliye vibhuja aba sa barAbara hai tribhuja dasava ke phala isaliye jo tribhuja ekahI AdhAra para aura ekahI samAnAMtara rekhAoM ke AdyopAMta-yahI sAbita karanA thA abhyAsa ( 138 ) aba sa diyA huA tribhuja hai eka aimA tribhuja banAyo ki umakA kSetraphala diye hue tribhuja ke kSetraphala ke barAbara ho aura usakA grA. dhAra dI huI rekhA ada jo aba ke mukAma para par3atI hai ho (140) abasa diyA huyA tribhuja hai eka aisA tribhuja banAyo ki usakA zIgha ba sa ke diye hue biMdu para ho aura umakA aAdhAra usI rekhA meM ho jisameM aba hai aura usakA kSetraphala diye hue tribhuja ke kSetraphala ke barAbara ho (141) aba sa diyA huA tribhuja hai eka aisA tribhuja banAyo ki usakA kSetraphala daye hue tribhuja ke kSetraphala ke barAbara ho aura usakA vyAdhAra usI rekhA meM ho jisameM aba hai aura usakA zIrSa eka rekhA meM jo aba ko samAnAMtara hai ho (142) aba sa da diyA huA caturbhuja hai usakebhuja aba para eka romA catubhuja banAyo ki usakA kSetraphala die hue caturbhuja ke barAbara ho aura usakI eka bhuja sada ke eka diye hue biMdu meM hokara gujare aura aba kI samAnAMtara ho (143) aba sa da diyA huyA caturbhuja hai eka aisA tribhuja banAyo ki usakA AdhAra aba kI sIdha meM ho aura usakA zIrgha bhuja sada ke die hue binduga para ho aura usakA kSetraphala diye hue caturbhuja ke kSetraphala ke barAbara ho (144) kimI diye hue Rjubhuja kSetra ke barAbara eka tribhuja banAyo For Private and Personal Use Only

Page #119
( 117 ) sAdhya 38 prameyopapAya sA. satra jo tribhuja barAbara AdhAroM para ekahI samAnAntara rekhAoM ke darmiyAna hoM vaha Apasa meM barAbara hote haiM vi0 satra faz2a karo ki ava sa aura da ya pha tribhuja barAbara AdhAroM va sa aura yapha para aura ekahI samAnAntara rekhAoM prada aura vapha ke darmiyAna haiM to vibhaja ja aba sa barAbara hogA vibhaja da yapha ke aM. ada ko donoM tarafa ja aura ha binduoM taka bar3hAyA va se baja samAnAntara asa kI ora phame phaha samAnAntara daya kI khoMco sA. 31 upa. to javasa a ora da yaha meM se hara eka samAnAM tara catubha ja hai pa. a.. ____ aura caki yaha samAnAMtara caturbhaja barAvara AdhAroMbasa aura phaya para aura eka hI samAnAMtara rekhAoM ke darmiyAna meM isa liye yaha samAnAMtara caturbhaja Apasa meM barAbara haiM (mA026) caki kA aba samAnAMtara catubhuja jaba sabha ke do ba. rAbara hisme karatA hai sA. 31 isaliye tribhuja abasa samAnAMtara caturbhuja javasa akA AdhA hai ora ca ki kAda pha samAnAMtara catubha ja da ya phaha ko dI barAbara hisse karatA hai sA0 34 isaliye tribhuja dayapha samAnAMtara caturbhuja dayaphaha kA prAdhA hai lekina barAbara coloM ke Adhe Apasa meM barAbara hote haiM (sva01) For Private and Personal Use Only

Page #120
( 118 ) isaliye vibhuja abasa barAbara hai tribhuja dapaka ke phala isaliye jo tribhuja darAvara AdhAroM para ora ekahI samAnAMtara rekhAoM ke AdyopAMta-yahI sAvita kAramAthA Ti01 isa sAdhya kI yaha bharata ki barAbara khApAroM para jo bijoM ke zIra ekahI viMdu para hai bar3I kAra cyAmada hai Ti. 2 ina mAdhya meM vaha bAta mAnajI gaI ki donoMtribhujoM ke AdhAra ekahI sIdha meM haiM agara prama meM hiMdu ya biMdu sa para aura miMTu da viMdu apara ho to eka tribhuja kA kona TUmare simAja ke kona kA pUrA hogA isaliye yaha natIjA sAbita huyA ki agara eka libhakakI lIrAja lo ki kI do bhaloM ke calarA bAlaga karAkara aura unakI se bane huda koma eka dUsare ke pUraka hai to donoM simujoM ke kSepaNa pApaDa barAbara hai Ti. 3 laiMtIsavIM aura bar3atIsavIM sAdhyoM ko raja tara mokyAna karate haiN| " tribhuja jo ekahI vyAdhAra para yA pa rAma ghAmA pau . jinakI uMcAiyAM barAbara hotI hai vApasa meM barAbara hote hai " paribhASA -bhinI niraja ko ucAI. vaha laMca ko vyApAra para unna ke sAmane ke kona me zirAyA jAtA anumAna-sIdhI rekhA jo kimI limana ke AdhAra ko do mIca bidu se usake sAmane ke koga taka khAco gaI ho basa jise do yarAvara hira karatI hai| abhyAsa ( 145 ) samAnAMtara caturbhuja jina cAra libhajo meM vyapa karA! yo TatA hai una vibhu joM ko kSetraphala mApasa meM barAbara hote hai| (16) aba sa da samAnAMtara caturbhuja ke kagovada ke dimAga sIdhI rekhA gaba pyora ga sa khIMcI gaI haiM jo nAvita daro ki vima kA gaaba aura ga sa ba vyApala meM barAbara hoMge (147) abasa eka tribhuja hai aura hara yamujo aba yaura para ke bIcoM bIca vo biMdu haiM rekhA baya aura sada viMdupha para ravA dUsarIko kATatI hai sAvita karo ki tribhuna va sa barAvara hai caturbhaja a da ka ya ke ( 148) ya aura pha tribhuja a ba sa kI bha ja aba aura asa ko pA~coM du haiM yora zrada AdhAra basa para laMbaI mANita karo ki koma ya da pha bAmara kona ba a sa ke hai aura catuja a ya da pha libhaNa a yasa kA AdhA For Private and Personal Use Only

Page #121
14) sakachI AdhAra para usako ghAmane sAmane kI taraphoM meM barAbAra kSetraphaloM ke do trimaNa haiM mAvita karo ki vyAdhAra yoho yA bakaratrigajoM ke zavoM ke milAne vAlI rekhA ko do barAbara hissoM meM bAMTatI hai 150) tIna samAnAMtara catmaNa jo maba taraha Apasa meM barAbara haiM isa saraha para pAsa pAna rakale gaye hai ki unake AdhAra ekahI sIdhIrekhA se pahale samAnAMtara catuka vyAdhAra ko aura tIsare samAnAMtara pat ja ke vyApAra ke mAmale ke bhugoM ke eka eka tarapha ke mire milAye gaye hai to sAdita karo ki yaha gayA samAnAMtara caturmana jo miroM ke milAne meM banatA hai usakA vaha hiramA ko dUsare mAmAnAMtara cApa jo darmiyAja harayaka samAnAMtara calamala kA vyAdhAle 151 . kimI trigaja kI rAka muja meM koI viMdu diyA huvAsa ramahI rakhA khoco ki vaha jima ke do 21 dima kare ( 152 . kimI divasa samAna eka aisI sIdhI rekhA sIcI ki vaha catuga ke do bAra kara diyaa| (153) yAra mA limaja banAyA jApa ki usakI do bhuja kisI cajaNa tela ke kaNoM ko kAlA ajaga barAbara hoM aura una bhaoM ke bIca ka! ko ka ke hAmiyAna ko kisI yoga ke barAbara ho to usa vibhA kA phala usa 'cAna ke kSetramA yo barAbara ho sAdhya 3 prameyopapAdya sAsana jI barAvara vinaja eka hI thAdhAra para aura usa - kI ekahI saraphA meM hoM vaha eka hI samAnAntara rekhAoM ko darmi tthi ki sUtrasaz2a karo ki barAbara vibhuja bhAva sa aura dabasa 1 kahI yAdhAna vasara aura ko pItA meM prada to vibhunA basa aura T basa eka hI samAnAntara rakhAoM ke darmiyAna hoMge aM0-ada milAo to ada samAnAntara basa ko hogI agara ada samAnAMtara basa kI gii| For Private and Personal Use Only

Page #122
Shri Mahavir Jain Aradhana Kendra mumakina ho to bada ko yAvada ke bar3he aura yasa milAo ( 120 ) bindu se praya samAnAntara va sa kI ora hue hisse ko ya para kATatI huI khIMcau Q upa cuMki tribhuja pra basa aura yabasa ekahI AdhAra basa para aura ekahI samAnAntara rekhAoM va sa aura aya ke darmiyAna hai isaliye tribhuja prabasa barAbara hai tribhuja ya ba sa ke (sA0 3 037) lekina liyA satriguNa da ba sa ke barAbara hai (faz2a) isaliye vijaya se barAbara hai vibhuja ya ba sa ke (kha0 1) yAnI bar3A tribhuja barAbara hai choTe tribhuja ke aura yaha nAmu makina hai priya samAnAntara sa kI nahIM hai aura isI taraha sAbita hotA hai ki koI sIdhI rekhA si vAyada ke samAnAMtara va sa kI nahIM khiMca saktI isaliyenma da samAnAntara sakI hai phala isaliye jo barAbara tribhuja ekahI AdhAra para Ayo pAMta - yahI sAbita karanA thA Ti0 yaha sAtha tamava mAdhya kA viloma hai abhyAsa 154) rekhA aba aura sada eka dUsarI ko biMdu para kATatI hai aura tribhuja a ya sa barAbara hai tribhuja va ya da ke mAvi karo ki ada samAnAMtara va sa kI hai (155) rekhA jo kisI tribhuja kI do bhujoM ke bIcoM bIca ke biMduoM ko milAtI hai vaha vyAdhAra kI vyAdhI aura samAnAntara hogI gaura ada aura ( 156) vibhuja va sa ke AdhAra basa meM eka biMda For Private and Personal Use Only

Page #123
( 122 ) dasa aura yora basa ko biMdu ya. pha, ja gaura aba ha para vyAdhA 2 karo sAbita karo ki jora pha ha vyApasa meM barAbara aura samAnAMtara haiM ta ( 157) sIdhI rekhA jo kimI samAnAntara caturbhuja ke bhujoM ke bIcoM bIca ke biMduvyoM ko milAveM aisA samAnAntara caturbhuja banAveMgI ki vaha caturbhuja kA vyAdhA hogA ( 158) kisI tribhuja kI bhujoM ke bIcoM bIca ke biMdu diye hue haiM usa tribhuja ko banAo sAdhya 40 prameyopapAdya sA0 mUtra jo barAvara tribhuja barAbara AdhAroM para jo eka ho sodha meM hai aura una AdhAroM para ekahI tarapha meM haiM vaha eka hI samAnAMtara rekhAoM ke darmiyAna hote haiM vi0 sUtra pharz2a karo ki barAbara vibhuja prabasa aura da ya pha barAbara AdhAroMba sa ora yapha para jo ekahI da sodha vapha meM haiM aura una AdhAroM ke ekahI tarapha haiM to yaha vibhuja ekahI samAnAMtara rekhAoM ke darmiyAna hoMge 0da milAo to pada samAnAMtara va pha kI hogI a ja ya sa ya agara da samAnAMtara phakI nahI mumakina ho tocpraja samAnAMtara va phakI aura ya dayAvada ke bar3he hue hisse ko biMduja para kATatI huI khIMcI auraja phamilAo For Private and Personal Use Only upa . cUMki vibhujacchA va sa aura ja ya ka barAbara AdhAroM basa 0 aura yapha para aura ekahI samAnAMtara rekhAoM ja aura pha ke darmiyAna haiM isaliye vibhuja pra va sabarAbara hai tribhuja jayapha ke sA038

Page #124
( 122 ) lekina vibhujaavasa barAbara hai vibhujada yapha ke (phaja ) isaliye vibhujadayapha barAbara hai tribhuja ja ya pha ke sva0 1 yAnI bar3A vibhuja barAvara he choTe tribhuja ke aura yaha bAta nAmumakina hai isaliye aja samAnAMtara bapha kI nahIM hai isI taraha sAbita hosalA hai ki koI sIdhI rekhA sivAya ada ke bapha kI samAnAntara nahIM hai isaliye bhAva samAnAntara aphako hai phala isaliye jo barAbara limaja barAbara AdhAroM para Adyogata yahI sAbita karanA thA di. 1 vaha mAya aDatIsa sAdhya kA viloma hai vyora vyatireka yukti #sAbita ko gayo hai isako barga ra vyatireka yukti ke isa taraha sAbita mArate hai bada aura sa da milAyo ki binuja da basa barAbara le ninuja da yapha ke (211038) paura tribhuja da ya pha barAbara hai tribhuja avasa ke ( phaja ) imaliye nimna abasa barAbara hai bibhuja da basa ke ( sva0 1) aura isaliye ada samAnAntara hai bapha kI ( mA 66) Ti0 2 saiMtIsavIM aura aDatImI sAdhyoM kA dUsarA bilo " vyagA barAbara tribhuja ekahI samAnAMtara rekhAyoM ke emiyAna ho yA sAdara u. cAI rakhate hoM to vaha yA to ekahI aAdhAra para yA barAkara jagAdharoM para hoMge" sahI hai imako sAbita karo Ti0 3 agara parSa una saba barAbara tribhujoM ke jo ekahI bAdhAra para yA ekahI sIdha ke barAbara AdhAroM para ekahI tarapha ze milAye jAMgato eka sIdhI rekhA paidA hogI jo una grAdhAroM kI samAnAMtara hogI isa sIdhI rekhA ko una tribhujoM ke zIrSa kI nidhi kahate haiM rekhAgaNita meM vinTuyoM kI nidhi vaha mIdhI yA kuTila rekhA hai jisakA 'haraeka bhindu eka khAsa prAnta ko pUrA kare aura koI aurabindu ima zarIko pUrA karane vAlA nahIM masalan dapaNodara dharAtala meM vaha nidhi vinduko kI jisakA hara minTu eka diye hue bindu se dI huI dUrI para ho usa vRtta For Private and Personal Use Only

Page #125
( 123 ) kI paridha hai jisakA keMdra diyA humrA bindu hai aura jisakA vyAsArddha dI huI dUrI hai aura una bindubyoM kA jo kisI do diye hue vinduvyoM se barAbara dUrI para hai nidhi vaha sIdhI rekhA hai jo una do miMTuyoM ke mila me bAlI sIdhI rekhA ke do barAbara di karatI hai aura usake sAtha samakona banAtI hai abhyAsa (15) una biMduoM kI nidhi dayIkRta karo jo dI huI rekhA se do huI dUrI para hoM (160) una vidravyoM kI nidhi daphana karo kI kisI diye hue kona kI mukhoM se barAbara dUrI para hai ( 161 ) una biMdu kI nidhi dIpta karo jo kisI diye hue ha kI huI dUrI para haiM ( 162) una sevAoM ke bIcoMbIca ke diyoM kI nidhi daphata karo yo eka biMdu se eka hI huI rekhA taka khIMcI gayI hai sabAlAta imtihAna 35 sAdhya se 40 sAdhya taka (1) 35 vIM mAdhyameM laphja "barAvara" kisa mAmI meM istemAla huyA ( 2 ) 35vIM mAdhyameM eka samAnAntara caturbhuja ko sIdhI rekhAoM se kisa taraha vAde ki yAra hissoM ko taratIba deM to eka aura samAnAntara caturbhuja vanajAve (3) samAnAntara caturbhuja kI uMcAI kI tArIpha karo aura sAvita kaze kivI sAdhya meM donoM samAnAntara caturbhujoM kI uMcAI barAbara hai ( 8 ) 35 vIM sAdhya kyoM bahuta jarUrI khayAla kI gaI hai| 5) tribhuja kI uMcAI se kyA surAda hai sAbita karoki barAbara tribhuva kI kI eka vyAdhAra para yA barAvara AdhAroM para haiM ucAI bhI barAbara hotI hai bAre meM tribhuNa gIdhI rekhA ke ekahI yora yA donoM yora hoM (6) sAbita karoki agara vo tribhujoM meM se ekatribhuja ke do bhuja dUsare vibhu ke do bhuSoM ke vyApasa meM barAbara hoM aura bIca ke kona pUraka hoM to ye vyApana meM barAbara hoMge * (7) nidhi kI tArIpha karo aura usakI misAleM pahale adhyAya se do sAvya 11 mevopapadya sA0 sUtra agara samAnAMtara caturbhuja aura AdhAra para aura ekahI samAnAMtara rekhAoM ke samAnAMtara caturbhuja tribhuja se dUnA hogA For Private and Personal Use Only vibhuja ekahI darmiyAna hoM to

Page #126
( 124 ) vi. mUtra farz2a karo ki samAnAntara caturbhuja kA aba sa da aura tribhuja ya ba sa ekahI AdhAra basa para aura ekahI samAnAntara rekhAoM vasa aura aya ke darmiyAna haiM to samAnAntara catubhuja avasada tribhuja yavasa kA TUnA hogA aM0-asa milAo upa. cUMki vibhuja abasa aura yavasa ekahI AdhAra vasa para aura eka hI samAnAMtara rekhAoM va sa aura bhaya ke darmiyAna hai isaliye trimuja aba sa barAbara hai libhuja ya ba sa ke (sA037) lekina samAnAMtara caturbhuja avasada tribhuja abasa se TUnA hai kyoMki karNa asa usake do barAbara hisse karatA hai (sA037) isaliye samAnAMtara caturbhuja pravasada tribhuja yasa sedUnA he phala isaliye agara samAnAMtara caturbhuja aura tribhuja AdyopAMta yahI sAbita karanA thA anumAna-agara samAnAMtara caturbhuja aura libhuja bara bara vyAdhAroM para aura ekahI samAnAMtara rekhAoM ke darmiyAna hoM to sAbita hosaktA hai ki samAnAMtara catubhuja tribhuga se dUnA hogA Ti. 1 isa sAdhya ke viloma " agara mamAnAMtara caturbhuja aura tribhuja eka ho grAdhAra para yA ekahI sIdha ke barAbara vyAdhAroM para hoM aura ma. mAnAMtara catubhuja tribhuja se dUnA ho to mamAnAMtara caturbhuja aura trimuja ekahI samAnAMtara rekhAyoM ke darmiyAna hoMge" yaura " agara samAnAMtara caturbhuja aura tribhuja ekahI samAnAntara rekhAyoM ke darmiyAna hoM aura samAnAMtara caturbhaja tribhuja se dUnA ho to samAnAMtara catubhuja aura tribhuja thA to ekahI aAdhAra para yA varAbara grAdhAroM para hoMge' sahI haiM unako sAvita karo Ti. 2 yaha sAdhya tribhujoM kI paimAiza kI aura ima liye saba Rjubhuja For Private and Personal Use Only

Page #127
( 125 ) kSetroM kI paimAiza kI ( kyoMki hara Rjubhuja kSetra ke tribhuja vyAsAnI se jana sakte haiM ) buniyAda hai kyoMki samAnAkara caturbhuja kSetra kA rakabA daryA - phula karane ke liye samAnAntara caturbhuja ke grAdhAra ko usakI caur3AI yAnI uMcAI ke sAtha guNA karate haiM isaliye tribhuja kA ravA daryAphuta karane ke liye tribhuja ke vyAdhAra ko usakI uMcAI se guNA karo aura sunaphala kA bAdhA karato vahIM tribhuSa kA rakabA hogA abhyAsa ( 163) agara tribhuja aura samAnAntara caturbhuja eka hI samAnAntara rekhAoM ke darmiyAna hoM aura cibhuja kA bAdhAra samAnAntara caturbhuja ke vyApAra se dUnA ho to cimuca sasAnA suna ke barAbara hogA C (164) aba sada samAvAntara caturbhuja hai aura kisI bindu ga se ko samAnAntara caturbhuja ke bandara se samAnAntara caturbhuja ke konoM taka rekhA khIMcI gayI haiM sAbita karo ki vikuna avatra aura laga damilakara sabhAnAntara caturbhuja ke vyAdhe haiM ( 165) samAnAntara caturbhuja abasada ke kona da se eka rekhA basa se bindu pha para aura ava bar3he hue se bindu ja para jilatI huI khIMcI gayI hai sAbita karo ki tribhuNa aba thora hau saphaja vApasa 'barAbara haiM (166) asada caturbhu kI caba bhuja saha rAja kI samAnAntara hai aura ada ke bIcoMbIca ke bindu ya se ba aura sataka bIdhI rekhA khIMcI gayI haiM nAmita roki vibhuja yaba sa caturbhuja kA bAdhA hai ( 167 ) diye hue samAnAntara caturbhuja ke barAbara viSamakona sama caturbhuja janAyo sAdhya 42 bastUpamAdya sAsUva-diye hue tribhuja ke barAbara eka aisA samAnAntara catubheja banAcI ki usakA eka kona diye hue bharala kona ke barAbara ho viki divAla a pha ja aura diyA huA saralakona hai N bhuja ca ya sa abasa ke barAbara eka aisA samAnAntara caturbhuja banAnA hai ki ji. sakA eka kona kona ke barAbara ho aeN basa ke bindu para do barAbara hisa karo O aura ayamitAo da For Private and Personal Use Only

Page #128
( 126 ) yasa ke diMdu ya para kona sayapha barAbara da ke banAo(sA023) sa se saja samAnAntara yapha kI khauMco aura ase aphaja samAnAntara yasa kI aura yapha ko biMdu pha para aura saja ko biduja para kATatI huI khauMco sA0 31 ____ to sa ya phaja samAnAntara caturbhuja hai pa0 a upa cUMki tribhuja aba ya aura ayasa barAbara AdhAroM ya ba au' ra yasa para aura ekahI samAnAntara rekhAoM basa aura aja ke damiyAna hai isaliye tribhuja aba ya aura a ya sa barAbara AdhAroM ya ba aura ya sa para aura ekahI samAnAMtara rekhAoM basa aura anake darmiyAna haiM isa liye tribhuja aba ya aura a ya sa Apasa meM barAbara haiM sA038 isaliye tribhuja a basa tribhuja a ya sa kA dUnA hai lekina samAnAMtara caturbhuja sa ya phaja bhI tribhuja a ya sa kA TUnA hai kyoMki samAnAMtara caturbhuja aura vibhuja ekahI AdhAra yasa para aura ekahI samAnAMtara rekhAoM ya sa ora aja ke damiyAna hai sA0 41 isaliye samAnAntara caturbhuja sa ya ka ja tribhuja aba sa ke barAbara haiaura usa kA eka kona saya pha diye hara kona da ke barAbara hai isaliye diye hue tribhuja aba sa ke barAbara eka aisA samAnAMtara caturbhaja saya phaja banagayA ki usakA eka kona sayapha gharAvara hai diye hue konada ke aura aisehI samAnAMtara caturbhaja ke banAne kI jarUrata thI Ti. 1 jisa taraha diye hue tribhuja ke barAbara samAnAMtara catubha ja banAyA gayA hai jisakA eka kona diye hue kona ke barAbara hai usI taraha For Private and Personal Use Only

Page #129
( 127 ) ya diye hue samAnAMtara caturbhuja ke barAbara aisA tribhaja banA sakta haiM ki usakA eka kona diye hue kona ke barAbara ho Ti0 2 sAdhA 42 usa tarIke kI pahalI maMz2ila hai jisake jariye se hama isa bAta ko kAyama karate haiM ki hara Rjubhuja kSetra ke rakabe ke barAbara eka barga daryAphata ho saktA hai bAkI maMz2ileM pahale adhadhAya ko sAdhA 44 aura 45 aura dUsare adhayAya kI sAdhA 14 meM dI huI haiM sAdhya 43 prameyopapAdya sA sUtrapUraka una samAnAMtara caturbhujoM ke jo kisI samAnAMtara caturbhaja ke karNa ke girda vAka haiM Apasa meM barAbara hote hai vi0 satra pharja karo ki avasada samAnAMtara caturbhujahai ji sakA karNaprasa hai aura yaha aurapha ja vaha samAnAntara caturbhuja haiM jo usake girda hai yAnI jinameM hokara asa karNa guz2aratA hai aura ba ka aura kada aura samAnAMtara caturbha ja hai jo avasadakSetra ko pUrA karate haiM aura / isaliye jinakA nAma pUraka hai to pUrakabaka barAbara hogA pUraka kada ke upa. cUMki abasada samAnAMtara caturbhuja hai aura asa usaka kA hai isaliye tribhuja aba sabarAbara tribhuja adasa ke hai (sA034) phira cUMki ayakaha samAnAntara caturbhuja hai aura praka usakA kaNa hai isaliye vibhuja athaka barAbara hai tribhuja prahaka ke sA034 aura isI taraha sAbita ho saktA hai ki tribhuja kajasa barA vara hai tribhuja kAphasa ke isaliye do tribhujaprayaka auraka jasa barAbara haiM do tribhaja prahaka aurakaphasa ke sva. 2 lekina kula tribhuja aba sa barAbara hai kula tribhuja pradasa ke isaliye bAkI pUraka vaka barAbara hai bAkI pUraka kada ke (kha03) For Private and Personal Use Only

Page #130
( 128 ) phala isaliye pUraka una samAnAMtara caturbhujoM ke AdyopAMta yahI sAbita karanA thA (168) tetAlIsauM sAdhya meM sAmita karo ki namAnAMtara caturmana bapha barAbara hai lamAnAMtara catubhuja hasa ke (16) tAlIsavIM sAdhya meM agara yaha, bada aura japA rekhA khIMcI nAMya to yaha tInoM ko Apasa meM samAnAMtara hoge (170 ) samAnAntara caturbhuja avasada meM binyu do sIdhI rekhA samAnAMtara caturbhala kI sujoM kI saharamAcI sakI hai aura samAnAMtara cala jaga ba aura gaha yApana meM barAbara sahita cArI viviyuga kase asa seN| sAsana dI huI sIdhI rekhA para ekA diye Dara tila ko barAbara aisA samAnAMtara caturbhaja banAno ki usakA eka kona diye hara saralakona ke barAbara ho nisana pharja karo ki abadI duI sodhI rezA porasa diyA thA tribhuja aura diyA huA sarala kona hai sothI rekhAmadhapara likhujalako harAkara aisA samAnAMtara catubhuja banAnA hai ki usakA ekA kona barAbara ho koSa da ko maM- vibhuja sa ke barAbara aisA yaka samAnAMtara caturbhuja kyAja banA- paracama ma) yo ki usakA kona dabAja kona na ke barAbara hai| (042) ___aura usa samAnAMtara catuma ja isa taraha rahatI ki apa aura aba ekahI sIdhI rekhA meM hI ase yaha samAnAMtara va jayApaka kI khoMco sA. 31 phako jaha taka baDhAo aura milAyo cUki socI rekhA ha pha dA samAnAMtara rekhAoM aura ghaka para giratI hai For Private and Personal Use Only

Page #131
128 isaliya kona ahapha aura haphaya milakara barAbara dI samakona ke haiM sA0 20 isaliye kona vahApha aura haphA mila kara do samajhona se mAra lekina jo do sIdhI rakhA eka aura sIdhA rekhA ke tAratasako ekahI tara meM aise do kona banAtI haiM ki yaha milAkara do samakona se kAma na to vaha donoM sodhI rakhA baDhAI jAne se mila jAyaMgI sva0 12 isaliye hava aura phAya baDhAyI jAna se mila jAyagI faz2a karo ki vaha baDhAI jAne se vinTaka para milatI kase kala samAnAMtara yamayA kahakI khoco sA. 31 aura hama aura jaba ko itanA baTAo ki bahakala se la aura mabinduoM para mileM __ upatohala kapha samAnAMtara caturbhuja hai jisakA karNa haka hai aura samAnAMtara caturbhuja aja aura maya kA haka ke girda aura lava aura vaha unake pUraka haiM isaliye pUrakalaba barAbara hai pUraka vapha ke sA 43 lekina ba phatribhuja sa ke barAbara banAyA gayA hai isaliyela va tribhujasa ke barAbara hai ora cUMki kona javayakona abama ke barAbara hai sA0 15 aura kona javaya barAbara kona i ke banAyA gayA hai isaliye kAna aba ma barAbara hai kona da ke sva0 1 isaliye dIhaI sIdhIrekhA ava para diTehara vija sa se barAbara aisA samAnAMtara caturbhajala ba banagayA jisakA kona avasa diye hue kona da ke barAbara hai isI samAnAMtara caturbhuja ke banAne kI jarUrata thI For Private and Personal Use Only

Page #132
( 130 ) anumAna isa sAdhya se sAmA mAhira hai ki kisa taraha dI huI mIdhI rekhA para diye hue tribhuja ke barAbara yAyata banAyA jAtA hai Ti. isa sAdhya meM ulaTsa ne yaha nadI sApita kiyA hai ki aha aura kaja mileMgo yaha vAsa sAmAnI sAbita homa viliyamasanatAha va nema sAya kA dama saraha banAnA tajavIja kiyA hai ki la Ta barAbara aba ke basAppo aura mAha milAo lo va sAya asamAnAMtara bana kI hogI (171) dI huI rekhA para diye 'hue samAnAMtara tapa ke barAbara se. sA nimuna banAyo jisakA eka kona diye hara kona ke barAbara ho __sAdhya 15 vastra papAdha sA.saba-diyehae Rjubhuja kSetrake barAbara samAnAntara caturbhaja banAnI ki usakA eka kona diyehae sadalakona ko barAbara ho bi. sU0 faz2a karAki abasada diyA huA Rbhuja kSetra aura ya diyAhA saralakona hai asada ke barAbara eka aisA samAnAzAra caturbhaja banAmA hai kiusakA eka kona barAbara ho yo aM0-damilAyo tribhujaadaba ke barAbara sAmAH basa hama caturbhuja phaha banAo jisakA kona phakaha barAbara kona pake ho aura sIdhI rekhAjaha para bina jabadasake barAbara samAnAMtara catubhujaja sa banAo jisakA komajahama barAbara kona ya sA0 34 to phakamala kSetra samAnAMtara patA hogA aura vaha i. rAbara abasada ke hogA aura usakA eka kona barAbara kIma yake hogA upa. cUMki kona phakaha aura jahama meM se hara eka kona pa ke barAbara hai maa 52 For Private and Personal Use Only

Page #133
( 131 ) isaliye kona phakaha kona ahamake barAbara hai (sva01) dUna barAbaroM meM se hara eka meM kona kahaja milAzrI isaliye koma phakaha aura kahaja barAbara 3 kola sahaja aura jahama ke | lekina koca phakaha aura kahaja milakara barAbara do samakola ke haiM sA. 28 isaliye kona kahaja aura jahama bhI milakara barAbara hai do samakIna kI ___ cUki sIdhI khAjaha ke bindu ha para do sIdhI rekhA kaha aura mAha usako Amane sAmane kI tarapho se Akara aise do Asanna kona paidA karatI hai ki vaha milakara barAbara do sama kona ke haiM 50 isaliye kaha aura hama ekahI sIdhI rekhA meM haiM sA0 14 __aura cUki sodhI rekhAja do samAnAMtara rekhAoM kama aura ka ja para giratI hai dUsaliye kolamaDaja barAbara hai ekAMtara kona apha sA. 28 ina barAbaroM meM se haraeka konajala milaao| isaliye kona mahaja aura hajala barAbara hai kona jala aura hajaphake lekina kona mahaja aura haja lasilapAra barAbara do samakI sA. 28 isaliye phona jala aura haja kamI milakara barAbara do samakona ke haiM isaliye phaja aura jala ekahI sIdhI rekhA meM haiM sA014 aura cUMki ka pha samAnAMtara hai haja kI aura haja samAnAMtara hai mala kI isaliye kapha samAnAMtara hai mAlakI sA0 30 aura phala sAmAna ruma ko sAbita hotI hai / For Private and Personal Use Only

Page #134
( 132. ) isaliye phakalama samAnAMtara caturbhaja hai aura cUMki samAnAMtara caturbhuja hApha barAbara cibha ja pravada ke aura samAnAMtara catarbha ja jama barAbara tribhu ja ba dasa kebanAye gaye haiM isaliye kula samAnAMtara catabhuja ka pha la ma barAbara huA kula RNubha ja kSetra avasAda ke isaliye diye hue Rjubha ja kSetra aba sada ke barAbara samAnAMtara catubha ja kala banagayA jisakA konaphakama barAbara diye hue kona ca ke hai isI samAnAMtara catuja ke banAne ko jarUrata thI anumAna isa sAdhAse mAfa nAhira hai ki dIhuI sIdhI rekhA para diye hue Rjubha ja kSetra kI barAbara eka samAnAntara caturbhaja jisakA eka kona diye hara kona kI barAbara ho isa taraha banasaktAhai ki pahale dIhaI rekhA para cavAlImavI mAdhavakI madada se tribhuja aba da ke barAbara samAnAntara caturbhuja banAyo jisakA eka ko diye hue konake barAbara ho Ti. yaha sAdhA cAra bhujake aTa jubha ja kSetrako muratameM hala kI gaI hai jaba bha, z2a kSetra meM cAra se adhika bhuja hotImahe usa Rjubha ja tetrako um ke kimI konase sAmane ke koja takamIdhI rekhA khIMcakara nima joMmeM bAMTo aura phira rekhA la sa para tIsare tribha ja ke barAbara eka galA bhamAnAntara catuja banAyo jisakA nAka kona vinTu ma para kona ba ke barAbara ho aura isI taraha saba tribhujoM ke barAbara jinameM bAjubhuja kSetra bAMTAgayA hai samAnAntara caturbhaja banAyo abhyAsa (12 no yA jiyAdA sa ja kSetroM ke yoga ke barAbara TAkAyata banAyo (173) donabha jAtroM ko pAka jamakara kA kAma samAnAntara caturbhaja banAyo sAdhya 6 vastUpapAdya sA hI huI sIdhIrekhA para eka bagale banAzrI mija mAz2a karo ki aba do huI sIdhI rakhA hai isa 5 bgrmaanaa| For Private and Personal Use Only

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( . 133 ) aM0 a se sIdhI rekhA asa sIdhI rekhA aba ke sAtha samakona banAtI huI khIMco sA011 pra da barAbara ava ke banAo sa. da bindu se da ya samAnAntara ava kI aura biMdu va seva ya samAnAntara = da kI daya se biMdu ya para milatI huI khIMco sA0 39 upa0 cUMki aba yada samAnAntara caturbhuja huA isaliye isa kI bhuja aba barAbara hai bhuja daya ke aura bhuja sA0 34. prada barAbara hai suja ya ke lekina ada barAbara aba ke banAI gaI hai ca isaliye cAroM suja aba, vaya, yada aura dama Apasa khA 1 3 tsu barAbara haiM aura samAnAntara caturbhuja avayada samabAhu hai usa ke saba kona bhI samakona haiM cUMki ada do samAnAntara rekhAoM pratra aura giratI hai isaliye kona va ada aura adaya milakara barAbara do samakona ke haiM sA0 28 lekina kona bacprada samakona banAyA gayA hai isaliye kona pradaya bhI samakona hai va For Private and Personal Use Only ya daya para lekina samAnAntara caturbhuja ke Amane sAmane ke kona Apasa # barAbara hote haiM sA0 34 isaliye sAmane ke konoM avaya aura bayada meM se hara eka samakona hai isaliye samAnAntara catubhuja aba yada samakIna samAnAtara caturbhuja hai aura yaha sAbita ho cukA hai ki vaha samabAhu bhI hai isaliye ava yada vargakSetra hai aura vaha dI huI sIdhI rekhA ava para banA hai aura isI ke banAne kI jarUrata thI

Page #136
( 134 ) anumAna isa sAdhAke subUtase sApha jAhira hotA hai kigisa samAgA. stara caturbhuja kA eka kona samakona hai usake saba kome samakona haiM abhyAsa (174) agara kisI tribhuja a ba sa ko bhu jo asaaura basa para bagaletra anadaya aura basa pha ha banAye jAve to mArita karoki apha aura badanApama meM barAbara haiM (115 samAnAntara catuja jo kisI varga ke karNa ke girda hote haiM varga hote hai ( 176 ) agara bagakSetrako haraeka bhujA meM eka 2 bindu konase barAbara darI para taratIbavAra liyA jAya aura ina bindayoM ke damiyAna taratIkavAra rekhA khIMcI nAveM to kSetra jo ina rekhAyoMse banegA vargakSetrahogA aura isa naye bagakSetrakA kSetraphala amala bagakSetra ke kSetra phalase choTA hotA jAyagA jisa kadara ki binduoMkI dUrI konoM se bahatI jAyagI yahAM taka ki yaha dUrI bargakSetrako bhajakI yAdhI ho aura usa saratameM naye sAkSatra kA kSetra phala sabase choTA hogaa| (177) eka bargakSatra ko aise pAMca barAbara hissoM meM takasIma karo ki jinameM se cAra samakona tribha ja hoM aura eka barga ho sAdhya 17 prameyopapAdya sA. sUtra hara sama kona tribhuja meM samakona ke sAmane kIbha jA para jo varga banAyA jAtA hai vaha barAbara hotA hai una bargakSetroM ke jo samakona banAne vAlI bha jo para banAye jAte haiM vi0 suna faz2a karo ki avasa samakona tribha ja hai jisakA kona asamakIna hai to vargakSetra jo vasa para banAyA jAyagAal vaha barAbara hogA una vargotroM ke jo bha joN| bA aura asa para banAye jAyage da la ya aMka-vasa para barga kSetra padayasa aura baa aura asa para varga kSetra jaba aura hasa bamAo sA. 46 ase ala samAnAntara badayA yasa kI khoco sA.31 aura pada aura phasa milAno For Private and Personal Use Only

Page #137
( 135 ) upacUMki kona basa samakona hai ( pharjI) aura kona va praja tamakomahe pa030 do sIdhI rekhA asa aura aja sIdhI rekhA ava ke Amane sAmane ko tarphI se pAkara viMdu a para milatI hai aura usa rekhA ke sAtha usa binda para Asanna kona barAbarako samakIna ke banAtI haiM dUliye sa a aura aja eka hI sIdhI rekhA meM haiM sA014 isItaraha yaha sAbita hosatA hai ki va aaura eka hI sIdhI rekhA meM haiM caki kona davasa barAvarahai kona phavaa ke payoki hara eka samakona hai kha011 ina barAbaroM meM se hara eka meM koma pravasa milAo isaliye kula kona davapra barAbara hai kula konaphavasa ke(sva02) cUMki vibhuja avada aura phavasa kI do bhuja prava aura vadaalaga 2 barAbara haiM do bhujoM phAva aura basa ke aura kona aba da barAbarahai kona phavasa ke isaliye vibhuja pravada barAbara hai tribhuja phavata ke sA04 abasamAnAMtara caturbhuja va la vibhuja abada se TUnA hai kyoMki samAnAMtara caturbhuja aura vibhuja eka hI AdhAra bada para aura eka hI samAnAMtara rekhAoM vada aura jala ke darmiyAna sA041 aura vargo jaya tribhuja pha ba sa se dUnA hai kyoMki bagadeva aura tribhuja eka hI AdhAra kaba para aura eka hI samAnAMtara rekhAoM kaba aura jasa ke darbhiyAna haiN| sA049 lekina jo cIz2a barAbara cIz2oM kI dUnI hotI hai vaha Apasa meM barAbara hotI haiM isaliye samAnAMtara caturbhuja bala barAbara hai barga kSetra jaba ke isItaraha aya bhIra ba ka milAne se yaha sAbita hotAhai For Private and Personal Use Only

Page #138
( 136 ) ki samAnAMtara caturbhaja sa la barAbara hai vargakSetra ha sa ke isaliye kula vargakSetra va da ya sa barAbara hai do vargakSetroM jaba aura ha sa ke sva0 2 aura vargakSetra va da ya sa bhuja va sa para banAyA gayA hai aura varga kSetra java aura ha sa bhujoM a va aura asa para banAye gaye haiM phala isaliye hara samakona tribhuja meM samakona ke sAmane kI AdyopAMta yahI sAbita karanA thA Ti :- 1 yaha mAdhya ula sAdhya kI jo chattIsavIM mAdhya ke vyabhyAsa nambarI 137 meM dIgaI hai sirpha eka khAma sUrata hai Ti0 2 isa sAdhya kI ukta dasa ne sirpha eka sUrata banAyI hai lekina isakI vyATha sUrateM bana saktI haiN| 1. tInoM vargakSetra vaya, baja gaura saha tribhuja abasake bAhara kI tarafa banAye jAyeM 2 tInoM bargakSetra baya, baja aura saha tribhuja avasa ke bhItara kI tarapha banAye jAveM 333 baya bhItara kI tarapha banAyA jAya aura vargakSetra baja aura saha kSetra bAhara kI tarapha banAye jAyeM 4 bhItara kI tarapha banAye jAve aura 5 bargakSetra baja bhItara kI tarapha banAyA jAya aura vargala baya bAhara kI tarapha banAye jAyeM gaura 6 bala baja bAhara kI tarapha banAyA jAya aura varga baya bhItara kI tarapha banAye jAyeM 7 saha bargakSetra bhItara kI tarapha banAyA jAya aura varga kSetra bAhara kI tarapha jAM 8 bargakSetra saha bAhara kI tarapha calAyA jAya bhItara kI tarapha banAyeM jAMya ina sUratoM meM ukta dasa kA subuta lagatA hai sirpha itanA yAda rakhamA cAhiye ki una meM se bAz2a mUratoM meM tribhujoM abada aura baphasa yA tribhujI asaya aura kasaba kI barAbarI bajAya ima sAdhya kI cauthI sAdhya ke usa natIje kI madada se jo hamane ar3atIsavIM mAdhya ke Tippana do meM likhA hai mAvita hotI hai ba bAhara kI tarapha banAyA jAya aura varga kSetra vaja aura varga kSetra For Private and Personal Use Only gora saha vaya saha saha gaura baya baja aura baja

Page #139
Ti 3 ima mApA hara gAya kA IjAda karI yAlA hakIma phImAmorama mAra rekhAgaNitajJone isa mAthya ko jaraha 2 rI sAbita kiyA hai nIce li de do lihAvata umadA savava haiM aJcala suta phArja karo ki aba sada aura ayaphaja do bAchola haiM aura vaha isa taraha 2 baje gaye haiM ki una ke sAdhAra ekahI sIdhI rekhA meM haiM jaha aura ya ka meM se harapanA ko barAbara aba ke banAyo hasa, sa ka , kapha aura phaha ko milAkara lo yaha jAkira hotA hai ki limajahabalapavalamA parAvara vijayayAtI aura / sa tribhuja phajanha barAbara tribhuja kA dasa ke he isaliye bAta abasa dagIra aya kA ja pA ravAyA na mAha silakara vazavara hai kSetra sa ka phaha ke yaha bhI isa adhyAya kI battIsavIM mAdhya se nAvita ho sakA hai ki kSetra rAkaphaha bolA hai aura bhuja saha uga sakakona vibhuja kA mArga hai jisa kI luja basa aura baha diye hue vanakSetra kI sujoM ke barAbara haiM ina mudrA meM battomavIM sAdhA ke Age kI sAdhanoM meM se kisI lAthA kA kAma nahIM par3atA hai aura isa se yaha bhI jAlaga hotA hai ki hama do kAlevoM ko kisa taraha katareM ki unako mana TakaDe silakara tIsarA vargala bana jAya "dasarA subata jArI ki abasa ekaApako gatima jajima kA kona vAsasasakoga bhAva ko da taka ilanA bahAyA ki bada ya ka ha . barAbara ho sakI aura ada para bargata va gAyocaura / aja aura phala meM haraeka varAvara asa ko banAyo aura .. yaja aura jada aura ha sa mila lo aura baka namAnAntara apha kI aura sala samAnAntara ada kI boco mA 31 da dha na nAka pAra vibhujAna sanda jaya, vahaja aura phasaha saba taraha Apa meM barAbara hai ( mA imalija saba baja,jaha aura hasa pana meM parA hai aura imaliye cala basahaja samabAhu hai bAra gajakona cnujmii| (bhA013332) isaliye basahaja kala basa para kA hai cAvantaMki ava karAnara cAra vimala abasa,hajaba, va haja caura phasaha ke aura karane va sahaja yoga ke aura bhI barAbara hai do - yatoM ama bauramaya aura jenoM sapA kama aura badalamake jobhujoM va a aura asa gharI kara le lA ke kavara hai aura cAra vibhuja aba sa, da jaja, jaaura phaisa mila kAra barAbara do cAvato asA aura maya ke isaliye kSetra va sahaja jo basa para kA vargale navarA bAgaura asa parakebarA kSetroM meM ( 0 3) Ti0 4 hama hama lAyA kI maradarI aura J2 aura 3 varagaz2I vA dayAphata kara mI For Private and Personal Use Only

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( 138 ) aba barAbara eka gaja ke lo aura basa rekhA aba ke mAtha samakona banAtI huI aura usa ke barAbara khIMco jaura asa milAyo aura sAda barAbara eka gaja ke aura asa ke sAtha samakona banAtI huI khIMco aura adA milAyo aura daya barAbara eka gaja ke aura ada ke mAtha rAmakoga banAtI huI khIMco aura a ya milAyo to saMtAlIsavIM mAdhya se sAbita hotA hai ki aba barAbara hai, rAja ke aura asa barAbara hai 2 gaja ke aura ada barAbara hai rAja ke aura aya barAvara hai ) 4 gaz2a ke / abhyAsa (108) 47 vI sAdhA meM mAbita karo ki ada aura sapha eka dUsare para laba hai (176) saiMtAlIsavIM sAdhadha meM agara jaha, pha da aura ka ya milAI jAyaM to sAbita karo ki tribhuja ja aha , phAsada aura ka sa ya meM se hara eka varAbara hai tribhuja ba asa ke (180) 47 vo sAdhA meM agara pha da yaura ka ya milAye jAya to sAbita karo ki pha da para kA varga barAvara hai aba para ke varga ke caugane aura asa para ke varga ke yoga ke gaura ka ya para vA varga barAbara hai a sa parake varga ke caugune aura aba para ko varga ke yoga ko aura phada aura kAyapara ke varga milakara basa bhara ke basa ke pAMcamAne ke barAbara hai (181) kinI do yA jiyAdA priya hue bama kSetroM kI barAbara eka varga kSetra banAyo 1282) eka aisA bAra kSetra banAyo jo diye hue vargoloM ke pharka ke cadAra ho (183) tija meM nakona banAne vAlI bhujoM para ke barga milakara usa kona kI mAmane vAlI aja para ke varga se bar3e hoto (184 ) libhaja meM adhika kona banAne vAlI bhabhoM para ke barga milakara choTe hoMge uma kona ke sAmane vAlI bha ja para bo varga se (185) agara tribhu na kI do sajoM para ke varga si.lakara tIsarI bha ja para ke varga se bar3e hoM to tIsarI bhuja ke sArane kA kona ndhana kona hogA aura agara choTe hoM to adhika kona hogA (186) tribhuja aba sa ke kona sa se usa kI mAmane kI bhuja aba para laMbha sa da girAyA gayA hai sAbita karo ki una varga kSetroM kA pharka jo asa aura basa para banAye gaye haiM varAvara hogA uga vargakSetroM ko pharka ke For Private and Personal Use Only

Page #141
jAMya gAmita to , Acharya Shri Kailassagarsuri Gyanmandir ( 238 ) jo ada aura bada para banAye jajaye aura ve varga jo asa aura bada para banAye jAyeMge milakara barAbara hoMge una vargakSetroM ke jo basa aura pada para banAye jAMge (187) agara kisI na biMdu senada aura nava aura na pha lamba abasa tribha uja ke aba aura basa aura sA bhujoM para taba vAra khIMce karo ki ( ada - dava) + (vaya - ya sa ) + 2 2 ( sapha pha a ) (188) agara kisI vindu se kisI RtusujakSetra ke bhujoM para unake do do hisse karate hue khIMce jAMya aura hissA bhukoM ke ekahI tarapha se tartI bAra zumAra kiye jAMya to pahale aura sare para ke vargoM kA yoga barA hogA TUsare aura ca * varga ra hissoM gaurava raha hissoM parake vargIya ka (180) kimI tribhuja kA cAha aura sujIta kI tara mAlUma hai uma triguNa ke zIrSakA nidhi (160) dasa i hai khAdaya pa ava aura asa ko daura java aura sada parake varga milakara sa (1:1) samavivAha putra ke ji hotA hai usa bala para varga ke caugune ke usa para khIMcA gayA hai ( 162 ) agara kisI vinduga se kisI yayA avasada ? koTI rakSa rekhA khIMcI jayaMtI aura gasa para ke varga milakara barAbara gava auaura ga da para ke vargoM ke ( 163 ) agara samakona tribhuja meM samakona banAne vAlI bhuja aisI hA ki eka kA varga dUsarI para ke varga se tigunA ho aura samakona se aisI do rekhAkhAMcI jAMya ki unameM se eka samakona ke sAmane vAlI supara laMba gho aura dUsarI ukha bhuja ke do barAbara hisse kare to nAbita karo ki yaha donoM deva sapakona ke tIna barAbara hisse kareMgI ( 163) a ba sa namakIna tribhuja hai jisakA kona a samakona hai aura konoM ba aura sa se bhujoM a sa aura a va ke bIcoM bIca ke biMduoM da aura ba taka rekhA sauMcoM gayI hai to sAbita karo ki ba da aura rAya parake vargoM kA caugunA barAbara hogA va sa para ke varga ke maMcane ke (165 ) agara ava sa da vargakSetra ke basa bhuja ke kisI baya hisse para romA vaya phaja varga banAyA jAya jisakA bhuja aba ke baDhe hue hisse para ho to sAbita karo ki kAya rekhA ha ya kA lamba jo ya se a ya para khIMcA jAya donoM vargoM ko aise hisse me vATeMge ki vaha hise isa taraha rakkhe jA "kate haiM ki saba milakara eka varga banAveM For Private and Personal Use Only

Page #142
(14. ) sAdhya 8abhayApapAdha RI sU.---agara tribhaja kI bhujoM meM se eka bhuja parakA varga bAkI do bhujoM para ke boM ke barAbara ho to kona jo una kSajoM se banatA hai samakona hogA vi0sa0 faz2a karo ki barga jo tribhuja abasa kI bhuja bala para banAyA jAya barAbara hai una vargoM ke jo majo aba aura asa para banAye jAMya to kona va anya samakona hogA biMdu ase adamaja asa ke sAtha samako n' banAtI huI khoMco sA. 11 ada barAbara aba ke banAo sA0 3 ora sada milAoM avA. 2 cUki ada barAbara hai aba ke isaliye ada parakA vaha barAbara hai| aba parake varga ke ina barAbarI meM se hara eka meM asaparakA baga milAyA isa liye Ada aura Asaparake varga milakara varAvara aba ora asaparake vargo ke lekina ada aura asaparake barga milakara barAbara, dasa parake varga ke kyoMki kona da anasamakona hai sA067 aura aba aura asa parake barga milakara barAbara hai basa parake vargaka isa liye dasa parakA barma barAbara basa parake bargake sva0 ? isaliye dasa barAbara hai barA ke cUki bhujada barAbara hai ajaba vo aurAsa donoM vibhujoM dannasa auraba asa meM ubhayaniSTa hai For Private and Personal Use Only

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( 242 ) isaliye do bhujada a aura usa alaga 2 barAbara haiM do bhujoM va aura sake aura AdhAra dasa varAbara AdhAra va sa ke sAbita ho cukA hai isaliye kona dasa barAbara hai kona va pra sa ke lekina kona dAsa samakona banAyA gayA hai isaliye kona va pra sa samakona hai phala-isaliye agara tribhuja kI bhujoM meMse eka bhuja para jo varga AdyopAMta yahI sAbita karanA yA - - Ti. 0 1 yaha mAdhya saiMtAlIsavIM mAdhya kA viloma hai ina sAdhya ke sAbita karane meM use hama ne ziyAlIsavIM sAdhya ke isa natIje ko ki barAbara rekhAyoM para ke varga vyApama meM barAbara hote haiM aura usake biloma ko mAna liyA hai sA08 Ti0 2 unI isa ne pahale vyadhyAya meM sirpha isI viloma ko anyayayukti se sAbita kiyA hai inako vyatirekyukti se isa taraha sA a vita karate haiM sa kAgara kona ba a sa samakona nahIM hai to aT bhuja aba va ke sAtha samakona banAtI huI khIMcI aura ada barAvara asa ke banAyo aura milAo For Private and Personal Use Only da va da cauMki ada barAbara a sa ke banAyI gaI hai isaliye ada aura aba para C12 ke ba milakara barAbara haiM asa aura a ba para ke vargoM ke lekina ada aura aba para ke varga milakara barAbara haiM ba da para ke varga ke (sA0 33 ) aura asa aura apara ke varga milakara barAbara haiM ba sa para ke varga ke (pharja) isaliye bada para kA varga barAbara hai ba sa para ke varga ke isaliye ba da barAvara hai basa vo isaliye ekahI grAdhAra a ba para aura usake ekahI tarapha aise do tribhuja adaba aura asava haiM ki unakI suna ada aura asa jina ke sire vyAdhAra ke eka sire a para haiM Apasa meM barAbara haiM aura suna bada aura basa jinake sire AdhAra ke sire ba para haiM vyApasa meM barAbara haiM lekina yaha nAmumakina hai ( mA0 7) isaliye a da bhuja a ba ke sAtha sa makona nahIM banAtI hai aura isaliye kona ba a sa bhamakona hai Ti 0 3 bagara kimI tribhuja kI bhuja aimI tIna sIdhorekhAoM se jAhira kI jAyaM jinakI lambAi bAra ka. eka, aura 5ka hoM aura ka kaisI

Page #144
( 142 ) hI choTo yA bar3I rAzi ho to kona jo una sIdhI rekhAyoM se lagA hai jinakI lambAiyAM ika aura 4ka haiM mamakona hogA kyoMki (ka)+(4ka)-ka+16ka-25ka--(5ka) grAma taura para cUki {(na+1)}:- {3 na2.1)} = {12+1) + (na' -1)} x 11(na' +1)-1(na...)} --na .. {3(12+1)}=na + { 1912-1)}' isaliye na aura (na2-1) lazakona tribhuja kI una bhujoM ko jAhira kareMge jinase namakona banatA hai aura na+1) una tribhuja ke karNa ko jAhira karegA-samakona tribhuja kI bhujoM ke dAMmata karane kA vaha kA yadA hakIma fIsAnorasa ne likhA hai agara koI saMkhyA UnI hai to kula bhuja pUrI saMkhyAoM se jAhira hoge pharja karo ki na-7 to (na2-- 1) --24 aura (na+1) =-25 imaliye bhuja 7, 24 aura 25 saMkhyAyoM se jAhira hoMge phira cUki {3(1+1)} =nara + {{(na-)} (na+1)2 (2 na)2+ (na2.1)2 isaliye 2 na gaura (na2-1) vaha bhuja haiM jinase samakona banatA hai aura (12 - 1) kArNa hai vaha kAyadA hakIla aphalAtUna kA diyA huA hai - gara hama japara ke kAma meM na ke badale ca rakakheM yaura ca yora ga zegoM ko pUrI saMsthA khayAla kareM to yaha hAsila hotA hai ki (2+1) (2) + (2-2) yAnI ( ca+ gare) =(zca x ga) + (ca2 -- za2 imaliye 2ca x ga aura (ca2 . ga) vaha bhuja haiM jinase samakona banatA hai aura (ca' + ga) karNa hai| Ti. 3 pahale adhyAya meM ukta dasa ne rekhAyoM konoM aura dharAtaloM ke banAne ke For Private and Personal Use Only

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( 143 ) tarIke aura tribhuja kI bhujoM aura konoM ke Apasa ke sambandha bayAna kiye hai aura tribhajoM aura sasAnAntara caturbhajoM kA mukAbilA isa taraha kiyA hai ki jisase unakA barAbara yA nAbarAbara honA mAlasa hotA hai rekhAgaNitajJoM ne isa adhyAya ke tIna hisse kiye haiM pahale hisse meM pahalI chabbIsa sAdhA haiM jinameM rekhA konoM aura nijoM kA banAnA dikhalAyA hai aura vimala kI khAmiyateM bayAna kI dara meM sattAIsavIM sAdhA se lekara cauMhaoNsvI sAdhA taka hai aura unameM samAnAMtara rekhAoM kI khAsiyatoM kA dhyAna ke tIsare hima meM jisameM paitAlavI sAdhA se lekara ar3atAlIsavIM sAdhA taka haiM khAsakara tribhujoM aura samAnAMtara caturbhajoM ke rakaboM kI parAmarI yA nAvarAvarI dikhalAne ke liye eka dUsare kA mukAbalA kiyAhai uko dasa para loga yaha aitarAz2a karate haiM ki usane mAdhyoMkI tIba majabhUna ke mutAbika nahIM dI hai isa aitarAz2aka dUra karane ke liye hamane apanI kitAbake gakhIrameM eka phaharista likhI hai jisase hara majamna kI kulasAvAstavavAra sApha 2 naz2ara par3atI hai savAlAta imtihAna 41 sAdhya se 48 sAdhA taka (1) sAbita karo ki pahale adhayAya kA 41 vI sAdhA Rbhuja kSetroM kI paimAiza kI jar3a hai (2) una saba sAdhanoM kA dAvA jikho ki jisake jariye se kisI Rjubhuja kSetra ke barAbara varga kSetra banAnA mumakina hai (3) sAgara 43 vIM sAdhAmeM pUraka varga kSetra hoto unakA kula samAnAntara caturbhuja se kyA saravaMdha hogA (4) kyA 45 vauM mAdhA kA subUta hara sUrata meM sahI hai (5) varga kSetra kI tArIfa jo kucha usameM phiz2ala thA jiyAdA ho nikAla kara kyAna karo aura usa tArIpha ke kamyUjiba kisI sIdhI rekhA para varSa hotra banAne kA tarIkA likho () "varga kSetra ke saba kona milakara cAra samakona ke barAbara hote haiM" kyA imakA viloma bhI sahI hai aura javAra nahIM to vajaha bayAna karo (7) 47 vI mAdhA meM yaha kyoM jarUrI hai ki eka bhuja hara varga kSetra kI jo tribhuja kI samakona banAne vAlI bhujoM para hai tribhuja ke dUsare suja kI ekahI sIdha meM ho (8)kyA tribhuja jisa ke bhuja 3, 4, 5 haiM samakona tribhuja hai (6) kyA eka vyAyata kSetra meM jisake bhujoM kI lambAI 160 aura 460 gaz2a hai eka sIdhI sar3aka 500 gaja lambo tayyAra karA sakate haiM -- isa sar3aka ko kAgaz2a para khIMcakara batAyo For Private and Personal Use Only

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( 144 ) (10) 47 vI mAdhA kI madada se 1 1 . 2 3 gaja kI lambAI kimataraha dAfata kara sakate hai vivecanA aura payA locanA kisI do yA jiyAdA cIjoM ke milAne aura unase eka nayI cIz2a paidA karane ko pathyA locanA kahate haiM masalana jarda aura nIlA raMga milA kara hama sajja raMga paidA karate haiM agara saja raMga meM se z2arda aura pIlA raMga judA 2 karadeM to usa adA karane ko vivecanA kahate haiM zAma mAnau vivacanA aura payA locanA ke vaha haiM jo Upara kyAna hue lekina khAsa sAno rekhAgaNita meM yaha haiM payA locanA se baha surAda hai ki hama una * niyamoM aura natIjoM se zurU kareM jo aba taka sAvita ho cuke haiM yAnI jinakA sahI aura sumakina yA galata aura nAmumakina honA mAlUma hai aura akhIra meM unase eka nayA natIjA nikAleM masalan prameyopapAya yA vastupapAya sAdhyoM kI madada se jinako hama sAbita kara cuke haiM yA jinakA banAnA jAnate hai eka nayI sAdhya prameyopapAdya sAvita kareM yA sAdhya varupa pAya vanAveM aura vivecanA se yaha surAda hai ki kimI nayI mAdhya ke sAkSita karane yA banAne ke liye hama isa bAtako pahale phaja karaleM ki vaha sAdhya sAbita ho gayI yA vanagayI ThAra phira silasilevAra dalIloM kI madada se imarja kI haI sAdhya se naye natIje nikAleM aura dekheM ki yaha natIje una natIjoM meM se kisI ke mutAbhika haiM yA nahIM jo aba taka nAvita ho cuke haiM aura isa taraha apanI phaz2a kI huI mAdhya kA nahI aura sumakina yA galata aura nAmumakina honA yA pAta kareM ulama ne kula mAdhya pAlocanA ke jariye se sAbita kI haiM yA banAyI hai lekina vija canA kA jisa nahIM kiyA hai jisakI madada se purAne jamAne ke rekhAgaNitajJAna bahutamI prameyomAya gaura vastarapAya sAdhya hAphata kI haiM caMki vivecanA kA tarIkA rekhAgaNita kI sAdhyoM kA mukta yA amala dAphale karane ke liye par3A suphIda aura kAragrAmada hai isaliye hama usake kAyade aura minAla nIce likhate haiM vivecanA se kisI prameyopapADhA sAdhya kA mubUta dA fata karane kA kAyadA (1) pharja karalo ki jo nAdhA tumha mAvita karanI hai usakA dAvA mahI ha (2) phira dekho ki usa dAve ke sahI phaja karalene se kyA 2 nanIne nikalate haiM (3) usake bAda dayA phala karo ki yaha natIje una natIjoM meM se kisI ke mutAbika haiM yA nahIM jinakA tuma mahI yA malata honA aba taka mAvita kara cuke ho (4) agara unameM se koI natI jA una natIje ke mutAbika hai jinako tuma For Private and Personal Use Only

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( 245 gulata mAvita kara cuke hoto kA dAvA bhI jisako tumane mahI pharz2a kiyA thA galata hai (5) agara yaha natIje tumhAre nAvita kiye hue natIjoM meM se kisI ke mutAbika nahIM haiM to una natIjoM se aura naye 2 gatIje nikAlate jAo jaba taka ki vaha naye natIje unake mutAbika hI jinakA ki tuma nahIM yA bhulata honA jAnate ho sAdhyaprameyopapAdya - agara samati kisIbiMdu da se laMba daya aura dapha muja ana kara barAbara vibhuja basa ke ke aura kasa para jAya to yaha no kisI kona se usa kosAmane kI bhuja para girAyA jAyagA vivecanA- phaje karato ki sAdhyakA dAvA jo tumhe sAtrita parA mahI hai yAgI laMba daya aura dapha milakara barAvara haiM taMba baja kejI kona avasa se bhuja asa para girAyA gayA hai| na sa da va dAve ke sahIphaz2a karalene se yaha natIjA nikalA ki jaba baja kA koI hisA jaha dapha ke barAbara hai to dUsarA zikhA vaha daya ke barAbara hai phira agara daha milAyA gayA to isa natIje se eka aura natIjA nikalA ki yadaba aura havada aise do vibhuja hai jinakI suna bada aura haba barAbara haiM - aura bhuJa yada donoM hameM upaviSTa hai aura kauna yadaba aura bada grAdhAra basa para ke barAbara konoM basa aura asada ke koTi hone ke nAma se vyApana meM varAvara haiM aura isaliye pahale pradhdhAya kI caudhI sAdhya se tribhuja barAbara haiM aura kona daba kona vayada ke barAbara hai aura isaliye mamakona hai yau mamakona saMjaya ke barAbara hai isaliye yaha IsavIM mAyAse daha gaura asa Apasa meM masAnAntara meM nA hama ima vyAkhira natIje se sAdhA ko paryAlojanA ke tarIke se isa taraha para nAhita karate haiM 1 pA For Private and Personal Use Only pha ya -2 paryAlocanA biMduda se daha samAnAntara asa kI khIMco caki dahaja mAnAntara catubhu jar3e isaliye dapha barAbara hai haja ke ( lAi 4) kina bahada untIva sAghAse namakIna sajaba ke barAbara hai isa liye samakona hai isaliye kona bahada samakIna dayaba ' ke barAbara hai aura kona hada aura yadava bhI vyApama meM barAbara haiM kyoMki unameM se hara eka mA vibhu ke AdhAra para ke konoM kA koTi hai.

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( 146 ) avaMki tribhuja habada aura yadana meM eka tribhuja ke kSe koja dahA aura badadusare tribhuja ke do kona bayada aura sadava ke bAlA karAra hai aura bhuja bada donoM meM ubhayaniTa hai inaliye mugabaha varAvara he bhuja daya ke lekina yaha sAbita hotA hai ki jabAbara hai kI isaliye daya aura dapha milakara barAbara hai vaja ke pahAvAzita karanA kA vivecanA sejisI batAegAvA mAyakA akala daryApta mArane kA kA (1) yAda rakakho ki AvAgAra zejA holA ki dohuI jamAnyA apanA vAI yora meyopapAya vA vara pAnA maadhy| ya auka kA hai pyora vaha pameyogyAvyathA vastUpapAlamA ya u dakSa kI zinI bhI pakAya yA rasapamAna sAdhya para maukA hotI hai . (2) jina jastApATA sAdhya ko pakAnA ho unako calogo karalo ki vaha dAvako muhAna jiMkAvI jIvAvI (3) phira isa khiMcI huI mAyA lAmA aura homa karako lApama ke malAko syAphala kAro aura da syo ki yaha dIphata vidhi samApI umI. dasa kI kisI balamapAla yA prameyopamA sAdhA ke savAtiyA nahIM amara kasa lA tuma na dartAkA kAraNa mokAmAnikI mAyA meM lAI manAnAnA rakhA jAnA ko virAra marata par3a to kAmI yo jora dasa ko ekIkA ko kisAna 2oM cora koka ke lona pAyoM se bAta meM rajata pasa ilAke kayA hai vaha ganI kA aura koSamA rahanI kA aura kogoM vagara: kyA ilAkI rakhate hai aura phira delI divArako dama kI kisI vasaghapAlA yA ameyopamAdA mAyA meM pAye jAte hai yA nahIM yA usase paidA hote haiM yA nahIM (5) jAgara isa kozizase mI tumhArA matalaya na nikale to yaha na samajho ki hamArI mahagata yekAyadA huI yAda rakho ki kAraNesA hotA hai ki isa kozizamA audhI mAstamAla vAyojAdA sAdhA syAphala hojAtI haiM sAdhyabastupayAdA- caturbhuja avasada ke varAna savA aisA tribhaja banAyo ki jima kI ekA bhuja zAma ho aura dUsarI basa ko dizA para ho vivecanA-aisA tribhuja abasa calo jinakI eka bhuja zAba ho aura TUmarI nuja basa ko dizA para 'hocaura pharja karalo ki usa libhuja kA skunA san maMja ke rakabe ko barAbara hai For Private and Personal Use Only

Page #149
aba isa khiMcohuI mAzya se yaura tribhuja avaza ko naturmA ko barAkA maja karane se yaha natIjA nikalA ki trinuja apha da barAbara hai tribhuja sapha ya ke aura ina dinoM ke bIca kA kada aura sa ka ya pahale adhayAya ko paMdrahI sAdhya se barAbara haiM lekina yaha batIjA biMdu va kA sukAma darvAphata karane kI lile kAkI nahIM hai isaliye asa milAyA asa ke li. tehI nA chummA ki agara liyuja aphasa do barAbara tribhu jo apha da aura samaya meM se kara ravA meM milA diyA jAya to tribhuja adasa barAhogA nija aya sake aura ki yaha barAbara libhuja ekahI vyAdhAra asagara gIra ula kI ekahI tarakArI bAliye agara da ya milAI jA nAmamA samIdogI sAmaliMka bidAusa jagaha bAlocanA ke tarIka se isa bAraha bnaa| pAlocana--kAla milAyo aura da da yajamAnA .. kaso kA turA hisse se vindu va 53 4. yA jilA gro-to lija aba canaja ra sada... bara saka sajAya aura bhI gujA bAhara kI dizA: 5.2, ki jima jAyasa aura ahasA yAho kara adara . bhara 4 pani nig: ayasa bAra hai ki adakSa ko ina joM meM se hara eka meM jina asA diyo sajima nija avaca barAbara hai caturbhuja 'avasAda ke - dusI / " / ; buli adhyAsa (166 ) tribhuja avana ke andara ekA hiMdu gate sAbita karo ki ma a. gaba aura gasa lilakAra jija kI puNoM ko yogase kAra ke (26.7 ) aura va zevakoM ke kendra meM aura aga aura ba ka unako manA bhAra sAmAI hai aura rekhA ra unako pariyoM se ra aura kha dubA ghara . zintatI mAphina ko kisAna aura basa mAlAkAra haiM For Private and Personal Use Only

Page #150
( 148 ) (148) samatribAhu tribhuja ke andara eka viMdu hai uma biMdu se jo laMba tribhuja ko bhujoM para girAye jAyaMge vaha saba milakara usa laMja kI barAbara hoMge jo tribhuja ke kisI kIna se usa kI sAmane kI bhuja para girAyA jAyagA (16) agara jaturbhaja avasada ko dharAvala ke kaNa asa se do barAbara hissa hote haiM to asa se karNa bada ko bhI do barAbara hisA hoMge (200) pahale vyavasAya kI pAMcavIM tAdhA meM vyAraM bhaja nIce kI tarapha bapAyI jAne ke bajAya poSake apara kI taraphA vAyI jAvaM lo pahale apAya kopaM drahavIM sAdhA kA subUta pahalI hI pAMca sAdhanoM se hAMsila ho saktA hai (201)rekhA daya kA sirA da mamadirA timuna kI suja aba para hai aura sirA ya bhuja asa ke bAda hara hisse para hai aura jibhuja kA aAdhAra usa rekhA ke do barAvara lisA karatA hai lAhita karo ki daja yora a ya milakara barA. vara haiM aba aura ala ke (202) jina samAnAntara caturbhujoka kase vApara hote haiM una meM niyamakoNa samara tuja saba se bar3A hotA hai (203) do varAvara rekhA asa aura bada samakona banAtI huI eka dUsarI ko kahA~ kATatI haiM sAbita karo ki caturbhuja aba sAda una rekhAyoM meM se hara eka para ke ko se aAdhA hogA (204) diye hue nija meM samA malAnAkAra catuja kamAyoni jisa ke ko eka dUsare ko diye hama jiMdAra joDinuja kI gandara kATe (205) tribhuja jisa kA rakabA aura do bhuja sAgara meM banAyo (206) tribhuja kA aAdhAra aura uma ke gujoM kA jor3a aura AdhAra para ke konoM kA antara mAlama hai to usa trina ko bnaayo| (207) tribhuja kA AdhAra aura ura kI do bhujoM kA phAka aura grAdhAra para ke konoM kA faka mAlUma hai usa tribhuja ko banAyo (5208) dI huI, paramiti rekhA ko adhAra banAkara ye kA siluja kamAyojima kI ajI kA pharka mAlama hai aura jinakI eka majaliye nara pira ho kara gujare (206) ena tribhuja kA AdhAra aura laphala aura usa resA kI kamAI jo aAdhAra ke bIcoM bIca ke diusabhI mAmI ke kona taka khIcA kAya sAlasahai una nimjaajnaayo| (2.10) aba aura asadI huI meM bayA haiM unameM se eka meM romA bindu ga dAphata karo ki agara ba ga ka dUsarI kA para girAveM to aga aura aka milakaradoI laMbAI kI barAbara hoM (11) nimaga aba aba aAsa se gAr3I hai aura rekhA ada For Private and Personal Use Only

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( 248 ) vo kona basa ke do barAbara hisse karatI hai basa se biMdu da para milatI hai khAbita karo ki bada bar3I hai sa da se (215) agara tribhuja kA eka kona dUsare se tigunA hai to vaha tribhuja do samAdivAhu tribhujoM meM baTa saktA hai (213) agara tribhuja kA eka kona dUsare se TUnA hai to usa tribhuja para eka aisA samadivo tribhuja z2iyAdA kara sakta hai ki yaha donoM tribhuja milakara eka samadvibAhu tribhuja banajAya (214) samadi vAhu tribhuja abasa kI bhuNa aba ke bIcoM bIca kA biMdu da hai aura suna aba grAdhAra basa ke nIce kI tarapha itanI bar3hAyI gayI hai ki baya barAbara hai ava ke sAbita karo ki saya dUnI hai sada se (215) usa biMdu kI nidhi yakRta karo jisakI eka diye hue bindu se dUrI uma kI TUmare diye hue biMdu se dUrI kI dUnI ho (216) rekhA aba ke bIcoMbIca kA biMdu sa hai asa aura sava ko karNa vanAkara samAnAntara caturbhuja a dasaya aura pha ba ja sa banAye gaye haiM aura daha samAnAntara sapha kI aura phaha samAnAntara sada kI aura jaka calAnAntara saya kI gaura ya ka samAnAntara saja kI khIMcI gayI haiM sAbita karo ki cora hasa saka ekahI sIdha meM haiM (217) vyAyatA basada ke grAmane sAmane ke kona a aura sa haiM biMdu yabhuja basa meM aura biMda pha bhuja sa da meM hai sAthi bAro ki lina a ya phase kSetraphala kA dUnA aura vaha bAyata jima kI vyAsanna bhuja bapa aura dapha ke barAvara hoM milakara barAvara hoMge grAyata basa da ke (218) ekahI grAdhAraba sa para do tribhuja abasa aura dabasa hai aura ti abasa kI bhuja ava bhuja asa ke barAbara joviMda sa aura para hokara guguratA hai uma kA kena bhuja saba para yA use ko hue aurata jo va aura da baDoM para gujaratA hai kA keMdra phabhuja badma para yA usa ke baDhe hue hisse para hai mAnita karo ki caturbhuja ayadapha ke do bhuja milakara usa kI bAkI do bhujoM ke barAbara haiM (218) do rekhA addha aura asa ke mukAma diye hue haiM aba meM aisA biMdu ga daryAkRta karo ki agara una bindu se a sa para laMba girAyA jAya to vaha laMba rekhA aga se bakadara hI huI laMbAI ke choTA ho ha (220) samAna ko vabhuja kSetra ke grAmane nAmane ke bhuja samAnAntara hote haiM aura usa kI koI do grAmanna bhuja milakara apanI samAnAntara bhujoM ke barAbara hotI hai For Private and Personal Use Only

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( 15. ) (1221) samako ja a ba sa ko karNa ba sa para barga ba da va la banAyA gayA hai usa vargake kona se lamba da ma tribhuja kI bhuja asa para girAyA gayA hai aura kona ya se laMba bha ja aba para girAyA gayA hai sAbita karI ki ama barAbara aba ke aura ana barAbara asa ko hai (222) tribhulabasa kA kona sasamakona hai aisI rekhA khIMco jo ekA dI huI rekhA ke samAnAntara ho aura jisake nire tribhuja kI bhujoM asa aura basa ho aura jinake bIcoMbIca kA bindu aba meM ho 1223 ) samavivAhu linuja abama kA kona ba aAdhAra asa para ke haraNakA kaunakara caugunA hai agara aja aba bindu da taka itanI batAyI jAya ki lahadAnI abakI ho gaura se davAI jAya to tribhuja asada ko kona jijAta kI koNA kI jAnakArI (228) sAmAna ra catubhujabAva sarahake asara kA vika hai usa vindu se ha kAja samAna para cava kI khIMcI gayI hai aura usakA girA yUTa 2 mAda para aura mirA ja bha ma basa para hai aura usI bindu se va kAka vasAyAtamAlIcI gayI hai aura usakA mirA va sujana para aura lina pAma jalada para hai mAlita kAza misajAnAdAra catuna jakAja aura yaha kA pAkA lina ja sakA dAdUnA he sonalija jisa makA bajA aura kasA jora dUsarI suTa kA esavAla hai blaayii| (226 minA ko kAga kI zaravara jara hilo bATomA pI viDu meM pahovAra gujaratI hai aura vaha miMTu libhuja kI bhujA se vazavara dUrI para hai (257) zilo libha ja ke do kahiH koSa aura nIcare kA bahAna ko do ze varAvara hA meM bAMTatI huI rekhA eka hI bindu meM hokara gujaratI (228) jija aba savA sa jo ja sa aura asake jIvAda pavitra T aura vaha caura bAda aura kaya ekA dUsarI ko biTupha para kATatI hai sAbita ho ki apha dUnohe pAda ko aura bapha TUgI pAya ko ( 228) tribha jabasa ke konoM a, ba ora se ada, va va yora sapha rekhA una konoM ke sAmane kI ma.joM ko bilu da, yajaaura jaghara dora barAbAhise meM bAMTatI haI khoMcI gayI sAbita karo ki tInA rekhA kisI eka hI biMdu meM hokara gujaregI aura vibhuja ajavAba jala aura saja aApasameM barAbara hoMge (230 ) tribhuja ke tInoM bhujoM ke bIcoMbIca kI binduoM se jo mAra For Private and Personal Use Only

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( 251 ) una a jI ke nAtha samakona banAtI huI khIMcI jAMyazI vaha saba ekAhI vindu para milegI aura vaha bindu tribha ja ke konoM se barAbara dUrI para hogA ( 231 ) hara vibha ja ka konoM se jo laMga unA sAmane ko jajoM para zirAye jAyage vaha sabakazI vindu hokara gujareMge (232 ) pahale adhyAya kI 47 va pAyAbhala aura vasA jora sapA eka ho vi para hokara gujaregI / 233 ) tija aba sa kI bha ja alara kina da yapha kI ajoM kI hanI hai yAnI bhuja aba,daya kI aura zuja saya pha kI aura bhuja sabhA bhaja phAda ko aura vijayAvasako ajoM ko vIcoMbIca kI vidhu mA para una ma jI ke sAtha samAna banAne vAlI rekhA vija para li. lilI hai jora li jAnha vapha kI ajoM kI bIcoMbIca ko vinoM para una sa jI kA sAtha manakona banAne vAlI rekhA biMdu ha para milatI haiM sAbita karo ki jamadanI ha da kI aura jo taMba jase tribha ja avasa kI bha ja aba para girAha dUnAhe usa laMba kA jo hase nibhuja da ya phA kI bha jada ya parahe (224)tribhuja avasa ke konoM se jo laMba una konoM ke sAmane kI gujA para jirAye jAyage vaha biTu ga para milate haiM aura jo rekhA bhajo cAka balA aura sa vI kIcoMbIca ke vinduko dAya aura phase una ma joM ke sAtha parAkona bagAlo naI khIcI jI kA biTa ca para miltii| sAbita rozimA ko ko banda ko aura yamadUnI kAma ko aura ga dUnI hai dana kI ( 235 ) kimI nimaja ke logoM se jo laMva unake sAmane se bhujoM para girAye gaye haiM vaha bindu ga para milate haiM aura jo rekhA usa konoM kI lAmane ke bhajoM ke bIcoMbIca ke vindujoM taka khIMcI gayI hai maha bindu ja para milatI hai aura jo rekhA una bhujoM ke bIcoMbIca ke viyoM para unake sAtha masakona banAtI huI khIMcI gayI haiM vaha binduka para milatI haiM sAbita karo ki viTu ga,ja kaura ka rakahI sIdhI rekhA meM hai (236 ) hara libha ja meM uga rekhAoM kA yoga jo tribhuja kI sujoM ke vIcoMbIca ke binduoM se unake mAmane ke kogoM taka khauca jAMyarga vibhaja kI bha joM ke yoga se choTA hogA aura usa yoga se bar3A hogA (237) eka tribha ja kI do bha ja aura vaha rekhA jo tIsare maja ke vIcoMbIca ke bindu se usake sAmane ke kona taka khIMcI gaI hai mAlama haiM usa tribhuja ko banAyo (28) tribha ja kA gAdhAra aura vaha do rekhA dI huI haiM jo For Private and Personal Use Only

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( 152 ) tribha ja ke do bhujoM ke bIcoMbIca ke binduoM se unake mArane ke konoM taka khIMcI gaI haiM usa tribha ja ko banAyo / (236) vaha rekhA jo kimI tribha ja ke konoM se unake mAmane ke bha - joM ke bIcoMbIca ke viMduoM taka khIMcI gayI haiM mAlamahaiM una trabhu ja ko banAyo (240 ) a va sa tribhuja ke a koma se a da lamba basa AdhAra para DA. lA gayA hai aura a ya rekhA va asa kona ko do varAvara hissA meM bAMTatI huI khacII hai sAvita karo ki da a ya kona tribhuja ke ba aura sa zogoM ko antara kA prAdhAhai (241 ) kA ladAnAntara catubha ja kI eka bha ja aura donoM karNa diye hue meM upa samAnAntara catuja ko banAyo (242 ) salakona trima ja aba sa ke samakoNa a ke eka rekhA do varAvara hirale karatI hai aura eka dUsarI rekhA bha ja basa ke piMTu da para do va raba hisse karatI hai aura usake mAdha samakona vanAtI hai yaha donoM rekhA viTa ya para milatI haiM sAbita karo ki da a aura da ya ca pamameM barAbara haiM ( 243) a ba aura a sa eka dUnarI ke sAtha samajhona banAtI hai da koI ghiddha aba meM yora ya koI bindu asa hai isako karNa banAkara grAdhA kI jisakA zIrgha ja hai banAyA gayAhai sAbita karo ki ja kI nidhi vaha saudho rekhA hai jo kona ba a sa ke do bara bara hisse karatI hai| ( 244 ) varga a ba sa da ka karNa asa para varga ke varAvara eka aimA vi. dhabhakona samacatubhuja a ya pha sa banAyA gayA hai jisakA nyana kona vindu aparahai agara apha milAyI jAya to kona ba asa ke tIna varAbara hi hine hojAMyage ( 245) samAnAntara caturbhajoM meM jinakI bha joM kA yoga eka hI hai varga kA rakavA sabase bar3A hogaa| ( 246) a ba sa tribha ja ke a ba aura ba sa aura sa a ma joM ke bIcoM : voca ke biTu toba bAra da , ya grAra pha haiM aura ha se da ja jA bapha kI samAnAntara khIMcI gaI hai yapha ke bahura hirama se ja biMdu para milatI hai nAvita karo ki da sa ja tribhuja kI bha ja una rekhAoM kI lIva bAra barAbara haiM aba sa tribhuja ke bha joM ko bIcoMbIca ke hiMduoM se una bhajoM ke sAmane ke konoM taka khoMcI jAyagI ( 247 ) diye hue varga meM aisA barga banAyo jisakA rakabA eka diye hue argaka rakabe ke barAbaraho aura batAyo ki diye haga rakI kI kyA kada honI cAhiye For Private and Personal Use Only

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sa ( 161 ) eka paimAnA dhana hai jisakI haraeka sauMmA sama dharAtala paimAnA dharAtala hai jese rekhAyoM ke liye eka phaTa lambA paimAnA mukarara kiyA jAya to eka varga phuTa dharAtala ke nApane ke liye aura eka dhana phaTa piMDa ke nApane ke liye sakarara hogA faz2a karo ki aba sa da eka Ayata kSetra hai jisakI bhuja aba pUre 2 cAra paimAne hai aura ada pUre 2 sAta paimAne hai isaliye agara aba ko cAra barAbara hissoM meM bAMTeM aura ada ko sAta barAbara hissoM meM bAMTeM aura aba ke bhAga binduoM se ada kI samAnAntara aura ada ke bhAga binduoM se a ba kI samAnAmtara rekhA khIMcI jAveM to sApha jAhira hai ki va jitane hisse usa grAyata kSetra ke ina rekhAyoM ke khIMcane se hoMge unameM se haraeka himmA eka barga paimAnA hai aura caMki hara grAyata kSetra kA kSetraphala jitane paimAne usameM hote haiM unakI tAdAda se daryAfata hotA hai isaliye aba sa da grAyata kSetrakA kSetraphala bhI unhIM bagoM kI tAdAda se jinameM vaha samAnAntara rekhAyoM ke khIMcane se baTagayA hai karAra pAvegA jaba hama dekhate haiM ki par3I huI rekhA jo ada ke samAnAntara haiM baha aAyata kSetrako cAra barAbara hissoM meM bAMTatI haiM aura khar3I rekhA jo aba ke samAnAntara haiM una barAbara hissoM meM se haraeka ke sAta barAbara hisse karatI haiM to kula choTe hissoM kI tAdAda sAta kA caugunA lene se yAnI mAta ko cAra gunA karane se mAlUma hojAyagI imaliye kisI yAyata kSetra ke barga paimAnoM kI tAdAda dayophata karane ke liye hameM una do aMkoM ko yApasa meMgaNA karanA cAhiye jo una paimAnoM kI tAdAda jo grAyata ko dopAsa kI bhujoM meM haiM jAhira karate haiM jaba dharAtala bargakSetra hai to usakI saba bhujA vyApasa meM barAbara haiM yAnI haraeka bhujA meM paimAne kI tAdAda ekahI hai isaliye usa bagakSetra meM varga paimAnoM kI tAdAda ryAphata karane ke liye usa aMka ko jo usakI ekabhuja ke paimAne tambAI kI tAdAda ko jAhira karatA hai usI graMka se guNa do aura yahI sababa hai ki graMkagaNita meM barga kA artha usa guNanaphala kA nAma hai jo kimI graMka ko usIse guNA karane se hAsila hotA hai lekina vidyArthI ko yAda rakhanA cAhiye ki rekhAgaNita meM varga kA zabda jisa artha meM bolA jAtA hai vaha artha aMkagaNita yA bIjagaNita meM nahIM liyA jAtA varanaharekhAgaNita meM barga use kahate haiM jo eka rekhA para banAyA jAya aura aMkagaNita va bIjagaNita meM varga usa guNanaphala kA nAma hai jo eka graMka ko usI se guNa dene se hAsila hotA hai agara va kisI vargakSetra kI kisI bhana ke paimAne kI saMkhyA ko jAhira kare to ba kA guNanaphala jaba ki usako usI aMka se guNA diyA jAtA hai yAnI ba x ba yA ba vargakSetra ke barga paimAnoM kI tAdAda ko jAhira karegA aura For Private and Personal Use Only

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( 162 ) isI taraha para agara ba aura sa kimI aAyata kI do pAma kI bhujoM ke paimAnoM kI tAdAda ko z2Ahira kareM to ba aura sa kA guNanaphala yAnI bax sa Ayata kSetra ke barga paimAnoM kI tAdAda ko jAhira karegA isaliye mAlUma hudhyA ki una tarIkoM ke vasaule se jo hamane Upara bayAna kiye haiM hara yAyata kSetra ke kSetraphala ke parimANako bayAna karasatI haiM aura usakI saba qhAsiyatoM para jina para rekhAgaNita kI rU se bahasa hotI hai bI. gaNita kI rU se vahasa karamato haiM lekina jaba baaura sa kI jagaha para koI khAsa mola yAnI mAna 2 yA 3 yA 4 ityAdi rakhanA cAhe to kAmI 2 aisA mAlUma hotA hai ki do parimANa jinako hama ba aura sa se jyAna karate haiM ekAnapavartA rAzi haiM aura caMki gesI hAlata meM koI mamApabartaka yA paimAnA go vaha kaisAhI choTA liyA jAya nahIM dAMpata ho. mAtA jiyo vasole se harA usa prAyata kI mujoM kI lambAI kA aMdAjA kara sakeM isaliye isa hAlata meM koI ThIka mAna va aura sa kI jagahoM meM nahIM kAma meM lAsakta haiM aura isaliye usa yAyata kA kSetraphala himAva kI rU se ThIka nahIM dayAphata ho sakatA hai ___ aba ki hamane yaha bAta jAhira karadI ki rekhA va dharAtala vara; aura graMka meM kyA sambandha hai aura kyA pharka hai isaliye hama isa kitAba meM dasare adhyAya kI una mAthyoM kA jinakA subUta vIjagaNita se ho sakA bIjagaNitIya sAdhana unake Age likheMge pahalI sAdhyakA bIjagaNitIya sAdhana faz2a karo ki basa rekhA kI lambAI a paimAne hai aura arekhA kI lambAI ba paimAne hai aura baTa,daya aura yasa rekhAyoM kI lambAI kramase ma.na aura kapaimAne haiM caMki kula apane saba hissoM ke barAbara hotA hai isaliye ama+na+ka agara ina barAbaroM meM se haraeka ko ba se guNadeM to aba== bara(ma+na+ka) isaliye aX babaX ma+vaxna+baxka isaliye una do aMkoM kA guNanaphala jinameM se eka kaI hismoM meM bAMTAgayA hai barAbara hai una guNanaphaloM ke yoga ke jo binA Tukar3e kiye aMka ko Takar3e kiye aMka ke hara hisse se guNa dene se hAsila hote haiM yAnI ( agara ina guNanaphaloM ke artha rekhAgaNita kI rU se khayAla kiye jAveM) varga paimAnoM kI tAdAda jo guNanaphala ax base bayAna hotI hai barAbara hai una barga paimAnoM kI tAdAda ke jo ba+ma,bax na aura baxka ke guNanaphaloM ke yoga se daryAta hotI hai For Private and Personal Use Only

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abhyAsa (1) agara do sIdhI rekhAoM meM se haraeka kaI 2 hisse meM bAMTI jAya to dharAtala do sIdhI rekhAoM kA barAbara hogA una saba dharAtaloM ke yoga ke jo eka rekhA ke saba hise jude 2 dUsarI rekhA ke saba hissoM ke sAtha banAte haiM sAdhya 2-prameyopapAdya sA.sa.-agara koI sIdhI rekhA do hissoM meM bAMTI jAya to dharAtala jo kula rekhA aura usake hara hisse se banate haiM milakara barAbara hoMge kula rekhA parake bargake vi.sa. karo ki sIdhI rekhA a ba a sa ba kisI do hissoM meM sa bindupara bAMTI gayI hai to aba aura ba sa kA dharAtala aura aba aura asakA phaya dharAtala milakara barAbara hoMge aba parake bargake aM.-ava para adaya va baga kSetra banAo (1 sA046 ) __ aura sa bindu se sapha rekhA ada yA baya kI samAnAntara khauM co (1 sA031) upa aba a ya kSetra barAbara hai apha aura saya kSetroM ke yogake lekina aya kSetra ava parakA bargahai auraapha dharAtala hai baa aura asa kA kyoMki vaha da a aura asa kA dharAtalahai jinameM se dasa barAbara hai aba ke aura sa ya kSetra aba aura basa kA dharAtala hai kyoMki baya barAbara hai aba ke isaliye aba aura asa kA dharAtala aura ava aura basa kA dharAtala milakara barAbara haiM abaparake barga ke / phala.isaliye agara koI sIdhI rekhA AdyopAnta- yahI sAbita karanA thA For Private and Personal Use Only

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( 164 ) Ti. yaha sAdhya isa adhyAya kI pahalI sAdhya kI eka khAsa sUrata hai pahalI sAdhA meM agara donoM sIdhI rekhA aApasameM barAvara hoM aura unameM se eka do hissoM meM bAMTIgayI ho to pahalI sAdhA aura yaha sAdhA eka ho jAyagI bIjagaNitIya sAdhata pharja karo ki aba lambAI meM gra paimAne haiM aura asa aura basa meM kramase ma aura na paimAne haiM to ma+naina barAbara cIjoM meM se haraeka ko a se guNa diyA isaliye ya--ama+x na yAnI agara koI graMka do hissoM meM bAMTA jAya to kula graMka aura usake hara hisse kA guNanaphala milakara varAbara hote haiM kula aMka ke vargake abhyAsa (2) kisI sIdhI rekhA para kA barga usa rekhA ke grAdhe para ke barga kA caugunA hotA hai (3) agara abasa samakona tribhuja kA a kona samakona hai aura ada, ba sabhujapara laspa hai sAvita karo ki basa aura bada kA dharAtala aura basa aura sa da kA dharAtala milakara barAbara haiM ba da aura da sa para ke vargoM aura ada para ke dUne varga ke sAdhya3-prameyopapAdya sA.sU. agara koI sIdhI rekhA kisI do hissoM meM bAMTI jAyato dharAtala jo kula rekhA aura usake eka hisse se banatA hai karA bara hogA usa hisse parake barga aura usa dharAtala ke yoga ke jI rekhA ke donoM hissoM se banatA haivi.sU. faz2a karI ki aba sIdhI rekhA sa va kisI do hissoM meM sa bindupara bAMTI gayI hai to aba aura basa kA dharAtala barAbara hogA - basa para ke barga aura asa aura saba ke dharAtala ke yogake pra0-vasa para sadaya va vargakSetra vAyo ( 1 sA-46) For Private and Personal Use Only

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( 165 ) aura da ya ko phataka bar3hAkara prabindu se apharekhA sadayA baya kI samAnAntara khoMco (1sA031) u10--aba apa Ayata barAbara hai adaaura sa ya AyatoM ke yoga ke lekina ayakSetra avaaura basa kA dharAtala hai kyoMki vaha aba aura baya kA dharAtala hai jinameM se vaya barAbara hai vasa ke ___ aura adakSetra asa aura saba kA dharAtala hai kyoMki sada barAbara hai saba ke aura sa ya kSetra vasa parakA bargahai isaliye aba aura vasa kA dharAtala barAbara hai basa para ke barga aura asa aura basa ke dharAtala ke yoga ke phala-dUsaliye agara koI sIdhI rekhA AdyopAnta-yahI sAbita karanA thATi01- yaha sAdhya bhI isa adhyAya kI pahalI sAdhAkI eka khAsa sUrata hai pahalI sAdhA meM agara eka sIdhI rekhA do hissoM meM bAMTI gayI hai aura unameM se eka hissA dUmarau sIdhI rekhA ke barAbara hoto pahalI sAdhA aura yaha sAdhA eka hojAyaMgI. Ti. 2. agara dUsarI aura tIsarI sAdhAoM meM aba aura basa judI 2 rekhA qhayAla kI jAveM to asa una rekhAoM kA aMtara hogA aura isaliye donoM sAdhA eka hI dAve meM isa taraha bayAna hoMgI ki donoM rekhAyoM kA dharAtala aura unameM se eka rekhA parake barga kA pharka barAbara hogA usa dharAtala ke jo usa rekhA aura donoM rekhAoM ke antara se banatAI vIjagaNitIya sAdhana phUla karo ki aba laMbAI meM a paimAne hai aura basa laMbAI meM ma aura asalaMbAI meM na paimAne hai __ to ama+na ina barAbara jIz2oM ko ma se guNa diyA isaliye maxvyama+mana yAnI agara koI graMka do hissoM meM bAMTA jAya to kula aMka aura usake eka hisse kA guNanaphala barAbara hotA hai usa hisse ke varga aura donoM hitoM ke guNanaphala ke yoga ke For Private and Personal Use Only

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( 166 ) Acharya Shri Kailassagarsuri Gyanmandir abhyAsa (4) eka rekhA ko itanA baDhAo ki baDhI huI sameta kula rekhA baura baDhe hue hisse kI gharAtala barAbara ho usa rekhA para ke varga ke TUne ke sAdhya - prameyApapAdya aM sA 0 sU0 agara koI sIdhI rekhA kisI do hissoM meM bAMTI jAya to kula rekhA para kA barga barAbara hogA donoM hissoM para ke bargoM aura usa dharAtala ke dUne ke yoga ke jo una hissoM se banatA hai vi0sU0 pharz2a' karo ki aba sIdhI rekhA kisI do hissoM meM sabindupara bAMTI gayI hai to ava ha sa va ja parakA barga barAbara hogA asa aura vasa para keda pha ya bargoM aura a sa aura va sa ke dUne dharAtala ke yoga ke 0 a ba para pra da ya va vargakSetra banAo ( 1 sA0 46 ) - aura vada ko milAkara sa bindu se sa ja pha rekhA adayA va ya kI samAnAntara aura va da se ja bindupara aura da ya se pha bindupara milatI huI khIMco ( 1 sA031 ) aura ja se ha ja ka rekhA ava yA da ya kI samAnAntara aura ada se ha bindu para aura va ya se ka bindu para milatI huI khIMco ( 1 sA031 ) upa . aba cUMki sapha samAnAntara hai ada kI aura bada una para giratA hai isaliye va jasa bahi: konabarAbara hai apane sAmane ke vada a aMtaH kona ke ( 1 sA029 ) lekina bada a kona barAbara hai da va a kona ke ( 1 sA05 ) kyoMki va a aura ada bargakSetra kI bhujA hone ke sababa A For Private and Personal Use Only ka pasa meM barAbara haiM isaliye sajava kona barAbara hai sa vaja kona ke ( 1 kha 0 2 )

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( 167 ) isaliye sava bhuja barAbara hai sa ja bhujake (1 sA. 6) lekina vasa barAbara hai jaka ke aura sa ja barAbara haivaka (1sA0 34) isaliye va sa sa ja ja ka aura kaba saba Apasa meM barAbara haiM aura kSetra sajakava samabhuja kSetra hai aura aisehI saba kona usa ke samakona haiM kyoMki jaba saja rekhA baka rekhA kI samAnAntara hai aura basa una para giratI hai ka basa aura basa ja kona milakara do samakAna ke barAbara hai ( 1 sA. 28) lekina kavasa samakona hai (1 pa. 30) isaliye basa ja bhI samakona huA aura isaliye sa ja ka aura ja ka va kona bhI jo una ke Amane sAmane haiM samakona hue (1 sA0 34 ) isaliye sa ja baka samakona caturbhaja hai aura vaha samabhaja pahale sAbita hocukA hai isaliye vaha vasa para kA barga hai aura aisehI dalIla se hapha barga haja para kA hai aura haja barAbara asa ke hai (1 sA0 34) isaliye ha pha aura sa ka barga asa aura sava para hue aura cUMki aja pUraka barAbara hai ja ya pUraka ke (1 sA043) aura aja pUraka asa aura sava kA dharAtala hai kyoMki jasa barAbara hai saba ke isaliye ja ya barAbara hai asa aura saba ke dharAtala ke isaliye ajaaura ja ya milakara barAbara haiM asa aura saba ke dharAtala ke dUne ke aura hapha aura saka barga haiM prasa aura saba para ke isaliye cAroM kSetra hapha, saka, aja aura ja ya barAbara haiM asa aura saba parake bagoM aura asa aura saba ke hune dharAtala ke yoga ke For Private and Personal Use Only

Page #162
( 168 ) lekina hapha, sa ka aja aura jaya milakara kulakSetra prada ya ba ko jo aba para kA barga hai banAte haiM isaliye ava parakA barga barAbara huA asa aura sapa parake boM ora asa aura saba ke hune dharAtala ke phala-isaliye agara koI sIdhorekhA AdyopAnta-yahI sAvita karanA thA anumAna-isa sAdhya ke subU se sApha jAhira hai ki varga kSetra ke karNa ke girda ke samAnAntara caturbhuja bhI vargakSetra hote haiM Ti. 1-isa sAdhya ko isa taraha para bhI sAbita karate hai aba para ada ya ba varga banAo aura apha,daja aura yaha barAbara basa ke kATo aura sapha, phaja, - ja ha aura isa milAo caMki tribhuja asapha, da phaja, ya ja ha aura bahasa meM bhuja apha, jada, haya aura sa ba yApasa meM barAvara aura suja saa, phada, jaya aura haba yApasa meM barAbara haiM aura koga a, da, ya aura ba para samakona haiM isaliye cAroM tribhuja saba taraha grApasa meM barAbara haiM yAnI aAdhAra sapha, phaja,jaha aura isa Apasa meM barAbara aura kona asapha, da phaja, ya ja ha aura bahasa Apasa meM barAbara aura kona apha sa, daja pha, ya ha ja aura basaha kApasa meM barAbara haiM (1-sA04) isaliye cAroM tribhuja milakara tribhuja asa pha ke caugune hai yAnI asa aura sabake dharAtala ke dUne haiM (1-sA-41) kA Timpana dekho aba caMki kona asapha barAbara hai kona ba ha sa ke isaliyekonaasapha aura vasAha milakara barAbara hai kona bahasa aura basa ha ke lekina kona bahasa aura basa ha milakara eka samakona haiM (1-sA-32) isaliye kona asapha aura basa ha milakara eka samakona haiM aura kona pha sa ha eka sa makona hai (1-sA-13) isI taraha sAbita hosaktA hai ki kona saphaja, phajaha aura ja ha sa meM se haraeka samakona hai isaliye pha sajaha kSetra samakona catubhuja hai aura usakI suna sa fa, phaja, ma ha aura hasa Apapsa meM barAbara haiM isaliye sa pha jahavarga hai aura barAvara hai a sa aura apha parake vargoM ke yAnI asa aura saba parake vargoM ke ( 1-sA-47 ) isaliye For Private and Personal Use Only

Page #163
( 160 ) cAroM tribhuja asa pha, da phaja,yaja ha aura bahasa aura bagai sapha jaha jo milakara aba parakA varga adaya ba banAte haiM barAbara haiM asa aura sa ba parake bargo aura asa aura sa ba ke dUne dharAtala ke isaliye aba parakA varga barAbara hai asa aura sa ba parake boM aura asa aura saba ke dUne dharAtala ke Ti02 - isa mAdhya ke mAbita karane kI tIsarI rIti yaha hai caMki aba parakA gaM barAbara hai aba aura basa a sa ma ke dharAtala aura aba aura asa ke dharAtaloM ke yoga ke (30mA02) lekina aba yaura basa kA dharAtala barAbara hai basa parake varga aura asa aura saba ke dharAtala ke yoga ke aura aba aura asa kA dharAtala parAvara hai asa parake varga aura a sa aura sa ba ke dharAtala ke yoga ke amA03) imaliye aba parakA varga barAbara hai asa aura sa ba parake vargoM aura asa aura sa ba ke dUne dharAtala ke yoga ke Ti03 - agara hama asa aura sa ba ko judI 2 rekhA khayAla kareM to yaha sAdhya isa taraha bayAna hogI ki do rekhAyoM ke yoga para kA barA varAvara hogA una rekhAoM para ke gAM ke yoga aura una rekhA ke ghagatala ke dUne ke yAda rakhanA cAhiye ki rakhAgaNita meM do rekhAoM ke yoga se vaha eka rekhA murAda hai jo una do rekhAoM ko isa taraha milAne se bane ki vaha milakara eka mIdha meM hoM bIjagaNitIyasAdhana pharja karo ki aba lambAI meM apaimAne hai aura asa aura saba lambAI meM krama se ma aura na paimAne haiM to gra=ma+na ina varAbara cIjoM kA barga kiyA imaliye a=(ma+na)" asAra 23 isaliye a--ma+2ma x na+na yAnI agara koI graMka do hissoM meM kAMTA jAya to kula aMka kA barga barAbara hogA donoM himmoM ke bagoM aura unake dUne guNanaphala ke abhyAsa (5) agara eka sIdhI rekhA kaI himaloM meM bAMTI jAya to kula rekhA para kA barga barAbara hogA saba himamoM para ke bAMya una gharAtaloM ke dUne ke jo hara do himamoM ke joDoM se banatI hai For Private and Personal Use Only

Page #164
} (6) a ba sa vibhuSaNa kA a kona samakona hai aura adarekhA nasa bhuja para hai sAbita karo ki bada para dasakA dharAtala barAbara hogA da para varga ke (7) vyagara kisI aba sasamakona tribhuja ke basa kaNa meM se badabara - bara aba ke aura saya barAbara asake kATI jAya to dayApara kA barga barAbara hogA baya aura sadake dharAtala ke TUne ke (8) agara kisI a ba sa sarakona tribhuja ke asamakona se adamya basa para girAyA jAya to basa aura ada ke yoga para kA varga bar3A hogA baura sake yoga para ke ba se basudara a da para ke varga ke (6) basalakona tribhuja ke jisakA a kona samakona hai bhujoM ke yoga bharakA va dUnA hai una dharAtala kA jo ba sacara asake yoga byaura saura aba ke yoga se banatI hai sAdhA 5 prameyamavAdya zA0 sU0 .. agara koI sodhI rekhA do barAbara aura do nAbarA bara hissoM meM bAMTI jAya to nAbarAbara hissoM kA dharAtala aura usa rekhA parakA varga jA bhAga binduoM ke bIca meM hai milakara barAbara hoMge AdhI rekhA para ke varga ke * saba para saya phaba varga netra banAo 0 pra vi0sU0 - farz2a karo ki aba sIdhI rekhA sa biMdu para do barAbara hissoM meM aura da biMdu para do nAbarAbara hissoM meM vAMTI gayI hai to ada aura da ba kA dharAtala aura sa da para kA varga milakara barAbara hoMge saba para ke varga ke For Private and Personal Use Only sa u gha ha 17 ka la ma ya cha pha 1- sA046 aura baya milAo aura da se ha ha ja samAnAntara sayayA basakI ora baya se ha biMdu para aura yapha se ja biMdu para milatI huI khIMco 1-sA031 ha se kala ma samAnAntara saba yA yapha ko aura aura

Page #165
saya se na biMdu ghara aura bapha se ma biMdu para milatI huI khauMco 1-sA031 ___aura ase aka samAnAntara sa layA bama ko aura malakA ve ka biMdu para milatI huI khauMco 1-sA031 upa-aba cUMki saha pUraka barAvara hai ha pha pUraka ke 1-sA.43 ina donoM barAbaroM meM se haraeka meM dama milAyo isaliye kula sama barAbara hai kula dapha ke 9kha02 lekina cUMki asa barAbara hai saba ke phaja isaliye ala barAbara hai sa ma ke sA036 lekina sama barAbara da pha ke sAbita hocukA hai isaliye ala barAbara hai Tapha ke ina donoM barAbaroM meM se haraeka meM saha milAo isaliye kula aha barAbara hai dapha aura sa ha ke 1-202 lekina ahakSetra ada aura dava kA dharAtala hai kyoMki vaha barAbara hai daba aura da pha aura saha mijAne se samajamApaka banA hai isaliye sa ma ja mApaka barAbara hai ada ora daba ke dharAtala ke ina donoM barAbaroM meM se haraeka meM baja jo sada parakA varga hai (2 adhyA04 sA0 anumAna ) milAmo ___ isaliye samajamApaka aura laamiladAra varAbara haiM ada aura daba ke dharAtala aura sada para ko barga ke 1kha02 lekina samajamApaka aura laja milakara saba phaba kSetra ko josa va parakA barga hai banAte haiM For Private and Personal Use Only

Page #166
( 102 ) isaliye ada aura daba kA dharAtala aura sada parakA barga mi. lakara barAbara haiM saba parake barga ke phala-isaliye agara koI sIdhI rekhA AdyopAnta-yahI sAbita karanA thA isa sAdhya ko isa taraha bhI sAbita karate haiM a...... _sa. da_ba caMki sa da aura da ba kA dharAtala aura da ba para kA varga milakara barAbara haiM sa ba aura ba da ke dharAtala ke (2-mA 3) aura asa barAbara hai sa ba ke isaliye sa da aura da ba kA dharAtala aura da ba para kA varga milakara barAbara haiM asa aura ba da ke dharAtala ke ina donoM barAbaroM meM se hara rAka meM sa da aura da ba kA dharAtala milAyA isaliye sa da aura da ba ke dharAtala kA dUnA aura da ba para kA bargamilakara barAbara haiM asa aura da ba ke dharAtala aura sa da aura da ba ke dharAtala ke yoga ke lekina a sa aura da ba kA dharAtala aura sa da aura da ba kA dharAtala milakara barAbara haiM ada aura da ba ke dharAtala ke (2-sA0 1) isaliye sa da aura da ba ke dharAtala kA dUnA aura da ba para kA varga milakara barAbara haiM ada aura da ba ke dharAtala ke ina donoM barAbaroM meM se haraeka meM sa da para kA barga milAyA isaliye sa da aura da ba ke dharAtala kA dUnA aura sa da aura da ba para ke baga milakara barAbara haiM sa da para ke barga aura a da aura da ba ke dharAtala ke yoga ke lekina sa da aura da ba ke dharAtala kA dUnA aura sa da aura da ba para ke barga milakara barAbara haiM sa ba para ke barga ke (2-mA0 4 ) isaliye ada aura da ba kA dharAtala aura sa da para kA barga milakara barAbara haiM sa ba para ke vaga ke Ti. 2 isa sAdhya ke pahale sabUta ke dekhane se mAlUma hogA ki ada aura daba kA dharAtala barAbara hai sa sa ja mApaka ke lekina sa ma ja mApaka sa pha aura la ja kSetroM kA jo asa aura sa da para ke varga haiM aMtara hai agara asa aura sa da judo 2 rekhA khayAla kI jAveM to ada rekhA asa aura sa da donoM rekhAyoM kA yoga hai aura da ba una rekhAoM kA aMtara hai aura isaliye yaha anumAna isa mAdhya se sAvita hai ki kisI do rekhAoM ke yoga aura aMtara kA dharAtala barAbara hai una rekhAyoM para ke nagA ke aMtara ke Ti. 3 isa sAdhya se sAvita huA hai ki ada aura da ba kA dharAtala saura sa da para kA varga minna kara barAbara hai asa yA sa ba para ke barga ke yAnI ho nAlaganara himmada aura hana mA dharAnana hara sasta meM choTA hai asa For Private and Personal Use Only

Page #167
( 173 ) yA sa ba para ke varga se lekina a sa yA sa ba para kA barga asa aura sa ba kA dharAtala hai isaliye isase yaha phala mAbita huyA ki kisI sIdhI rekhA ke do hissoM kA dharAtala usa sUrata meM sabase bar3A hogA jaba bhAgAna bindu usa rekhA ke Adhe para hai Ti. 4 pAMcavIM sAdhya kA dAvA isa taraha bhI kyAna hosaktA hai ki do rekhAoM ke yoga ke Adhe para kA barga una rekhAoM ke dharAtala aura rekhAoM ke aMtara ke aAdhe para ke varga ke barAbara hai kyoMki agara ada aura da ba rekhA judI 2 khayAla kI jAve to asa una rekhAoM ke yoga kI grAdhI hai aura sa da unake aMtara kI vyAdhI hai aura a i una rekhAoM se vanA huchA dharAtala hai bIjagaNitIya sAdhana phaja karo ki aba lambAI 2 a paimAne hai aura usakA haraeka AdhA asa yA sa ba lambAI meM a paimAne hai aura sa da lambAI meM ma paimAne hai ___ to aba ke do nAbarAbara hissoM meM bar3A hissA a da lambAI meM (a+ma) paimAne hai aura choTA hissA da ba lakhAI meM (a-ma) paimAne hai aura ma hai(a+ma) aura (a-ma) ke aMtara kA AdhA caMki (a+ma) (a-ma)= a-ma ina donoM varAbaroM meM se haraeka meM ma milA diyA isaliye (a+ma) (a-ma)+ma=a yAnI agara koI aMka do varAbara aura do nAbarAbara hissoM meM bAMTA jAya to nAbarAbara hissoM kA guNanaphala aura una hissoM ke aMtara ke grAdhe kA varga milakara barAbara hai usa graMka ke grAdhe ke varga ke abhyAsa (10) samakona tribhuja kI una do bhujAoM meM se jo usake samakona ko banAtI hai kisI bhujA kA barga barAbara hotA hai usa dharAtala ke jo tribhuja kI dUsarI bhuja aura karNa ke yoga aura aMtara se banatA hai (11) aisA dharAtala banAyo jo do diye hue bagoM ke aMtara ke barAbara ho (12) kisI sIdhI rekhA ko aise do hissoM meM bAMTo ki una hissoM kA dharAtala narAbara ho diye hara varga ke For Private and Personal Use Only

Page #168
( 174 ) ka la sAdhya 6 prameyopapAdya sAsU- agara koI sIdhI rekhA do barAbara hissoM meM bAMTI jAya aura kisI bindu taka bar3hAyI jAya to usa kula sIdhI rekhA jo baDhAne se banI hai aura baDha hue hisse kA dharAtala aura usa sIdhI rekhA ke Adhe para ke barga jo do barAbara hissoM meM baTI hai milakara barAbara hoMge usa sIdhI rekhA parake barga ke jo AdhI rekhA aura bar3ha hara hisse se banI hai bi.sa. pharja karo ki aba sIdhI rekhA sa bindu para dI barAbara hissoM meM baTI hai aura da bindu taka bar3hAyI gayI ho to ada aura da ba kA dharAtala aura basa a sa ba da parakA barga milakara barAbara hoMge sa da para haZ ke barga ke aM. sada para sa ya pha da barga banAnI (1 sA046) ya ja pha aura ya da milAo ba bindu se ba ha ja rekhA sa ya yA da pha kI samAnAntara aura da ya se ha bindu para aura ya pha se ja biMdu para milatI huI khoMco aura ha se ka la ma rekhA ada yA ya pha kI samAnAntara aura Tapha se ma biMdu para aura sa ya se la biMdu para milatI huI khauMco aura abiMdu se a ka rekhA sa la yA da ma kI samAnAntara aura sa la ka se ka biMdu para milatI huI khauMcI 1-sA0 31 upa. cUMki asa barAbara hai sa ba ke isaliye ala samakona caturbhuja barAbara hai sa da samakona caturbhuja ke 1-sA0 36 lekina sa ha barAbara hai ha pha ke 1-sA0 43 isaliye ala barAbara hai ha pha ke 1-kha. 1 ina donoM barAbaroM meM se haraeka meM sa ma milAyA For Private and Personal Use Only

Page #169
( 175 ) isaliye kula ama barAbara hai sa ma ja mApaka ke 1-khA0 2 lekina ama kSetra ada aura da ba kA dharAtala hai kyoMki dama barAbara hai da ba ke isaliye sa ma ja mApaka barAbara hai ada aura daba ke dharAtala ke ina donoM barAbaroM meM se haraeka meM la ja jo saba para kA varga hai milAyA ___ isaliye ada aura da ba kA dharAtala aura sa ba para kA barga milakara barAbara haiM samaja mApaka aurala ja ke yoga ke 1-kha. 2 lekina sa ma ja mApaka aura la ja kSetra milakara sa ya pha da kSetra jo sa da para kA barga hai banAte haiM __ isaliye ada bhaura dava kA dharAtala aura saba para kA varga mila kara barAbara haiM sa da para ke varga ke phala isaliye agara koI sIdhI rekhA AdyopAnta-yahI sAbita karanA thA Ti. 1 chaThI sAdhya kA dUsarA subUta yaha hai na a sa ba da asa ko na taka bapAyo aura sa da ke bagabara sa na banAo caMki sa na barAbara hai sa da ke aura sa ba barAbara hai asa ke isaliye kula na ba barAbara hai kula ada ke aba cUMki na ba aura ba da kA dharAtala aura sa ba para kA valiva ra barAbara haiM sa da para ke varga ke (2- sA05) aura adabAvara na ba ke sAbita ho cukI hai isaliye ada aura da ba kA dharAtala aura sa ba para kA balikara barAbara haiM sa da para ke varga ke Ti. 2 chaThI sAdhya ke pahale subUta ke dekhane se mAlUma hogA ki aha aura da ba kA dharAtala barAbara hai sa ma ja sApaka ke lekina sa ma ja mAyaka sa pha aura la ja kSetroM kA jo sa da aura a sa para ke barga haiM yaMtara hai agara asa aura sa da 'judI 2 rekhA khayAla kI jAya to ada rekhA asa yaura sa da rekhAcyoM kA yoga hai yaura da va unakA aMtara hai aura isaliye yaha anumAna jo hama pAMcavIM sAdhya ke Tippana meM likha cuke haiM isa chaSTI For Private and Personal Use Only

Page #170
sAdhya se bhI sAbita hai ki kimI do rekhAoM ke yoga aura antara kA dharAtala barAbara hai una rekhAoM para ke vargoM ke aMtara ke Ti. 3 agara ada aura da ba judI 2 rekhA qhayAla kI jAveM to sa da una donoM rekhAoM ke yoga kI grAdhI hai aura sa ba unake aMtara kI AdhI hai aura ama unase vanA huyA gharAtala hai aura imaliye isa sAdhya kA vahI dAvA ho saktA hai jo pAMcavIM sAdhya kA hai (sA0 5 ke Tippana 4 meM dekho) yAnI do rekhAoM ke yoga ke grAdhe para kA barga barAbara hai unake dharAtala aura unake antara ke grAdhe para ke varga ke bIjagaNitIya sAdhana pharja karo ki aba lambAI meM 2 a paimAne hai aura usakA AdhA asa yA sa ba lavAI meM a paimAne hai aura ba da lambAI meM ma paimAne hai to a da lambAI meM (2 a+ma) paimAme hai cUMki (2 a+ma) x ma=24 ama+ma ina donoM barAbaroM meM se haraeka meM abhilAyA isaliye (2 a+ma) 4 ma+ a+24 a4 ma+ma lekina a+24 ama+ma-(a+ma) isaliye ( 2 a+ma) x ma+2 -- ( a+ma )2 yAnI agara koI aMka do barAvara hissoM meM bAMTA jAya aura koI dasarA aMka pahale kula graMka aura usake eka hisse meM milAyA jAya to TonI aMkoM ke yoga aura dUsare graMka kA guNanaphala aura pahale graMka ke Adhe kA barga milakara barAbara hai usa aMka ke varga ke jo pahale graMka ke Adhe aura dUsare aMka ke yoga se banatA hai abhyAsa (13) kisI sIdhI rekhA ko itanA bAAo ki kula vahI huI rekhA aura usake bAda hara hisse kA dharAtala barAbara ho diye hue barga ke (14) abasa tribhuja ke kisau akona se ada lamba basa bhuja para DA. lA gayA hai sAbita karo ki aba aura asa ke yoga aura grantara se jo dharAtala banatA hai vaha barAbara hogA usa dharAtala ke jo basa aura uma antara se jo badanaura sada ke bIca meM hai banatA hai (15) aba sa tribhuja ke kisI a kona se ada lamba basa bhuja para DAlA gayA hai sAvita karo ki aba aura asa kA antara choTA hai bada aura sada ke antara se For Private and Personal Use Only

Page #171
( 199 ) (16) aba sa mamadvibAhu tribhuja hai aura unake aba AdhAra para yara usake bAda hue hisse para da biMdu hai to sAbita karo ki a da aura daba kA dharAtala barAbara hai asa aura sa da para ke varSoM ke antara ko (17) aba, sa da aura ya pha aisI tIna mIdhI rekhA hai ki aba aura sa da kA yaMtara varAbara hai sada aura yapha ke aMtara ke sAbita karo ki aba aura yapha kA dharAtala aura aba aura sada ke yaMtara parakA barga milakara barAbara haiM sa da parake varga ke (18) abama vighamabAhu tribhuja he sa da lamba aba para hai aura ya vindu avabhuja ke bIcoMbIca kA biMdu hai mAbita karo ki asa aura savaghara ke bI kA vyantara barAbara hai usa dharAtala ke TUge ke jo java aura dabase banatA hai aura isa natIje se limaja kA chalaphala dIphala karane para kA banA likhI jaba ki usake donoM bhujoM kI lambAiyAM mAlUma hai sAdhya-prameyopapAya sA.sa . agara koi sIdhI dekhA kisI do hissoM meM bAMTI jAva to kula sIdhI rekhA aura usake eka hisse para kA barga milavAra barAbara hoMge kula sIdhI rekhA aura usa hisse ke dharAtala ke dUne aura dUsare hisse para ke barga ke bisa z2az2a karo ki aba sIdhI rekhA ki- sa ba sI do hissoM meM saviMdu para bAMTI gayo hai to aba aura vasa parake barga milakara barAbara hoMge aba aura basa ke TUne dharAtala aura asa parake barga ke a..ama para adAya babaga banAo aura bAda milAo sa biMdu se sapha rekhAada yA vaSa kI samAnAntara aura bada se ja para aura daya se phapara milatI huI khauMco 1-sA031 aura jase ha ja ka rekhA avayA daba kI samAnAntara aura ada se ha para milatI huI aura baya me kA biMdu para milatI huI khoco 1-sA 31 ___ 6 1-sA. For Private and Personal Use Only

Page #172
( 178 ) 1- sA0 43 upa. aba cUMki ma ja barAbara hai jaya ke ina donoM barAbaroM meM se hara eka meM la ka milAyA isaliye kula ake barAbara hai ku lagha ke isaliye aka aurasa ya milakara dUne eka ke 2- kha02 lekina zaka aura saya milakara a ka pha mApaka paurasa ka 1 - kha02 varga haiM isaliye kapha mApaka aura sa ka varga milakara TUne aka ke lekina ndhra va aura vasa ke dharAtala kA TUnA bhI aka se TUnA hai kyoMki va ka barAbara hai basa ke isaliye a ka pha sApaka aura laka varga milakara barAbara hai cada aura barA ke dharAtala ke dUne ke ina donoM barAbaroM meM se haraeka meM haTha jo yala parakA varga hai milAyA ikaliye caSaka sApaka cora savA varga aura hapha varga milavAra parAvara va aura basa ke gharAtala ke TUme aura asa parake barga ke ha lekina akafa mApaka aura sa ka varga aura varga ni lakara cadayava aura sa ka kSetroM ko jo aba aura basa para ke barga haiM banAte haiM isaliye ava aura basa parake varga milakara barAbara aba aura va sa ke dharAtala ke dUne aura n sa para ke varga ke pAla- isaliye agara koI sIdhI rekhA AdyopAnta yahI sAbita karanA thA Ti01- sAtavIM sAdhya kA dUsarA mubUta yaha hai asa para adaya sa varga banAo aura daa, aura sayako bar3hAkara ca pha da ja aura yaha yada CTET a ke banAo aura vapha, phaja, janha aura haba ko milAyo For Private and Personal Use Only VII | U sa kha

Page #173
Shri Mahavir Jain Aradhana Kendra hai ( 178 ) a, da, ya cUMki triva a pha pha da ja ja va ha aura ha sa ba meM bhujA pha, da ja, yaha aura saba Apasa meM barAbara haiM gaura bhuNa cava, da pha, yaja aura saha vyApama meM barAbara hai aura kona aura sa samakona haiM isaliye cAroM tribhuja va taraha vyApasa meM barAbara haiM yAnI vyAdhAra vapha, pha ja ja ha hU ba grApasa meM barAbara haiM aura kona a a phA, da pha ja ya ja ha aura sa ha va vyApasa meM barAbara haiM aura kona apha va da japha, yaha ja aura sa vaha vyApama meM barAbara hai ( 1 - sA0 4 ) isaliye cAroM tribhuja milakara tribhuja va sa ke caugune haiM yAnI a va aura basa ke barAla ke dUne haiM (1- sA0 41 ke Ti02 ko dekho ) caura meM barAbara haiM isa lAya ki kona ya ba pha barAbara hai kona da pha ja ke isaliye kona aura bapha aura phaba barAbara haiM kona da pha a pha ba ke yAnI barAvara haiM kula kona baja ke lekina koca va pha aura a pha ba milakara eka mamakona haiM ( 1 - sA0 32 ) isaliye kona ba pha ja samakona hai aura aura isI taraha sAbita ho saktA hai ki kona pha ja ha ja ha ba bapha meM se haraeka samakona haiM isaliye kSetra ba pha ja ha samakona caturbhudha hai aura usakI bhuja va pha, pha ja ja ha aura ha va vyApasa liye ba pha ja ha varga bapha parakA hai aura barAbara hai vargoM yAnI aba gaura parake vargoM ke (1- sA0 varga barAbara cAra tribhutra a va ka pha da ja ja ya ha hai aura ke dharAtala aura dasa ke yoga ke jo bahAvara ke dUne aura sa para ke varga ke isaliye a va aura basa para ke varga mila ke dharAtala ke chUne aura kara barAbara haiM a ba aura Ti. 2 sAtavIM sAdhya kA tIsarA subUta yaha hai aura basa kA dharAtala barAvara hai asa va sa zrava vala ba sa yasa parake varga ke sa saba ke ghara tala sa va aura aura parake varga ke ( 2- sA0 3 ) isaliye ava basa ke aura dharAtala kA TUnA barAbara hai a sa aura sa ba ke dharAtala ke TUne aura saba para ke varga ko dUne ke ina donoM barAbaroM meM se varayA meM asa para kA va milAyA isaliye a ba ra ba sa ke dharAtala kA dUnA aura ca sa para kA varga milakara barAbara haiM asa ke dharAtala ke dUne aura la va para aura saba ke varga ke TUne ke aura a sa para ke varga ke lekina ca sa aura aura asa para ke varga milakara barAbara hai yava cora sa va para ke varga ke (20) isaliye aba aura va sa para se saba ke dharAtala kA dUMgA milakara para bAvara nya ja www.kobatirth.org aura Acharya Shri Kailassagarsuri Gyanmandir va sa ke mAnasa ke dUne aura For Private and Personal Use Only va caura a pha para 07, lekina ba phajaha paura hasa ba

Page #174
( 180 Ti 3 agara hama aba aura basa ko 'judI 2 rekhA khayAla kareM aura isaliye asa ko unakA vyantara samajhe to isa sAdhya kA dAvA isa taraha kyAna hogA ki do rekhAoM para ke varmA kA yoga barAbara hai unake dharAtala va TUne aura unake gaMtara paraka varga se| sAtavA sAdhya ke isa dAve aura cauthI sAdhya kI usa dAve se jo usake Tibha pana 4 meM likhA hai hama ina donoM sAthyoM kA yaha saMbaMdha nikAlate hai sAdhya 8 se yoga kA barga -- boM kA yoga + dUnA gharAtala sAdhya 7 se bAntara kA baga- vagoM kA yoga - dUnA gharAtala bIjagaNitIya sAdhana / paNa pAro ki aba lambAI meM a paimAne hai aura unake hisA asa aura saba lambAI le ma aura na mAne haiM to a=(ma-na-na) ina donoM varAvaroM kA varga kiyA imaliye ama+2 X ma x na+ga ina donoM barAbaroM meM se haraeka meM na milAyA isaliye a+ ma+2 x wx na+2 na ravina 24 mana+24 na- 2(sa+na)- na -2xx na iliye ajasa-2xxja yAnI agara koI aMka visI do hissoM meM bAMTAjAya to kula saMka aura kahile ke barA milakara barAbara hai kula graMka aura usa hisake guNanaphAlA ke dUne aura dUsare hisI ke jau ke malyAsa (26) amarAva rekhA sa bindu para isa taraha vAMTI jAya ki asa para kA barga TUnA ho sa va para kI varga se to sAbita karo ki aba aura basa para ke bamoM kA bAntara dUnA se ava aura basa ke gharAlA kA sAdhya 8 prameyopapAdya mA0 sa0 - agara koI sIdhI rekhA do hissoM meM bAMTIjAya tola rekhA aura usa ke kisI hisse kA caugunA pAtala aura dUsare hisse para kA baga milakara barAbara hoMge usa sIdhI rekhA para ke varga ke jo kula rekhA aura pahale hisse se banatI hai For Private and Personal Use Only

Page #175
( 182 ) bi0 sU0 - pharja karo ki aba sIdhI rekhA kisI do hissoM meM sa bindu para bAMTogayI hai to aba aura basa ke dharAtala kA caugunA aura asa para kA varga milakara barAbara hoMge usa rekhA para ke barga ke jo ava aura saba se banatI hai saba ke Acharya Shri Kailassagarsuri Gyanmandir cprada para pra yapha da varga banAo daya milAo isaliye jaka barAbara hai kana ke isItaraha rakhara barAbara hai raca ke a ma 21 ta For Private and Personal Use Only sa va da bAka kha ra na 421 0 prava ko da taka itanA bar3hAyA ki ba da barAbara ho 1 sA0 3 1- sA0 46 ca ya ha la pha va ora sabinduoM se va la aura saha rekhA aya yA dapha kI samAnAntara aura daya se ka cora va para aura yapha se la auraha para milatI huI khIMco (2 sA0 39 ) ka aura kha se majakana aura ta kharaca rekhA cprada yA bapha kI samAnAntara khIMco ( 1 sa0 31 ) upa0 -- aba cUMki saba barAbara hai bada kI aura saba barAbara hai jaka kI aura bada barAbara hai kana ke cUMki sada barAbara hai bada ke aura ja ka barAbara hai kana ke isaliye saka usakona caturbhuja barAbara hai va na samakona caturbhuja ke aura jara barAbara hai rana ke ( 1 sA0 33 ) lekina sa ka barAbara hai ra na ke ( 1 sA0 43 ) isaliye va na saka. jara ora rana cAroM samakona caturbhuja

Page #176
( 182 ) Apasa meM barAbara haiM aura cAroM milakara kisI eka saka ke caugune se ___ cUMki saba barAbara bada ke aura bAda barAbara baka ke hai yAnI barAbara saja ke hai aura cUMki saba bAbara jaka yAnI jaba ke hai isaliye saja barAbara jakha ko hai cUMki sa ja barAbara jakha ke aura svara barAbara ra ca ke hai isaliye aja barAbara mazva ke aura khala barAbara eka ke hai ( 1sA0 36) lekina makha barAbara khala ke hai (1sA0 43 ) isaliye aja barAbara rapha ke hai ( 1rU. 1) isaliye aja,makha,khala aura rapha cAroM samakona catubhaja Apasa meM barAbara meM aura cAroM milakAra kisI eka aja ke caugune haiM aura yaha sAbita hocukA hai ki samavana,jara aura ramacAroM samakIna caturbhuja milakara saka ke caugune haiM ___ isaliye AThoM samakona caturbhuja jinase avaha mApaka banatA hai aka ke caugune haiM ____ cUMki akakSeta ava aura basa kA dharAtala hai kyoMki vaka barAbara hai basa ke isaliye aba aura basa ke dharAtala kA cogunA aka kA caugunA hai lekina yaha sAbita ho cukA hai ki acaha mApaka aka kA caugunA hai isaliye aba aura nasa ke dharAtala kA caugunA barAbara he acaha sApaka ke ( 1sva. 1) For Private and Personal Use Only

Page #177
( 183 ) ina donoM barAbaroM meM se haraeka meM taha jo asa yara kA barga hai milAyA isaliye aba aura basa ke dharAtala kA caugunA aura asa parakA barga mila kara barAbara haiM acaha mApaka aura taha vargake lekina acaha mApaka ora taha barga milakara ayaphada kSetra ko jo ada para kA barga hai banAte haiN| isaliye aba aura basa ke dharAtala kA caugunA aura prasa para kA varma likhavAra barAbara haiM adapara ke barga ke yAnI usa rekhA para ko dA ke jo aba aura basa se banatI hai phala-isaliye agara koI sIdhI rekhA Adyopanta-yahI sAbita karanA thA Ti. 1 pAThavauM sAya kA dUsarA subUta yaha hai abako da taka itanA bAhAyo ki ba da barAvara ho basa kI caurAha para a ya pha da varga banA-sa yo ( 1 a0 mA0 46 ) a ya meM se aja aura yapha meM ho yaha aura kada meM se pAka parAvara badAko samAyona kha jala rekhA ada ko samAnAntara aura hama rekhA yaha pha aya ko samAnAntara aura kana rekhA yapha kI samAnAntara aura vakha rekhA dazaka kI samAnAntara khIMco baMki ada, aya, yapha aura pha da aApasa se barAbara haiM aura aja, yaha, phaka, aura daba vyApama meM barAbara haiM isaliye aba, jaya, hapha paura bAda DAyala meM barAbara hai (1 ga0-kha03) isaliye ala,jaha,ha ka aura kAra samakona catubhuja jyApasa meM barAbara haiM (1 asA036) aura cAroM milakAra kisI eka ala ke caugune haiM lekina aba aura basa ke dharAtala kA caugunA bhI alakA caugunA hai kyoMki bala barAbara hai basa ke isaliye bhala, jaha, haka aura kaba khadAkona catuja milakara barAbara haiM DAva aura basa ke caugune dharAtala ke phira ki jala, maha, na ka aura kha ba vyApasa meM barAbara haiM kyoMki hara eka barAbara hai abake aura jama, hana, ka kha aura bala lApana meM / For Private and Personal Use Only

Page #178
( 184 ) barAvara haiM kyoMki hara eka barAbara hai basa ke isaliye lama, mana, nakha, kha la aura asa yApasa meM barAbara hai isaliye makha samakona caturbhuja asa parakA varga hai lekina yaha sAvita hocukA hai ki ala, jaha, haka aura kaba sammakona caturbhuja milakara varAvara haiM aba aura basa ke caugune dharAtala ke isaliye ala, jaha haka, kaba aura makha yAMcoM sasakona caturbhuja milakara barAbara haiM aba aura basa ke caugune dharAtala ke aura asa parake varga ke lekina yaha pAMcoM samakona caturbhuja milakara ayapha da ko jo ada parakA varga hai banAte haiM isaliye aba aura basa ke dharAtala kA caugunA caura asa parakA varga milakara barAbara hai ada parake varga ke yAnI usa rekhA parake varga ke jo aba aura basa se banatI hai Ti. 2 AThauM sAdhyakA tIsarA subUta bATa hai .........ma. va Ta ko dalakA uttama mAyA ki bada barAbara ho basa ke ki aba aura ba da ke dharAtala kA dUnA aura aba aura vada paraka varga milakara barAbara hai aha gharako varga ke ( 2-sA04 ) lekina ba da barAbara hai basa se isaliye saba aura basa ke dharAtala kA dUnA aura aba aura barAbara maga milakAra barAbara meM ada parakebarga ke lekina aba aura basa parake varga mila kara barAbara haiM aba aura basa ke dharAtala ke TUne aura asa paraka varga ke (2-07) italiye aba kaura basa ke dharAtala kA caugunA aura asa parakA kaI milabAra barAbara meM ada parako vA vAnI usa rekhA parake varga ke jo aba aura ba sa se banI hai Ti0 3- nagara aba aura ba sa judI 2 rekhA khayAla kI galio ina sAdhya kA dAvA isa taraha bayAna honatA hai ki do rekhAyoM ke yoga parakA varga unake aMtara paraka vA se bakadara unakI dharAtala ke caugune ke jiyA. dA hotA hai bIjagaNitIya sAdhana faz2a karo ki aba rekhA lambAI meM a paimAne aura usa ke asa aura sa bahira lambAI meM kama se bha aura na paimAne hai to a-sa+na ina donoM barAbaroM meM se haraeka meM se na nikAlA isa live sa-a-na ina donoM barAbaroM kA varga kiyA For Private and Personal Use Only

Page #179
( 185 ) isaliye mara= are-24 ana+mara ina donoM barAbaroM meM se haraeka meM 4 x x na milAyA isaliye 4xx na+ma=a +24 a4 na+na lekina a+24 ax na+na =(a+na )2 isaliye 44 ax na+ma=(a+na)2 yAnI agara koI graMka do hissoM meM bAMTA jAya to kula aMka aura usake eka hisse kA caugunA guNanaphala aura dUsare hisse kA varga milakara barAbara hai usa aMka ke varga ke jo kula graMka aura usake pahile hisse ke yoga se banatA hai abhyAsa (20) dUmare adhyAya kI 8 vI sAdhya ko usI adhyAya kI 5 vauM yA 6 voM sAdhA kI madada se sAbita karo sAdhya, prameyopapAdya sA.sU. -agara koI sIdhI rekhA dI barAbara aura do nAbarAbara hissoM meM bAMTIjAya to do nA barAbara hissoM para ke barga milakara dUne hote haiM AdhI rekhA para ke varga aura usa rekhA para ke barga ke jo bhAgabinduoM ke bIca meM hai vi0sU.-pharja karoki aba sIdhIrekhA AL sa biMdu para do barAbara hissoM meM aura da bindu asale para do nA barAbara hissoM meM bAMTI gayI hai to ada aura daba para ke barga milakara TUne hoMge asa aura sada para ke bagoM ke yoga ke aM. sa biMdu se sa ya rekhA aba ke sAtha samakona banAtI huI khA~co 1-sA0 11 saya barAbara asa yA saba ke banAo 1-sA0 3 aura ya a yA yaba milAzrI dase dapha rekhA saya kI samAnAntara aura yaba se pha biMdu para milatI huI khoMcI aura pha se phaja rekhA praba kI samA For Private and Personal Use Only

Page #180
nAntara khoMcI 1-sA031 aura prapha milAo upa. aba cUki asa barAbara hai saya ke isaliye ayasa kona barAbara hai yaasa kona ke 1- sA0 5 ___ cUMki asaya kona samakona hai isaliye ayasa aura yaasa kona milakara eka samakona hai (1-sA0 32) aura cUMki yaha donoM kona Apasa meM barAbara haiM isaliye hara eka dUna meM se AdhA samakona hai isI taraha saghava aura pavasa konoM meM se bhI haraeka AdhA samakona hai isaliye kula ayava kona samakoma hai cUMki jayapha kona AdhA samakona hai aura yajapha samakona hai kyoMki vaha barAbara hai apane sAmane ke yasavaantaH konake (1-sA0 28) isaliye yaphaja AdhA samakona hai isaliye jaya pha kona barAbara hai yaphaja kona ke isaliye japha bhuja barAbara hai jaya bhuja ke (1-sA. 6) phira cUMki phabada AdhA sasakona hai aura phaba samakona hai kyoMki vaha barAbara hai apane sAmane ke yasaba aMta: kona (1-sA. 28) isaliye baphada AdhA samakona hai isaliye phavada kona barAbara hai vaphada kona ke isaliye dapha bhuja barAbara he deva bhuja ke (1-sA. 6) cUMki asa barAbara hai sasa ke isaliye asa para kA barga saya ghara ke barga ke barAbara hai For Private and Personal Use Only

Page #181
( 187 ) isaliye asa aura saya para ke barga milakara dUne haiM asa para ke barga ke (2-kha0 2) lekina aya para kA barga barAbara hai asa aura saya para ke bargoM ke yoga ke (1-sA0 47) isaliye aya para kA barga TUnA hai asa para ke barga kA phira cUki ya ja barAbara hai japha ke isaliyeyaja para kA barga barAbara hai japha para ke barga ke isaliye yaja aura japha parake barga milakara dUna haiM japha para ke barga ke (2-sva0 2) lekina yapha para kA barga barAbara hai yaja aura japhapara ke bagoM ke yoga ke (1-sA0 47) isaliye yapha para kA barga TUnA hai japha parake barga kA lekina ja pha barAbara hai sada ke (1-sA0 34) isaliye yapha para kA barga dunA hai sada para ke barga kA lekina aya para kA barga dUnA hai asa para ke bargakA isaliye aya aura yapha para ke barga milakara dUne haiM prasa aura sada para ke bagoM ke yoga ke lekina apha para kA barga barAbara hai aya aura yapha para ke bagoM ke yoga ke (1-sA0 47) isaliye apha para kA barga dUnA hai asa aura sada para ke bagoM ke yoga kA lekina ada aura da pha para ko barga milakara barAbara haiM apha ghara ke barga ke (1-sA0 47) isaliye ada aura dapha para ka barga milakara dUne haiM asa aura sada para ke bagoM ke For Private and Personal Use Only

Page #182
( 188 ) laikina dapha barAbara hai dava ke isaliye ada aura dava para ke barga milakara dUne haiM asa aura sada para ke bagoM ke phala-isaliye agara koI sIdhI rekhA AdyopAnta-yahI sAbita karanA thA Ti. 1- bhavauM sAdhA kA dUsarA subUta yaha hai zrAsa daba caMki ada parakA bagai barAbara hai asa aura sada ke dharAtala ke dUne aura asa aura sada para ke bagoM ke (2-sA 4) aura basa aura sada ke gha. rAtala kA dUnA aura da ba para kA barga milakara barAvara haiM basa aura sada para ke bagoM ke (2 a0-sA0 7) isaliye ada aura daba para ke varga aura basa aura sa da ke dharAtala kA dUnA mila kara barAvara haiM asa aura sada ke dharAtala ke dUne aura sada para ke varga ke dUne aura asa aura basa para ke bagoM ke (1 a0-sva02) lekina basa barAbara hai asa ke isaliye ada aura da ba para ke barga aura asa aura sada ke dharAtala kA dUnA milakara barAbara haiM asa aura sada ke dharAtala ke dUna aura asa aura sada para ke boM ke dUne ke ina donoM barAbara meM se hara eka meM se asa aura sada ke gharAtala kA dUnA nikAla DAlA isaliye ada aura da ba para ke barga milakara dUne haiM asa aura sada para ke boM ke (1 a0 kha0 3) Ti. 2 navI sAdhya meM sAbita huyA hai ki do nAbarAbara hissoM ada aura da ba para ke barga milakara dUne hai asa aura sa da parake vargoM ke yAnI barAbara hai a sa aura sa ba para ke vargoM ke aura sa da para ke varga ke dUme ke isaliye do barAbara hissoM asa aura sa ba para ke varga milakara do bhAbarAbara hissoM ada aura da ba para ke bagoM se hamezaha kama haiM isaliye isa sAdhya se yaha anumAna sAbita huA ki kisI rekhA ke do hissoM para ke bagoM kA yoga usa hAlata meM sabase kama hogA jaba ki bhAgabiMdu rekhA ke Adhe para hai bIjagaNitIya sAdhana pharja karo ki aba rekhA lambAI meM 2 a paimAne hai aura usakA AdhA masa yA sa ba lambAI meM apaimAne hai aura sa da rekhA jo bhAgabiMduoM ke bIca meM hai ma paimAne haiM to a da lambAI meM (a+ma) paimAne hai aura da ba lambAI meM (a-ma) paimAne hai For Private and Personal Use Only

Page #183
( 180 ) S 3 ava ( a + ma) = a + 2 x ax ma + ma 2 2 aura ( ama) = a - 2 x a x ma + ma 2 Acharya Shri Kailassagarsuri Gyanmandir 2 isaliye (a + ma) + (a-ma) = 2a +2ma yAnI agara koI vyaMka do barAvara aura do gAvarAvara hissoM meM bAMTA jAya to do nAvarAvara hilmoM ke varga milakara dUne hai Adhe aMka ke varga aura nAbarAbara hissoM ke antara ke vyAdhe ke varga ke 2 abhyAsa (21) kisI sIdhI rekhA ko aise do hissoM meM gAMTo ki donoM hissI parake varga milakara barAbara hoM diye hue varga ke aura batAo ki kima hAlata meM isa sAdhya kA mAvita honA nAmumakina hai (22) agara koI aba sIdhI rekhA sa bindu para do barAbara hissoM meM aura da vindu para do nAvarAvara hissoM meM bAMTI jAve to ada aura daba parako varga milakara barAbara hoMge sa da parake varga ke caugune aura ada aura dabako dharAtala ke dUne ke (23) agara aba sa mamakona mamadivAhu tribhuja ke basa karaNa meM koI. da vindu liyA jAya to aT parake varga kA TUnA barAbara hogA bada aura dasa para vargoM ke sAdhya 10 prameyopapAdye sA. sUtra - agara koI sIdhI rekhA do barAbara hissoM meM bAMTI jAya aura kisI bindu taka bar3hAyI jAya to kula bar3hI huI rekhA para kA varga aura bar3ha e hue hisse para kA barga milakara TUne hoMge yA - dhI sIdhI rekhA para ke barga aura usa rekhA para ke varga ke jo AdhI rekhA aura bar3he hue hisse se banatI hai dUne hoMge asa aura sada para ke vargoM ke 0 sabindu se saya rekhA aba ke sAtha samakIna banAtI huI khIMco? - sA0 11 vi0 sUtra farz2a karo ki va sIdhI rekhA sa bindu para do barAbara hissoM meM bAMTI gayI hai aura da taka bar3hAyI gayI hai to prada aura daba para ke varga milakara Ming For Private and Personal Use Only sa yaM a pha 5

Page #184
aura sagha barAbara asa yA saba ke banAo aura aya aura yava milAyo ya se yapha rekhA ava kI samAnAntara aura da se dapha rekhA sagha kI samAnAMtara aura yapha se pha bindu para milatI huI khauMco 1-sA0 31 upa aba cUMki yapha rekhA saya aura pada do samAnAntara rekhAoM para giratI hai isaliye sayapha aura yAda kona dosamakona ke barAbara nA isaliye bAika aura thakada kona do samakakSona se kama haiM isaliye yaba aura kada agara ba aura da kIvara baDhAyo jAya to mila jAyagI 1-10 12 maz2a karI viyaca zora kada bar3habAra jabindu para milatI haiM aba milAyo aya cUMki asa barAbara hai saya ke isaliye sayaa kona barAbara hai basa kona ke sA. 5 aura prasaya samakona hai isaliye sagha a aura yaprasa konoM meM se haraeka AdhA samakona hai (1-sA032) isI taraha sa yava aura bavAsa meM se haraeka bAdhA samakona hai isaliye kula ayaba samakona hai cUMki pavasa kona AdhA samazIna hai isaliye da baja kona bhI AdhA sabhakona hai 1-sA015 lekina vadaja samakIna hai kyoMki vaha barAbara hai dasa ekAntara kona ke 1-sA028 isaliye dajaba AdhA samakona hai aura isaliye barAbara hai davaja kona ke For Private and Personal Use Only

Page #185
( 181 ) isaliye va ha bhaja barAbara hai daja bhujako 1-sA06 phira cUMki yajapha AdhA sama kona hai aura ya phaja samakona hai kyoki vaha barAbara hai ghasada kona ke 1-sA 34 isaliye phayAja AdhA samakAna hai aura isaliye barAbara hai 7 ) ( lnn isaliye japha barAbara hai phaba ko cUMki yasa barAbara hai lAbha ke isaliye yasa paratA va varAvana hai sabha parakI barga ke isaliye yA mora labha para ke mArga milakara dUne se saapara ko vargo lekina aparakA barga barAbara hai yasa aura satra parake bagoM -sA 40 isaliye yatra para kA barga TUnA hai isa parake bargakA phira cUMki jaya barAvara hai phava ke isaliye naphA gharakA barga barasara hai pAya para ke barga ke __ iliya japha aura phaya parake barga milakara dUne meM kaya para ke varga ke lekina va japarakA barga barAbara hai jaka aura phaya parake bagAke 1-sA047 durAliye yaja parakA barga dUnA hai phaya parake vargakA lakina kaba barAbara hai sa ha ke 1-sA034 isaliye ya ja parakA varga dUnA hai sAdA parake vargakA lekina yaha sAbita hocukA hai ki yaja para kA barga TUnA hai isa para ke vargakA isaliya ya a aura yaja para ke maga milAkara dUna re AsAra For Private and Personal Use Only

Page #186
( 182 ) lekina aja parakA barga barAbara hai ya a aura yaja parake bA~ke 1-sA047 isaliye aja parakA barga dUnA hai asa aura sada parake bagIkA lekina ada aura daja para ke barga milakara barAbara haiM aja parake barga ke 1-sA047 isaliye ada aura daja parake barga milakara dUne haiM asa aura sada parake bagIke lekina daja barAbara hai dana ke isaliye ada aura dAna parake baga milakara dUne haiM asa aura sada parake bagAke phala-isaliye agara koI sIdhI rekhA AdyopAnta-yahI sAbita karanA tho Ti. 1 - dasavIM mAdhyakA dUsarA mubUta Toka vaimAhI hai jaisA ki navIM sAdhya kA dUsarA subUta hai ___ ki adaparakA varga barAbara asa aura sadana ma ba 'Ta ke dUne dharAtala aura basa aura sada parako bAMke (2-sA04) __yora basa aura sa da kA dUnA dharAtala aura dava parakA barga milakara barAbara hai basa aura sa da ghara ke bA~ke (2-sA07 ) isaliye ada aura da ba parake varga aura basa aura sa da kA TUnA dharAtala milakara barAbara haiM asa aura sada ke dUne dharAtala aura sa da parake dUne barga aura asa aura sa ba parake bA~ke (1-kha02) lekina basa barAbara hai asa ke isaliye ada aura da ba para ke varza aura kAsa aura sa da kA dUgA dharAtala milakara barAbara haiM asa aura sada ke dUne dharAtala aura asa aura sa da para ke vargAke dane ke ina donoM barAbaroM meM se asa aura sa da kA TranA dharAtala nikAla DAlA isaliye ada aura da ba parake barga milakara dUne haiM asa aura sa da para ke bargoM ke Ti0 - 2 dasarvI sAdhyakA tIsarA sucUta vaha hai ya.._sa_vada baa ko ya taka bAjAo aura a ya barAbara bada ke banAyo ki TU a aura aya parake varga milakara dUne hai dasaura sa aparake bIke For Private and Personal Use Only

Page #187
( 183 ) (2-mA0 ) aura aya barAbara hai da ba ke isaliye ada aura bada parake barga milakara dUne haiM asa aura sa da parake vargoM ke Ti0 3 4 vIM aura 10 vauM sAdhya kA ekahI subUta jo "misa halDAhaDasana ne IjAda kiyA hai nIce likhA jAtA hai aba biMdu sa para do barAvara hissoM meM bAMTI gaI hai aura biMdu da para do nAbarAbara hissoM meM ( anta: khaMDa sAdhya ! adhyAya 2) yA (bahiH khaMDa mAdhya 10 adhyAya 2) bAMTI gaI hai ada aura asa aura sada para aba ke ekahI tara phaadayapha aura a sa ja ha aura sada ka la la / vargabana yo 1-sA0 a sa da ba a sa ba da la pa +naka - - -ka ha a ya varga ke andara phaha para phahama na varga banAyo 1-sA0 46 yaha barAbara hai sa da para ke varga ke pharja karo ki na ma aura ka la ( bar3hakara agara jarUrata ho) pa biMdu para milate haiM vyaba pa ya barAbara hai a sa para ke varga ke aura pa ja barAvara hai ba da para ke varga ke ada aura da ba para ke vargoM kA yoga barAbara hai a ya vyaura pa ja kSetroM ke yAnI barAvara hai a ja aura pa ya aura saka aura pha ma ke yAnI dUnA hai aja aura sa ka ke yoga kA yAnI asa aura sa da para ke bargo kA dUnA hai Ti. 4 yaha jAhira hai ki navauM sAdhya kA kalpita artha vahI hai jo pAMcavauM sAdhya kA hai aura dasavIM sAdhya kA kalpita ardha vahI hai jo chaTI sAdhya kA hai . dasarvI mAdhya navauM sAdhya ke sAtha vahau ilAkA rakhatI hai jo chaThI sAdhya pAMcavIM ke sAtha rakhatI hai aura isaliye nIce likhe do dAvoM meM haraeka navIM aura dasavIM donoM mAdhyoM kA dAvA ho sakatA hai 1 do rekhAoM para ke barga milakara una rekhAoM ke yoga aura grantara ke AdhoM parake vargoM ke dUne hote haiM kyoMki agara ada aura da ba judI 2 rekhA khayAla kI jAveM to sa da aura asa meM se eka una rekhAoM ke yoga kI bhayAdhI nyaura dUsarI unake vyantara kI prAdhI hai| For Private and Personal Use Only

Page #188
( 184 ) (2) do rekhAoM ke yoga aura antara para ke barga milakara dUne hote hai una rekhAoM para ke vargoM ke kyoMki nagara a sa aura sa da juhI 2 rekhA khayAla kI jAveM to ada unakA yoga aura va da antara bIjagaNitIya sAdhana pharja karo ki a ba lambAI meM 2 a paimAne aura usake Adhe asa yA sa ba lambAI meM apaimAne haiM aura ba da lambAI meM samAne hai isaliye aTa lambAI meM (2+ma) meM mAne aura sa da lambAI meM (a+ma) phi (2+ja):- +8x ama+ma isaliye (2a+ma)ma-4 a-+3xxma+2 ma lekina a+xx a ma+2ma-2a-+2+8xxsa--- rasa =2 + 2(a+ma) isaliye (2+ma)+ma=2(a+ma)+2 isaliye agara koI diyA huA aMka do varAvara hissoM meM bAMTAjAya aura kula aMka aura usake eka hisse meM koI dUsarA aMka milAyA Aya to bAdAhuA kula aMka aura dUsare vyaMka ke barga milakara dUne haiM diye hue baMka ke aAdhe aura usa aMka ke varga se jo diye hue graMka se gAye aura dUsare jaMka se banA hai abhyAsa (24) a na sa tribhuja meM ada rekhA a koga se ba sa ko da biMdu para do barAbara hissoM meM kATato huI sIMcI gaI hai mAvitaH zAze kiyA thA aura aza para ke varga milakara dUne haiM ba da aura da apara ke bagI ke ( 25 ) sAbita karo ki samAnAntara caturbhaja ke cAroM bhujoM para ke va milakara barAbara haiM usake donoM vANAM para ke boM ke (26) a ba sa da caturbhuja ke asa aura ba da karNa ke bIcoM bIca ke ya aura pha biMdu haiM sAvita karo ki cAroM bhujoM para ke varga milakara barAbara hai donoM karNAM ghara ke vargoM ke aura ya pha para ke caugune varga ke For Private and Personal Use Only

Page #189
( 195 ) (27) kinI a biMdu se kisI ba sa da ya samakona samAnAntara caturbhuja ke cAroM konoM taka a ba aura a sa yaura a da aura a ya rekhA khIMcI gaI haiM mAmila karo thiA aba aura ada para ke varga milakara barAbara hai asa aura ava para ke boM ko (28) cAra zaka vibhuja ke aAdhAra kI lambAI aura jagaha mAlUma hai aura usake guNoM para ko voM kA yoga ekahI he sAbita karo ki isa trisuja ke zI kA nidhi eka vRtta hai (28) udAra aba sa trinuja ke basa AdhAra para da aisA biMdu hai ki va aura ba da ghara ke varga milakara barAbara haiM asa aura sa da para ke ghI kI no ada ke bIcoM bIca kA vidava aura sa se varAvara dUrI para hogA (30) bAnIdhI rekhA aura do vi diye hue hai usa rekhA meM eka zezA niMda dAMpata bAro ki una rekhAjoM para ke varSoM kA voga jo diye hue biloM se una viMdu taka khIMcojAya sava se choTA ho sAdhya 11 varalUpapAya sA hI huI rekhA ko ai meM do hissoM meM bAMTa ki kula rekhA aura usake eka hisse kA gharAtala barAbara ho dUsare hisse para ke vadha ke bi. sa. phaz2a karo ki aba dI huI sIdhI phaja rekhA hai usako aise do hissoM meM bAMTanA hai ki kula .. aba rekhA aura usake eka hisse kA dharAtala ahAra ko dUsare hisse para ko varga ke sIdhI / -aba para asahana baga banAyo 1-sA0 46 asa ko biMdu para do barAbara hissoM meM bAMTo 1-sA0 10 baba milAo aura sa a ko ka taka itanA bar3Ao ki barAbara ho ba ba ke amA para mAjaha tra baga banAo 1-sA. 46 ba For Private and Personal Use Only

Page #190
( 286 ) to aba rekhA ha biMdu para aisI baMTI ki aba aura baha kA dharAtala barAbara hogA aha para ke varga ke ja ha ko bar3hAo ki vaha sa da se ka para mile aba cUMki asa rekhA ya biMdu para do barAbara hissoM meM baMTI hai aura pha taka bar3hAyI gayo hai isaliye sapha aura pha a kA dharAtala aura aya para kA varga milakara barAbara haiM phaya para ke barga ke 2-sA. 6 lekina yapha barAbara hai ya ba ke isaliye sa phora pha a kA dharAtala aura aya para kA arga milakara barAbara haiM ya ba para ke barga ke lekina ba a aura a ya para ke barga milakara barAbara ya ba para ke barga ke 1-sA0 40 isaliye sapha aura phana kA dharAtala aura aya para kA barga milakara barAvara haiM va aaura aya para ke bagoM ke ina donoM barAbaroM meM se aya para kA varga nikAla DAlA isaliye sapha aura phaprakA dharAtala barAbara hai ava para ke varga ke 1-sva. 3 lekina phaka kSetra sapha aura phana kA dharAtala hai kyoMki phaa barAbara hai phaja ke aura ada kSetra aba para kA barga hai isaliye phaka barAbara hai ada ke aka hisasA jo donoM meM zAmila hai nikAla DAlA isalithe bAkI hapha barAbara hai bAkI hada ke 1-sva0 3 lekina hada kSetra ava aura vaha kA dharAtala hai kyoMki aba barAbara hai vada ke For Private and Personal Use Only

Page #191
( 197 ) aura hapha kSetra aha para kA baga hai isaliye aba aura baha kA dharAtala barAbara hai aha para ke barga ke isaliye ava sIdhI rekhA ha biMdu para aisI baTagayI ki aba aura baha kA dharAtala barAbara hai aha para ke barga ke / isI rekhA ke isa taraha bAMTane kI z2arUrata thI anumAna 1 isa sAdhA meM sapha rekhA apara usI taraha sebaTa gayI hai jaise aba rekhA ha vidu para gaMTI gayI hai anumAna2- agara koI sIdhI rekhA do nA barAbara hissoM meM isa taraha bAMTI jAya ki kula mIdhI rekhA aura usake choTe hisse kA dharAtala barAbara ho bar3e hisse parake bargake to bar3A hissA bhI usI taraha bAMTA nAsaktA hai agara usameM choTe ke barAbara hissA kATA jAya aura choTA hissA bhI usI taraha baTa saktA hai agara choTe hisse meM se donoM ke aMtara ke barAbara hissA kATA jAya Ti.-gyAravauM sAdhyameM ukta dasa ne rekhAgaNita kI rUse bIjagaNita ke dUsare darje ke samIkaraNa ko hala kiyA hai dUsare darje ke samIkaraNa aura isa sAdhya kA ilAkA hamane isa jagaha nahIM sAbita kiyA kyoki vidyArthI jisane bIjagaNita ko dUsare darje ke samIkaraNa taka nahIM sIkhA hai usako bakhUbI nahIM samajha saktA hai abhyAsa (31) kisI sIdhI rekhA ko itanA bar3hAyo ki kula bar3I huI sIdhI rekhA aura usake bar3e hue hisse kA dharAtala barAbara ho usa rekhA parake dhake (32) agara koI sIdhI rekhA do hissoM meM isa taraha bAMTI jAya je se ki gyAravauM sAdhya meM bAMTI gayI hai to donoM hissoM ke vargIkA antara barAbara hogA donoM hissoM ke dharAtala ke (33) 11vIM sAdhya meM jaba aura pha da aura aka rekhA Apasa meM svamAnAntara hai For Private and Personal Use Only

Page #192
( 198 ) (34) gyArahavIM sAdhAmeM agara saha rekhA bahakara bapha se la vindu para mile to sala pha samakona hai (35) gyArahavIM sAdhA meM agara baya aura saharekhA na vindu para mileM to ana rekhA sa ha rekhA ke sAtha samakona banAvagI (36) agara aba rekhA sa bindu para aise do hissoM meM asa aura saba meM bAMTI gaI ho ki aba aura basa kA dharAtala barAbara ho asa parake varga ke to sAbita karo ki aba aura basa parake bargIkA yoga tigunA hogA asa parake bargakA aura aba aura basa ke yoga parakA varga pAMcagunA hogA asa parake bargakA (37) abasa samakona tribhuja hai jisake basa karNa para a da lamba DAlA gayA hai aura jisa kI aba bar3I bhujA parakA varga barAbara hai basa aura asa ke dharAtala ke sAbitakaro ki basa karaNa da bindupara kaTatA hai jaisA ki dUsare adhyAya kI 11vIM sAdhya meM hotA hai| (38) abasa samatribhuja hai jisake aba bar3e hue bhujapara da eka ai. sau biMdu hai ki sada rekhA parakA varga dUnA hai aba parake barga kA sAvitakaro ki ada biMdu ba para misla 11vIM sAdhya ke kaTegI (36) aba sa samakona tribhuja hai jisakA a kona samakona hai aura jisakI aba bhuja asa bhuja se dUnI hai agara aba meM se aha barAbara basa aura asa ke grantara ke kATI jAve to aba viMdu ha para misna 11vIM sAdhA ke kaTegI sAdhA 12.prameyopapAdya sAsa -agara adhika kona tribhuja ke kisI nya na kona se usa sAmane kI bar3hI huI bhuja para laMba DAlA jAya to adhika kona ke sAmane ke bhuja parakA barga una do bhujoM parake bagau se jinase adhika kona banatA hai bar3A hogA bakadara usa dharAtala ke dUne ke jo usa bhuja jisake bar3he hue hisse para laMba girA hai aura usa rekhA se banatA hai jo darmiyAna laMba aura adhika kona ke hai For Private and Personal Use Only

Page #193
( 198 ) bi.sa -pharjakaro ki abasa adhika kona tribhuja hai jisakA asa va adhika kona hai aura abiMdu se ada laMba basa bar3hI huI bhujA para DAlA gayA hai to aba parakA barga bar3A hogA asa aura sa baparake bagoM se baqadara basa aura sada ke dUne dharAtala ke upa cUMki bada rekhA do hissoM meM sa biMdu para bAMTI gayI hai isaliye bada parakA barga barAbara hai basa aura saTa parake bagIke aura basa aura sada ke dUne dharAtalake 2-sA04 ina donoM barAbaroM meM se haraeka meM daa parakA barga milAyA isaliye ba da aura daa parake barga milakara barAbara haiM basa, sada aura daa parake bagIM aura basa aura sada ke dUne dharAtalake ___ lekina na a parakA barga barAbara hai vada aura da aparake bagI ke aura aparakA barga barAbara hai sada aura da aparake bI ke 1-sA047 isaliye ba a parakA barga barAbara hai basa aura sa a parake bagI aura basa aura sa a ke dUne dharAtala ke yAnI vaa parakA barga bar3A hai basa aura saMbha parake bagI se baqadara basa aura sada ke dune dharAtala ke phala-isaliye agara adhika kona tribhuja AdyopAnta- yahI sAbita karanA thA Ti0-yaha sAdhA pahale pradhAAya se isa taraha sAbita hotI hai tribhuja aba sa ko bhujoM para aja, a ka aura bala barga banAyo 1-sA046) aura sa ra, baca aura ana laMba una boM kI bhujo para DAlo aura haba sapha, ama, ala, ba ka aura saja milAyo bha For Private and Personal Use Only

Page #194
( 200 ) aba ThIka usI taraha jaisA ki pahale adhayAya kI saiMtAlIsavIM sAdhA maiM sAbita huA hai sAbita hosaktA hai ki tribhuja asapha barAbara hai tribhuja ahaba ke aura tribhuja sa ba ja barAbara hai tribhuja sabaa ke aura tribhuma la sa a barAbara hai tribhuja basa ka ke isaliye aAyata ara barAbara hai aAyata aca ke aura yAyata bara barAbara hai yAyata bana ke aura aAyata saca barAbara hai aAyata sana ke ( 1-sA041 vakha0 6) isaliye aja barAbara hai aca aura bana ke yoga ke lekina aja varga aba parakA hai aura aca aura ba na milakara barAbara haiM aka aura bala vargoM ke yaura grAyata sana aura sa ca ke yoga ke jo asa aura basa parake varga aura dUne dharAtala basa aura sada haiM isaliye aba parakA varga asa aura ba sa parake boM se baqadara dUne dharAtala basa, sa da ke jiyAdA hai anumAna- agara lamba a aura ba konoM se sAmane ke bhujoM para DAle jAMya aura una bhujoM se da aura ya viduyoM para mile to dharAtala asa. sa ya barAbara hai dharAtala ba sa,sa da ke bIjagaNitIya sAdhana pharja karo ki ba sa, sa a aura aba lambAI meM krama se a,ba aura sa paimAne haiM aura sa da aura da a lambAI meM ma aura na paimAne haiM to ba da lambAI meM (a+ma) paimAne hai isaliye sa=(a+ma+na kyoMki aba da samakona tribhuja hai aura bama+na kyoMki a sa da samakona tribhuna hai isaliye sava= (a+ma)ma =a+2xxma+ma-ma =a+2xxma isaliye sa=a+ba+2xxma yAnI sa bar3A hai a+ba se bakradara 24 ma ke abhyAsa (40) agara kisI tribhuja kA a sa ba adhika kona samatribAhu tribhuja For Private and Personal Use Only

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ke eka kona se dUnA ho to umake a ba bhuja ghara kA barga ba sa aura sasa bhujoM ke vargo se bakadara ba sa aura sa a ke dharAtala ke adhika hogA (41) tribhuja a sa ba samavibAhu hai a da rekhA aisI khIMcI gayI hai jo ba sa bar3I huI se da biMdu para milatI hai ki ba da aura da sa kA dharA tala barAvara hai tribhuja a ba sa ke kiso suja para ke varga ke mAbita karo ki a da para kA varga dUnA hai tribhuja aba sa ke kisI bhuja paraka vargakA (42) aisA samadibAhu adhika kona tribhuja banAyo ki adhika kona ke sAmane kI bhuja parakA jaga usakI hara bhuja para ke barga se tigunA ho sAdhya 13 pramayApapAdya sA0 sa0 kisI tribhuja ke kisI nya nakona ke sAmane kI bhaja para kA barga una do bhujoM para ke vargoM se jinase vaha nyU na kona banatA hai baqadara usa dharAtala ke TUne ke jo una bhajoM meM se kisI bhaja aura usa rekhA se banatA hai jo darmiyAna nyU nakona aura usa laMba ke hai jo usa bhuja para usake sAmane ke kona se DAlA gayA hai bi. satra phaja karo ki abasa tribhuja hai aura usakA va nyU nakona hai aura usakI bhaja basa yA bala bhuja bar3hI huI para usake sAmane ke akona se prada a laMba DAlAgayA hai to asa bhuja / ghara kA barga jo va kona ke sAmane bada sa / hai sabaurava aparake bagI se choTA hogA bakadara -1 saba aura bada ke dUne dharAtala ke upa. cUMki saba rekhA da biMdu para aura bada rekhA sa biMdu para bAMTI gayI hai ___isaliye sava aura vada parake barga silakara barAbara hai saba ora bada ke dUne dharAtala aura sada parake barga ke sA __ ina donoM barAbaroM meM se hara eka geM da para kA gema lAyA For Private and Personal Use Only

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1 202 isaliye saba, bada aura daa parake varga milakara barAbara haiM saba aura bada ke dUne gharAtala aura prada aura sada para ke bagoM ke 1-kha0 2 lekina bama para kA barga varAbara hai va da aura dacchA para ke bargoM ke aura a sa para kA varga barAbara hai ada aura dasa para ke ba ke 1- sA0 47 isaliye saba aura bama para ke barga milakara barAbara hai saba aura bar3ha ke dUne gharAtala aura a sa para ke varga ke yAnI prasa para kA varga saba aura ba a para ke bargoM se koTA hai bakadara saba aura bada ke dUne gharAtala ke aura jaba ki basa para mala laMba hai to basa vaha sIdhI rekhA hai jo va kona aura laMba ke bIca meM hai aura yaha bAta z2Ahira hai ki dravya aura vasa para ke barga milakara barAbara hai sa para ke varga aura basa para kaTUne varga ke ---isaliye agara kisI tribhuja meM bAyopAMta yahI sAbita 60911 31 dina yasa kAya pahale adhyAya isa taraha sAbita hotI hai tribhuja aba sakau bhujoM para saja, vaha aura ala varga banAyo (1 - sA0 26) dhaura lamba aca, sana aura vara se basa, barasaloM para DAlo ( 1 sA0 12 ) aura ha a, ba pha, baja, sama, sala aura kamilAko krama Acharya Shri Kailassagarsuri Gyanmandir p D ka sa pha For Private and Personal Use Only Ta gha gra la Huan sa s 6

Page #197
( 203 ) praba loka usI taraha jaisAki pahale adhyAya kI saMtAlIsavIM sadI meM sApita huyA hai sAbita ho saktA hai ki tribhuja bapha sa, ba a ja aura a ba ka krama se barAbara haiM tribhuja ha sa a, ma a sa aura la ba sa ke isaliye Ayata sara, ra a aura ba ca krama se barAbara haiM aAyata saca, bana aura ba na ke (1-mA0 41 va svA0)saliye sara aura na adila kara yAnI kula sa ja barAbara hai sa ca aura ana ke yoga ke aura ba ca aura bana milakara TUne haiM baca ke isaliye sa ja choTA hai sa ka aura ala ke yoga se baqadara yAyata ba ca ka dRne ko lekina sa ja, sa ka aura ala krama se DAsa, sa ba aura ba a para ke varga haiM aura ba ca dharAtala basa-bada hai kyoMki vasa barAbara hai ba ka ke isaliye asa para kA varga a ya aura basa para ka vago ke yoga se bakadA dUne dharAtala basa aura sadaka choTA hai Ti. 2 bArahavIM aura tarahavIM sAdhyoM ke dAve ekahI dAve meM isa taraha bayAna hote haiM ki tribhuja kI eka bhuja parakA varga aura donoM bhujoM parake boM ke yoga kA antara barAbara hai usa dharAtala kI dUne ke jo ina do bhugoM meM se kisI bhuja aura usa rekhA se banatA hai jo bIca usa kona jisake girda vaha donoM bhuja hai aura laba ke hai jo usa bhujA para usake sAmane ke kona se DAlA gayA hai Ti0 3 isa adhyAya kI bArahavIM aura terahavIM sAdhya aura pahale adhyAya kI saMtAlIsavIM sAdhya krama se adhika kona tribhuja nyU nakona tribhuma gaura samakona tribhujoM kI bhujoM ke grAyasa ke sambandha bayAna aura mAbita karatI haiM pahale vyadhyAya kI saiMtAlIsavIM sAdhya kA pratiloma ukta dasa ne usI adhyAya kI ar3atAlIsavIM sAdhya meM sAbita kiyA hai lekina dUsare adhayAya kI bArahavIM aura terahavIM sAdhA ke pratiloma ukta rasa ne nahIM mAvita kiye hai vaha yaha haiM ki "agara tribhuja kI kisI bhaja para kA varga usta kI bAkI bhujoM para ke varSoM se bar3A ho to usa bhuja ke sAmane kA koga adhika kona hogA dhyaura agara tribhuja kI kisI bhuja para kA varga bAkI mujoM para ke varSoM se choTA ho to usa bhuja ke sAmane kA kona nyU nakona hogA" isa pratiloma kA vaha subUta hai ___ pharja karo ki aba sa tribhuja meM agara aba para kA varga asa aura saba para ke vargoM se bar3A hai to asa ba vyadhika kona hai aura vyagara choTA hai to a sa ba nya nakona hai sa se sa da rekhA saba ke mAya samakona banAtI huI khA~co (1- sA. 12) For Private and Personal Use Only

Page #198
( 206 ora sa da barAbara sa a ka banAyo aura ba da milAyo cuMki ba sa da samakona hai isaliye basa aura sa da para ke varga milakara barAbara haiM ba da para ke varga ke (1-sA0 47) lekina ba sa aura sa da para ke barga milakara barAvara haiM basa aura sa a para ke vargoM ke kyoMki sa da barAbara sa a ke banAyI gayI hai isaliye ba da para kA barga barAvara hai basa aura sa a para ke vargoM ke agara ba a para kA varga bar3A hai basa aura sa a ghara ke bargoM se to vaha ba da para ke varga se bhI bar3A hai aura vaha choTA hai ba sa aura sa a para ke bargo se to vaha ba da para ke varga se bhI choTA hai ____phaja karo ki aba parakA bagai bar3A hai basa aura sa a paraka bargoM se isaliye ba a parakA base bar3A hai ba da para ka varga se imalithe ba a bar3I hai ba da se ___ cUMki a ba sa tribhuja kI do bhuja a sa aura sa va alaga 2 barAbara haiM da sa ba tribhuja kI do bhujoM da sa aura sa ba ka yAnI asa barAbara hai da sa ke aura sa ba donoM meM zAmila hai lekina a sa ba tribhuja kA aba AdhAra bar3A hai da sa ba trimubha ka da ba grAdhAra se isaliye a sa ba kona bar3A hai da sa ba kona se (1-sA0 25 ) lekina da sa ba lamakona hai isaliye a sa ba adhikakona hai phira pharja karo ki ba a parakA varga choTA hai basa aura sa a paraka bargoM se isaliye ba a parakA varga choTA hai ba da parake varga se isaliye ba a choTI hai ba da se __caMki a sa ba tribhuja kI do bhuja a sa aura sa ba alaga 2 barAbara haiM da sa ba tribhuja kI do bhujoM da sa aura sa ba ke yAnI asa barAbara hai dasa ke aura sa ba donoM meM zAmila hai lekina a sa ba tribhuja kA aba aAdhAra choTA hai da sa ba tribhuja ke da ba AdhAra se isaliye asa ba kona choTA hai da sa ba kona se (1-sA0 25 ) lekina da sa ba samakona hai isaliye a sa ba nya nakona hai bIjagaNitIya sAdhana marja karo ki basa, sa a aura aba lambAI meM kama se a,ba aura sa pemAne haiM aura na da aura ada lambAI meM sa gaura na paimAne hai pahalI marasa dekho ana da sa lambAI meM ( savimAna hai For Private and Personal Use Only

Page #199
( 205 ) caMki sama+na kyoMki a da ba samakona hai aura ba=na+(a-ma) kyoMki a da sa samakona hai imaliye se ba-ma (a-ma) -ma-a+2ama-ma 2 =-a+2aX ma isaliye a+sa-ba+2x aX ma 5 yAnI choTA hai gra+ma se bakadara 24 arma ke dUsarI sUrata dekho ava da sa lambAI meM (ma-a ) paimAne hai caMki ma-ma+ne kyoMki adaba samakona hai aura ba-(ma-ThA)+na kyoMki adasa samakoga hai isaliye sa-ba-ma-(ma-gra) -ma-ma+24 ya ma -gra =24 yama-a imaliye a+ma-ba+24 grama yAnI va choTA hai gra+sa se vakadara 24 graxmake tIsarI sUrata dekho isa sUrata meM ma barAbara hai ya ke aura ba+ya-sa ina donoM barAbaroM meM se haraeka meM amilAyA isaliye ba+2x -a+ma pAnI bamoTA +sameM kaTara x cA 4 lA For Private and Personal Use Only

Page #200
( 206 ) abhyAsa (43) a ba sa namahibAhu tribhuja ke aba vyAdhAra parake kilI a kona se usake sAmane kI bhuja basa para ada lamba DAlA gayA hai sAbita karo ki aba parakA varga dUnA hai saba gaura bada ke dharAtala kA nAbha (44) aba savibhuja kA sa samakona hai aura sa ke kimI da biMdu se daya laMga aba para DAlA gayA hai to sAbita karo ki aba aura aya kA dharAtala barAvara hai asa aura ada ke dharAtala ke (45) aba sada samalaMba caturbhuja kI ava aura saha bhuNa samAnAtara hai sAbita pAkisa aura vada RNoM para ke milakara parAvara aura yava aura sada ke dUne gharAtala ke zrada aura bala para asarAsa tiluja kAca va kona namavivAha vibhu ke kona ke barAbara ho to aba parakA va asa aura basa para ke vargoM se badara basa aura ca sa ke dharAtala ke bAma hogA sAdhya 16 - vastupapAca dina caitra kI barAbara varga banAyo ... karoki divA DabA kSetra hai isake barAva barga banA nA hai aM - a ke barAbara basa daya sama kauna 0 samAnAntara caturbhuja vanAo (sA0 45 ) aba agara isa samAnAntara caturbhuja kI baya aura yada bhuja Apasa meM barAbara haiM to yaha varga kSetra hai aura hamArA matalaba pUrA hogayA a a For Private and Personal Use Only ha sa 'ya pha da agara baya aura yaT barAbara nahIM haiM to una meM se eka baya ko pha taka bar3hAo aura yapha barAbara yada ke banAo ba pha ko ja biMdu para do barAbara hissoM meM bAMTo ((sA0 10) ja kendra meM jaba yA japha dUrI para bahapha aSTata khIMco

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( 207 ) aura daya ko itanA bar3hAo ki vaha ha biMdupara paridhi se mile to yaha para jo varga banAyA jAyagA barAbara hogA diyehue a Rjubhuja kSetra ke jaha milAo upa.....cUMki apha rekhA ja biMdu para do barAbara hissoM meM aura ya para do nAyarAbara hissoM meM bAMTIgayI hai iyive vaya aura yapha kA dharAtala aura yaja para kA barga milakara barAbara haiM japha para ke barga ke (2-sA. 5) lekina japha barAbara he jaha ke (1-50 15 ) isaliye baya aura yapha kA dharAtala aura yaja para kA barga milakara varAvara haiM jaha para ko barga ke lekina haya ora yaja para ke barga mila kara barAbara haijaha para ke vara ke (1-sA 47) isaliye baya aura capha kA dharAtala aura yaja para kAbaga milakara barAbara haiM hapa ora yaja para ke bI ke yaja para kA barga jo ina donoM meM zAmila hai nikAla DAlA isaliye baya aura yapha kA dharAtala barAbara hai haya para ko barga ke lekina bagha aura yapha kA gharAlala bada samAnAntara catuTuMja hai kyoMki yapha barAbara hai bar3hake isaliye bada barAbara hai yaha dara ke varga ke lekina bada nevaca Rjubhuja kSetra ke barAbara banAyA gayA isaliye yaha para kA barga barAbara hai ajubhuja kSetrake isaliye diye hue Rjubhuja kSetra ke barAbara eka barga bana gayA jo yaha para banAyA jAya aura isI ke banAne kI z2arUrata thI For Private and Personal Use Only

Page #202
anumAna-isa sAdhA meM sApha jAhira hai ki agara kisI vRtta ko pari dhi ke kisI viMdu se usake vyAsa para laMba DAlA jAya to usa laMba parakA varga barAbara hogA yAsa ke hissoM ke dharAtala ke jinameM baha laMba se bAMTAgayA hai abhyAsa (47) die hue barga ke barAvara eka aAyata banAo jisakI eka bhuja dI huI sIdhI rekhA ke barAbaraho dasare adhAyako sAdhyoMpara mizrita prazna (48) agara koI sodhI rekhA pAMca barAbara sismoM meM bAMTI jAya to kula rekhA para kA barga barAbara hogA una do rekhAyoM para ke boM ke jo una hissoM meM se cAra aura tIna hissoM se banate haiM (46) diye hue tribhuja kI kisI bhuja ko itanA vATAyo ki usa bhuja aura vahue hisse kA dharAtala barAbara ho bAko do bhujoM para bagAke antara ke (50) eka mIdhI rekhA ko aise do hissoM meM bAMTo ki kula rekhA aura usake eka hisse parakA varga milazara dUne ho dUsare hisse para ke bargaka (51) dI huI sIdhI rekhA ko itanA vADhAyo ki usa rekhA parakA barga aura bAr3e hue hisA parakA bA milakara hune hoM usa dharAtalaka jo bar3I huI rekhA aura bar3e hue hirama se banatA hai (53) dI huI sIdhI rekhA ko itanA bAyau ki dInhAI rekhA parakA bA aura kula bar3hI huI rekhA parakA varga mila kara Tne hoM usa dharAtalaka jo kula bAdI huI rekhA aura bar3e hue hisse se banatA hai (53) agara kisI aba sa da samakona samAnAntara catubhuja ke pAma ke aba aura basa bhujoM para abayapha aura ba sa ja ha barga banAye jAya to boM ke karNa bapha aura ba ja kA dharAtala dUnA hogA a ba sa da samakona samAnAntara caturbhuja ke (54) caturbhuja ke karNo parake vargoM kA yoga dUnA hogA una rekhAyoM parake boM ke yoga se jo caturbhuja kI Amane sAmane kI bhujoM kI bIcoMbIca ke binduoM ko milAtI hai (55) agara kisI graha vRtta ke aba yAsa meM ga eka biMdu haiM aura sa da rekhA aba ke samAnAntara aisI khIMcI gaI hai ki usake sa aura da sire vRtta kI paridhi para haiM sAvitakaro ki sa ga aura gada paraka barga milakara barAbara haiM aga aura gava parake boMka For Private and Personal Use Only

Page #203
(56) uma viMTu ko jahAM kimI bhamAnAntara catubha ja ke kaNe yAsa meM eka dUsare ko kATate haiM kendra mAnakara hatta khIMcA gayA hai mAmilakarI ki una rekhAyoM paraka boMkA yoga jo utta kI paridhi ke kinnI bidra se samAnAntara catubhuja ke konoM taka khauMvI gayI haiM hamezA ha eka hI mi. kadAra hogI (57) kimI vRtta ke vyAsa aba meM sa aura da biMdu uma ko keMdra meM kararAvara dUrI para liye gaye aura paridhi ke kisI viMdu ya se ya sa aura yada rekhA khIMcI gaI haiM mAmitakaro ki yasa aura ya da parake jarga mila. kara barAbara haiM asa aura ada paraka varga ke (58) a basa mamastribAhu tribhuja meM ada aura ba ya bhuja basa aura sa a para lamba haiM aura eka dUsare ko viMdu pha para kATate haiM sAvita karo ki aba parakA varga tigunA hai apha para ka vargakA (56) agara tribhuja kI bhujoM ke bIcoMbIca ke biMduvyoM se unaka sAmane ke konoM taka rekhA khIMcI jAveM to ina rekhAyoM parake boM kI yoga kA caugunA barAvara hogA tribhuja ko bhujoM para ke bagoM ke yoga tigune ke (60) agara dasa aura ya a aura pha ba rekhA jo kimI aba sa tribhuja ke aba aura basa aura sa a bhujoM ke bIcoM bIca ke da aura ya aura pha biMduoM se una bhujoM ke mAmane ke konoM taka svIMcI gaI hai ja biMdu para mile mAvitAkarI ki jaa aura jaba aura ja sa paraka vargAMka yogakA tigunA varAvara hai aba aura basa aura sa a paraka bagAMka yogaka (61) barga kSetra ke bhItara jo sabase choTA barga banegA vaha usa vargakA bAdhA hogA (12) ekAdaye hara baga ke barAbara eka aimA mamakona samAnAntara catubhuja banAyo jima do pAma kI bhujoM kA yoga eka dI huI rekhA ke barAbarahA (63) eka didhe hara varga ke barAbara eka romA mamakona samAnAntara catubhuja banAyo jimako pAmakI do bhujAoM kA antara eka dI huI rekhA ke barAbara ho (64) aba sa da mamAnAntara catubha ja kA vyagara asa kaNa barAbara ho ava ke to asa karNa parakA baga bada kaNa paraka vA se basa parakI varga ke dUne ke samAna choTA hogaa| (65 ) agara aba sa da baga ke konoM se a ya aura da ha aura bapha aura sa ja lamya kisI ya ha pha na rekhA para girAye jAya to aba aura For Private and Personal Use Only

Page #204
( 210 ) aura daha ke dharAtala ke dUne se bakadara saja paraka varga milakara bafa varga ke bar3e hoMge aba sada (66) diye hue kSetraphala ke samakona samAnAntara caturbhuja ko mujoMkA yoga usa sUrata meM saba se choTA hogA jaba vaha samakona samAnAntara caturbhuja varga hai ba aura daviMdra krama se eka hI sIdhI (67) agara a aura aura sa rekhA meM, hoM to aura sada kA gharAtala aura aba gaura basa ada kA dharAtala milakara barAbara haiM asa aura bada ke barAtala ka (68) eka sIdhI rekhA ko itanA bar3hAyI ki kula mIdhI rekhA bar3hI huI aura kisI dUsarI dI huI mIdhI rekhA kA dharAtala barAbara ho bar3e hue hine para vargaka (66) do samakoga samAnAntara caturbhujoM ke kSetraphala vyApama meM barAbara haiM aura unakI bhujoM ke yoga bhI Apasa meM barAbara haiM sAbitakaro ki vaha saba taraha se vyApasa meM barAbara haiM ( 70 ) agara kisI a ba sa tribhuja ka e zra va vyAdhAra ko ma+na narAvara hisma kiye kAMya aura agara ada meM na hi yara vada meM mahisma hoM to sAbitakaro ki 2 2 3 2 (71) ma x asa + na X basa (ma + na ) x mada + sa X da + na X bada ( 72 ) agara kisI a ba sa tribhuja ko aba AdhAra ko ma-navarAbara vhisase kice jAMya aura bagara baca ko da biMdu taka itanA baDhAyA jAve ki cchAda meM na hisse auaura va da meM ma hisse hoM to sAbita karo ki 3 2 (73) ma x yasa - na X basa - ( ma - ma ) x sakS + ma X graha - ma X bada (74) kisI diye hue ga biMdu se ehI tIna rekhA ga aura gasa dI huI lambAI ke khIMco ki unake sire aaura aura ba For Private and Personal Use Only ga ba aura sa sIdhI rekhA meM hoM aura aba barAbara ho basa ke (75) vyagara kisI a basa samakona tribhuja ko a ba ka ka da aura afgbyoM para tIna barAbara hisse kiye jAMya to sa da aura saya byaura daya para bargoM kA tigunA barAbara hogA a va parake varga ko chUne ko iti

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( 211 ) savAlAta imtihAna dUsarA adhyAya (1) DUmare vyadhyAya meM kina bAtoM para bahana kI gaI hai (2) mApaka kI tArIpha karo- ekahI samAnAntara caturbhuja meM ekahI banAvaTa meM kitane mApaka paidA hote haiM - una kA pharka batAo l (3) rekhAgaNita meM do yA jiyAdA sIdhI rekhAoM ke yoga se kyA mu rAda hai ( 8 ukaledadma ne dUsare adhyAya kI pahalI 8 sayoM ke sabUta meM kaunasI svayaMmiti ko mAna liyA hai ( 5 ) rekhA ke granta: khaMDa aura mahi: khaMDase kyA murAda hai ( 6 ) agara koI nIdhI rekhA do barAbara gaura do nAbarAbara hissoM meM bahi: khaMDa yA granta: khaMDa meM bAMTokAya to sAbita karo ki sIdhI rekhA ke bAhi: khaMDoM kA yoga yA anta: khaMDoM kA vyantara dUnA hai usa rekhA se jo bhAga vinduvyoM ke bIca meM hai (7) agara koI sIdhI rekhA do barAbara aura do nAbarAbara hissoM meM vAMThIjAya to sAbita karoki sIdhI rekhA kA vaha bhAga jo bhAga bindudhoM ke bIca meM hai nAbarAbara histoM ke antara ke vyAdhe ke barAbara hogA (8) gragara do nAvarAvara saudhI rekhAyoM ke vyAdhe yoga meM una ke antara kA vyAdhA joDa diyA jAya to yoga baDI sIdhI rekhA ke barAbara hogA aura gara una donoM sIdhI rekhAyoM ke vyAdhe yoga meM se una kA bAdhA antara ghaTA diyA jAya to bAkI choTI sIdhI rekhA ke barAbara hogA 1 (6) sAbita karo ki dUsarI aura tIsarI mAyA mahatI yAtrA kI khAkha marate haiM EN (10) DramarI aura tomarI sAdhA kA ekahI dAvA likho (11) dUsare adhyAya kI cauthI mAdhA ko dUsarI aura tIsarI sAdhA kI madada se bagaira zakala khIMce hue sAbita karo (12) dUsare adhyAya kI cauthI sAdhA kI sahAyatA se pahaye badhyAya kI 47 vIM mAdhA ko sAbita karo (13) sAbita karo ki yAra dUsare dhAya kI cauthI sAdhA meM donoM gUraka milakara barAbara hoM donoM vargo ke to dI huI sIdhI rekhA do barAbara hissoM meM baTegI (14) eka sIdhI rekhA kI kima taraha Ta kina ho kA bharAudha sabase bar3A ho For Private and Personal Use Only

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( 212 ) (15) dUsare vyadhAAya kI chaTI mAdhA pAMcauM sAdhA kI madada se phauran hI kisa taraha sAbita ho sakatI hai (16) cauthI aura sAtavIM sAdhA kA mukAbilA karo (17) mAbita karo ki do mIdhI rekhAoM ke yoga para kA varga unake antara para ke varga se vaqadara unake caugune dharAtala ke bar3A hotA hai (18) rekhAgaNita kI sahAyatA se mAbita karo ki do mIdhI rekhAyoM ke yoga aura antara para ke vaga una sIdhI rekhAyoM para ke bargoM se dUne hote haiM (16) eka tribhaja kI bhaja 13. 14, 15 haiM to una sIdhI rekhAyoM kI lamvAI batAyo jo usa tribhuja kI bhujoM ke bIcoM bIca ke binduoM se una bhujoM ke sAmane ke konoM taka khoMcI jAyagI gaura uma tribhuja ke lasboM ko mau lambAI batAyo aura yaha bhI sAbita karo ki usa tribhaja ke nInoM kona nya nakona haiM (20) dUmare adhAAya kI gyArahoM mAdhA ke ba sIdhI rekhA ke mutAbika bAMTI huI aura rekhAoM kI katAra kisa taraha dAfata kara makate haiM (21) rekhAgaNita kI 11 vI mAdhA meM aba rekhA kA choTA hissA diyA huA hai to bar3A hissA ryAphata karo (22) pahale pradhAya kI 47 vo sAdhA aura dUsare adhayAya kI 12, 13 sAdhA kA mukAbilA karo ( 23) eka bighama kona samacaturbhuja (a barga) ke kagA 16.13 phITa haiM to usake kisI bhuja kI lambAI batAyo (24) kisI tribhuja kI ja 8, 11, 15 haiM to mAbita karo ki vaha adhikakona tribhuna hai ( 25 ) kisI tribhuja kI bhuja 3, 4, 5 hai to batAo ki koMna jo 3, 4 ke darmiyAna aura jo 4, 5 ke darmiyAna aura jo 5, 3 ke darmiyAna hai vaha samakona se bar3A yA varAvara yA choTA hai (26) yagara dUsare adhayAya kI caudahA mAdhA meM diyA huyA Rjubhuja kSetra eka samakona vibhaja ho jimake bhuja 8, 6 haiM to vatAyo ki uma varga kI maja kitanI hogI jisakA kSetraphala una vibhaja ke barAbara hai aura yaha bhI sAbita karo ki varga ko mujoM kA yoga tribhuja kI bhujoM ke yoga se choTA hogA (27) hara Rjubhaja heva ke barAbara barga banA sakate haiM" una rana kAyatoM kA jinakI sahAyatA se ulla dasa ne jaba daje isa sAdhA ko gAvita kiyA hai ballayo For Private and Personal Use Only

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Shri Mahavir Jain Aradhana Kendra ( 213 ) maz2amUna ke mutAbika rekhAgaNita ke pahale aura dUsare adhyAya kI sAdhyoM kI phaharista 13 nambara sAdhya kalpita vyartha 11 anumAna | agara do rekhA aisI haiM ki vaha sIdhI haiM 14 13 granumAna 15 sAdhya prameyopapAdya koMna jo sodhI rekhAoM ke Apasa meM karane se banate haiN| www.kobatirth.org 15 pratiloma 13 anumAna 13 granumAna gregara eka sIdhI rekhA dUsarI sIdhI rekhA para khar3I hokara do kona banAye gragara do mIdhI rekhA fhat tIsarI sIdhI rekhAkI grAmane sAmane kI tarphe se vgrAkara eka hI bindu para mileM aura grAmanna kona barAbara do samakona ke banAveM gragara do sIdhI rekhA grAma meM kisI bindu pa Acharya Shri Kailassagarsuri Gyanmandir raka yagara do sIdhI rekhA Apasa meM kisI biMdu pa ra kaTeM cure cAra sIdhI rekhA! vyApasa meM kisI biMdu para milakara manmakha kona barAbara banAveM J arre koI sIdhI rekhA kisI sIdhI rekhA ke eka tarala se grAkara uma ke / kisI bindu para jo usa ke sire kA nahIM hai bhileM aura kone banAveM agara eka biMdu se kaI mIdhI rekhA nikale phala unakA koI hissA ubhayaniSTanahIM hotA yaha kona yA to donoM samakona hoMge yA milakara barAbara do sama kona ke hoMge yaha donoM sIdhI rekhA ekahI sIdhI rekhA yAnI ekahI sIdha meM hoMgI cAra kona jo usa bindu para baneMge milakara barAbara cAra samakona ke hoMge manmukha ke kona vyApasa meM barAbara hoMge pahalI sIdhI rekhA tIsarI sIdhI rekhA kI sIdha meM hogI baura dUsaro cauthI kI usa biMdu para ke saba kona milakara do samakona ke barAbara hoMge kona jo una rekhAoM se usa biMdu para baneMge milakara barAbara cAra ma makona ke hoMge For Private and Personal Use Only

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( 214 ) 28 dUsarA samAnAntara sIdhI rekhA nambara sAdhya kalpita artha phala agara eka sodhI rekhA yaha donoM sIdhI rekhA samAnAntara kisI do sIdhIrekhAyoM hoMgI para jo ekahI dharAtala meM haiM girakarasamAnAntara kona barAbara banAveM 28 pahalA agara eka sIdhI rekhA yaha donoM sIdhI rekhA samAnAntara histA kimI do sIdhI rekhAoM hogI para jo ekahI dharAtala meM haiM girakara vahi: kona apane grAmane sAmane ke aMtaH konoM ke barAbara banAveM agara eka sIdhI rekhA yaha donoM sIdhI rekhA samAnAntara do mIdhI rekhAyoMpara jo hoMgI hissA eka haudharAtala meM haiM gi rakaraapanI eka tarapha ke do aMta: kona aise banAne ki vaha milakara do samakona ke bArabara hoM agara eka mIdhI rekhA vaha rekhA una rekhAyoM ke sAtha ho samAnAntara mIdhI hissA ekAntara kona barAbara banAvegI rekhAnoM para gire 26 dUsArA ___ agara eka sIdhI rekhA vaha apanI eka tarapha kA bahiH hissA | do samAnAntara sIdhI re. kona aura usa ke sAmane kA aMta: khaoM para gire kona eka dUsare ke barAbara banAvegI 26 tIsarA agara eka mIdhI rekhA / vaha apanI eka tarapha ke do aMta: himA do samAnAntara sIdhI re kona aise banAvegI ki vaha milakara khAnoM para gire barAbara do sasakona ke hoMge gragara do sIdhI rekhAoM vaha donoM sIdhI rekhA Apana meM meM se haraeka kilo tI- bhI samAnAntara hogI sarI sIdhI rekhA ke samAnAntara hai 26 pslaa| For Private and Personal Use Only

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( 215 ) S - nambara sAdhya kalpita artha phala / agara do sIdhI rekhA | vaha donoM sIdhI rekhA bhI prApasa kimI do barAbara aura meM barAvara aura samAnAntara hoMgI samAnAntara maudhI rekhAtroM ke eka 2 tarapha ke sira ko milaa| vimajA kI barAbarI ke liye mukAbilA karanA agara do tribhuja ekahI sumakina nahIM ki unakI vaha vyAdhAra para aura usakI bhuja jinake sire aAdhAra ke eka ekaho tarapha meM hoM sire parahoM Apasa meM barAbara hoM aura vaha bhuja jina ke mireyAdhAra ke dUsare sireparahoMDApasa meM barA bara hoM 32 anumAna agara eka tribhujake do usa tribhuja kA tIsarA kona kona dUsare tribhuja ke bhI dUsare tribhuna ke tIsare kona do konoM ke barAbara hoM ke barAbara hogA vyagara eka tribhuja ke do bAkI kona aura mana bhI una kona dUsare tribhuja ke do tribhajoM kI alaga 2 barAbara hoMgI konoM ke alaga 2 varAvara aura tribhaja bhI prApasa meM barAbara hoM aura eka 2 bhuja bhI hoMge una tribhujoM kI barAbara ho khAha yaha bhuja barAbara konoM ke dabhiyAnako hoM yA unake sAmane kI kAgara eka tribhujakI do grAdhAroM ke mAmane ke kona Apasa bhaja dUsare tribhuja kI do meM barAbara hoMge aura barAbara bhajoM bhujoMke alaga 2 barAvara ke sAmane ke kona bhI prApasa meM hoM aura unake vyAdhAra barAbara hoMge aura donoM tribhuja bhI Apasa meM barAbarahoM bhI Apasa meM barAbara hoMge agara eka tribhujakI do bar3e AdhAra ke sAmane kA kona bhaja dUsare vibhAjakI choTe aAdhAra ke sAmane ke kona se bhujoM ke alaga 2 barAbara bar3A hogA hoM lekina eka tribhujakA mAdhAra dUsare tribhuja ke mAdhArase bar3A ho For Private and Personal Use Only

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( 216 ) - - nambara sAdhya kalpita artha agara eka tribhuja kI do tribhujoM ke grAdhAra Apasa meM bhuja dUsare tribhuja kI do barAbara hoMge aura AdhAroM parake bhujoM ke alaga 2 barAbara kona jinake mAmane ke bhaja barAbara hoM aura una bhujoMse bA| I Apasa meM barAbara hoMge aura tri. ne hara konabhI aApasameM bhaja barAvara hoMge barAbara hoM agara eka tribhuja kI bar3e kona ke sAmane kA AdhAra do bhuja dUsare tribhuja kI choTe kona ke mAmane ke AdhAra se do bhajoM ke alaga 2 varA-bar3A hogA bara hoM lekina eka tribhuja ke una bhujoM se banA huyA kona kaimare kI una bhujoM se bane hae kona se bar3A ho agara tribhuja eka grA- una tribhujoM ke rakabe barAbara hoMge dhAra para ekahI samAnAntara rekhAoM ke darmiyAna ho agara tribhuja barAbara una tribhujoM ke raqave barAbara hoMge AdhAroM para ekahI samAnAntara rekhAyoM ke / dabhiyAna hoM agara barAvara tribhuja / vaha tribhuja rakahI samAnAntara ekahI grAdhAra para aura rekhAyoM ke dabhiyAna hoMge usa ke ekahI tarafa meM 3 la... hoM agara varAvara tribhuja vaha tribhuja ekahIsamAnAntara reekahI mIdhI rekhA ke khAnoM ke darmiyAna hoMge barAbara aAdhAroM para aura usa kI ekahI tara phahoM agara barAbara tribhuja vaha tribhuja yA to ekahI AdhAra eka hI samAnAntara para yA varAvara grAdhAroM para hoMge rekhAoM ke darmiyAna hai 37 va 38 pratiloma For Private and Personal Use Only

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Shri Mahavir Jain Aradhana Kendra nambara sAdhya tathA damadamAna 18 5 anumAna 32 anu06 da anumAna 16 pakSamA histA 70 pratitola 13 adhyAya pratiloma www.kobatirth.org ( kalpita artha aura bagaravarAvara su bahAvI bArya ravibhuja namakIna vivAha bAra kisI vibhuja kI eka guNa dUtarI tumase par3I hai cAra tribhuja samatibAhu hai agara tribhuja samahi / 207 vAha agara vibhuNa samAna kona hai yagara visuna kI eka nAgara vimuca phona suja bar3hAyI jAya yam vibhuNa kI eka bhana bar3hAyI jAva mama upa vinaSa pana guNa para kA nahIM barAbara hai una vI ke jobA para bAvAyeM gaye hai agara kisI barAja kI kimI guNa para kA banA vAcA varga bar3A hai bAkI do mukha para va bAye kucha vargoM ke yoga se agara vibhu kI za so muja para kA banAyA hunyA baga choTA hainA kI do supara ke nAye dA vargoM ke yoga ; Acharya Shri Kailassagarsuri Gyanmandir AdhAra ke bI meM gavara hoga AdhAra para kAphI pAla yA namakIna hai maja ke sAmane kA kona hodAmane ke kauna se bar3A hogA vaha vibhaga samAna koSa bhI hai usa kA eka kona namakInakA do vidhA sa fear bhI hai: ba: kona apane sAmane harayogA kona se bar3A doSa kona apane sAmane se donoM aMtaH konoM ke barAbara doga varga zrI samakoNa kI sA para banAyA zrAyAro unake vo bAkI pa | vAye jAyeMge usa se bAnane kA kona hai saguNa va nAle kA dhika dona suNa ke sAmane kA kona yA kona hai For Private and Personal Use Only Le

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( 18 ) A nimmmmmmmmmw-- sIdhI rekhA jo vibhuja ke andara khIMcI jAyaM nambarasAdhya kalpita artha 38anumAna vyagara tribhuja kI ki- vai sIdhIrekhA tribhuja ke do barA sI bhuja ke vIvoM vIca | para histe karegI kI bindu se usa ke sAmane ke konataka rekhA khIMcI jAya grAra nizuja ko vyApAra yaha donoM rekhA milakara tribhuna ke siroM se do rekhA ki- ko bAkI bhujoM se choTI hoMgI lesI viMda taka jo tribhaja kina rekhA se banA huyA kona gara hai khIMcI jAya bhujoM se bane hue kona se bar3A hogA jAgara ji ko una adhikA kona ke sAmane kI maja / bhajI meM se jo bAdhika para kA varga bAkIdIma joM para ke kona ke gida 3 kimI bge| ke yoga se bar3A hAgA .kadara ja bar3I huI para usa usa dharAtala ke dUne ke jo usabhu - ke sAmane ke konase laM- jase jisa para laMba girAyA gayA hai ba girAyA jAya aura uma ke usa bahara hisse se jo darmiyAna adhika kona aura laM ba ke hai banatA hai 13cya dhAyara agara kisI tribhuja kI uma nyUna kona ke sAmane kI bha ja una bhajoM meM se jo nyAna- para kA vA choTA hogaH bAkI do kona ke gida hai kisI bhujoM para ke bagAM ke yoga se bakadara maja yA uma bahI haI uma dharAtala ke dAne ke jo umabha - bhaja para usa ko bhAmane | jase jisa para laMda mirAyA gayA ke kona se laba girAyA aura usa rekhA se jo usa nyanako - jAya na aura laMba ke darmiyAna hai vanatA hai samAnAntara caturma ja aura tribhuja kA mukAbilA agara sama ntira ca- mabhAgAntara catula ja tribha ja se turbhaja aura tribhuja e-dunA hogaa| kahI AdhAra aura ekahI samAnAntara rekhAyo ke darmiyAna hoM 41 anumA0 agara samAnAntara ca- samAnAntara catuma ja libhaja tubha ja aura tribhu na varA- dUnA hogA AmARILALLADINomanimoonaanam 41 For Private and Personal Use Only

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( 218. ) 1 - .-. - nambara sAdhya kalpita atha phala bara yAghAroM para ekahI mamAgAntara rekhA goM ke darmiyAna hoM 41 patilo bhAra manAnAntara cata- rUsAnAntara caturbhaja aura vimaja maja aura timaja eka ekahI samAnAntara rekhAkoM ke T. ho aAdhAra para yA eka siyAna ho| hI sIdhI rekhA ke va rAbara grAdhAroM para ho gaura samAnAntara caturmaja tribhuja se TUnA ho 42 yatilo- agara mamAnAntara catu- samAnAntara vitu yora tribhuja ma2 bhuja aura trirAja eka thA to gavAhI yAcAra para yA hI namAnAntara rekhA barAbara vyApAroM para hoMge yoM ke darmiyAna hoN| aura mamAnAntara catu muMja tribhuja se TUnAho samAnAntara caturbhajoM kA barAbarI ke liye mukAbilA karanA agara samAnAntara catu- vaha samAnAntara catuja aApala bhaja ekahI gAdhArapara meM barAbara hoga aura kahI samAnAntara rekhAyoM ke darmiyAnahIM 35pratiloma __ vyagara barAbara lamAnA- vaha samAnAntara catuma ja ekahI | ntara caturbhaja ekahI samAnAntara rekhAoM ke darmiyAna vyAdhAra para aura usake hoMge | ekahI tarapha meM hoN| / bAgara mamAnAntara catu-vara samAnAntara manuja vyApana bhaja barAbara vyAdhAroM meM barAbara hoMge para aura eka hI samA.. nAntara rekhAgoM ke darmi yAna ho 66 pratiloma agara barAbara samA- baha samAnAntara caturbhaja eka hI gAtara catarbhala eka hI samAnAntara rekhAyoM kI darminAna hoMge mIko rekhA kA barAbara sApAsa para 't For Private and Personal Use Only

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Shri Mahavir Jain Aradhana Kendra nambara sAdhya 25 va 26 pratiloma ma 1 pamitI ma samAnAntara caturbhuja kI gujoM kAnoM aura gharAtaloM ke Apasa ke tathA 3 49 vilo bagara kisI catu kI ghAsa sAvAne anumAna PS3 www.kobatirth.org p j kalpita artha agara bAbara kamAnA tara caturbhuja rAhI sAmAntara rekhA ke darmitI kadavyAya kI galI nA kona barAvarahI bAgara kisI patna na kA vI gharAta kArya una dIDa a a padAvarahI 3 sAgara kimI calAuja samAnAntara caturbhuja lai savara hI kare agara koI kSetra bAntara catuma, go kamara sajAnAntara pa tasa kA eka kIna namakIna hai agara samAnAntara bhA 2yacAva ka vyagara koI vIvI phala yaha mamAnAntara caturbhu'na yA to hI vyAdhAra para yA barAvara vyAdhAroM para hoMge se hiMsA meM baDhI se Acharya Shri Kailassagarsuri Gyanmandir ghagarakoI sIdhI re se meM nI vaha caturbhuja samAnAntara catuma, pa hogA rAma kI kahAi se cIra pavAra camana hai AyatoM kA jo sIdhI rekhA cIra caturbhuja rAmArAkara caturbhu $171 usakI sAmane nAmane kI gaNa Apaka kara hogI aura usake zAmane zAsana ke kI bhI barAbara phoye cIna unakA hara kama usake do barasa kA samaya ko kIna ho unake barAbara kSatri 11 se banate kula sIdhI rekhA aura unake paraeka sirpha ke milakara barAbara hai sauMdhI yA parake bhAta gIdhI rekhA aura unake eva hi kA parAmara For Private and Personal Use Only

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( 221 ) ave - nambarasAdhya kalpita artha hirasoM ke dharAtala ke pAdhyAya agara koI sIdhI rekhA ala sIdho rekhA parakA vargavarAhimma meM vaTIvara donoM himaloM parake varga aura ! unahissoM ke dune dharAtala ke yoga ke 7 vyadhyAya : nAgara koI mIvIrekhA to kula sIdhI rekhA para aura do hissoM meM baTI hai usake eka hisse parake ko mila kara barAbara meM kula rekhA aura usa ke usa hisse ke dUne dharAtala aura gare hinA parako varga ke 8 vyadhyAya 3 agara koI sIdhImA kula bhIgI kA gaura urake do hissoM meM bAika dina kA caugunA barAlala aura dUsare hisse para kA yA milakara barAka hai una jara ke varga ke jo dhIre pahale hisase se to pAra mAra ko sIdhA sA pAsa donavara hissoM bhokara mAra do mAsa kAra kA ko kArakiloM bhakto zAdiyoM ko naI rika mAyAko khAkAmAvara kasA parI barI doyagAvara dhaura ko nA zikAra hune hai sonI rekhA ke rAmarahima meM gaDI bAdhe dhara aura usa rekhA parako nIlo mAga dieko dakSiAko / yadhyAsa. umara kA loko rkhaa| bAla yA hAI sIdhI jA / barAmara hiramoM meM sarakAra hamI kA karatAta kI aura kisI aura sIdhI rekhA ke aAdhe paramA manukA kAyo rAmI baga sikAra barAbara hai usa rekhA para ke varga ke jo sIdhI rekhA ke khAye aura kAhise banI 10 zrApa / nagara ko lIjI rekhA : bI huI ana sIdhI resA para kSerAmA nistoM meM paTI aura bAhue hinA kara ke kaI ko kilIna pikAra sIdhazAkekAle para unakI mAM ke misa sahA For Private and Personal Use Only

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( 222 ) nambarasA dhya kalpita atha phala 1 adhyAya agara do mIdhI rekhA- do sIdhI rekhAoM kA dharAtala oM meM se eka kaI hi-barAbara hai una dharAtala ke yogaka moM meM baTI hai jo kula do barI repa aura haraeka hissa baTI huI se barI hai bahubhuja kSetra 32 anu- agara koI Rjubha ja / usake maba aMta: kona aura cAra mAna 1 kSetra hai lamakona milakara utane samakonoM ke barAbara hoMge jo ginatImeM usa kI sajoM kI tAdAda se Trene hoMge 32 anumAna agara kimI Rjuja saba bahiH kona jo mujoM ko ba kSetra kI saba maja eka pAne se bane 'ge milakara cAra samadUsarI ke bAda eka hI kona ke barAbara hoMge dizAmeM bar3hAyI jAyaM / sAdhyavastapapAya nambarasAdhya nirdiSTa sIdhorakhA karaNIya eka parimiti miidhii| usa biMdu se usa rekhA kI barAbara rekhA aura eka viMTarekhA khIMcanA eka sIdhI rekhA aura uma biMduse una mIdhI rekhA ko eka biMdu samAnAntara rekhA khIMcanA do choTI bar3I mIdhI bar3I sIdhI rekhA meM se choTI sI. dhI rekhA ke barAbara kATanA eka sIdhI rekhA usa rekhA ke do barAbara hisse karanA 11 adhyAya eka sIdhI rekhA uma mIdhI rekhA ke naze se do hi. sse karanA ki dharAtala kula sIdhI rekhA aura eka hisse kA barAbara ho dUsare himsa paraka varga ke saralakona eka sarala kona aura usa rekhA ke una biMdu para usa kona eka sIdhI rekhA aura ke barAbara kona banAnA usameM eka biMdu eka saralakona umma koga ke do barAbara hisse karanA eka mIdhI rekhA aura usa bisT se eka romI sIdhIrekhA usameM ekA biMda rekhA For Private and Personal Use Only

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( 223 ) - nambara sAdhya kalpita artha phala khauMcanI hai ki vaha usa rekhA ke sAtha samakona banAve eka aparamita sodhI / 'usa viMda se usa rekhA para laMba rekhA aura usake bA- DAlanA hara eka biMdu (tribhuja) tIga sIdhI rekhA jina- aisA trimuja banAyo ki jisakI meM se hara eka do mila- muja una rekhAtroM ke alaga 2 kara tIsarI se bar3I haiN| barAbara hoM eka pamiti sIdhI rekhA usa para samalibAhu tribhuja banA. nA hai (samAnAntara caturbhuja) eka tribhuja aura eka tribhuja ke barAbara eka aisA samAsaralakona nAntara catuja banAnA ki usakA eka kona usa kona ko barAvara ho eka sIdhI rakhA eka usa rekhApara usa vimuja ke barAvija aura eka larala- bara rosA sasAnAntara calubhuja kona | banAnA jisakA eka kona usa ko na ke barAbara hobe eka Rtu aura uma Rjamaja kSetra ke barAbara eka rAka sarala kona aisA samAnAntara catuma ja banAnA ki usakA eka kona usa kona ke barAbara ho pAnamAna eka sIdhI rekhA aura usa rekhA para usa Rjumaja kSetra eka RjumajakSetra aura ke barAbara zesA samAnAntara catueka sarala kona | ma ja banAnA ki usakA eka koga usa kona ke barAbara ho eka parimita siidhii| usa rekhA para bA banAnA rekhA 14adhyAya eka namunakSetra umake barAbara eka varga banAnA iti For Private and Personal Use Only

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C . . IT17 TFTTH QiG6BCEASY ACAC For Private and Personal Use Only

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sarI yaura para hAI skUla alavihAra meM mAmalA gauce likhI huI kivAveM bikriyArtha hamAre pAsa maujUda hai aura hara eka kitAba kI kImata usake sAmane dana hai hisAba kitAba ke himo badajiba naye gavarmenTa raz2oliyUzana phira taramIma kiye gaye hai aura savAlAta mutafarika banAye gaye haiM mambara mAma kitAba kImata (1) yUliDa ( pahilo aura dUsarau buka eka jilTa meM ) mauli bAbU AtmArAma bI, e. haiDamATara hAI kala alIgar3ha (2) yUkliDa ( tIsarI yaura cauthI buka eka jilTa meM) , (3) taharIra ukaleTsa mikAlA abbala mikAlA doyama , (4) taharIra ukleTsa nikAlA aJcala va doyama , (5) rekhAgaNita 1 adhyaay| , 2 azzAyA, 1 vyaura adhyAya , (6) ilaulanatAyA ( uda) jinameM bAyU aAtmArAma bI. e. taharIra uphUledasa kA hala hai mau0 bAbU dugAM pramAda sI iba' (7) ilaulagatAyaja hindI jisa meM rekhA gaNina kA hala hai (8)hisAbakitAba urdU kulara zikhara meM mau0 bAyU AtmArAma bI.e (..) hisAba kitAya hindI) hisAbakitAudo nimA 1 hissA hitA (26) hisAba kitAba likhI (13) , 500 4 . . (16) . En . (15) , , , // (21) . 6 . jo sAhaba pAMca rupaye yA z2iyAdA kI kitAbeM kharIdeMge una kAmozana dasa to nadI aura jo ma po yA jibhAdA kI kharauM umako bIma fo sadI ke hisAba se kATa diyA jAyagA mahamUla Da z2imma kharIdAra hai sivAya he umAdarAna jilA skala va DipaTI / paikarAna madArima ke saba parIkSAroM ne kImata nakadala jAgI ba haiDamAerAna va DipI zAsakrAna ke kImata adA karane ke liye mAha kI mauhalata hai lakSmInArAyaNa kakkar3a nAja ko khir3akI Aga For Private and Personal Use Only

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