Ganitasara Sangraha of Mahavira

SR No.: 011112
Original Sutra Author: N/A
Author: Rangacharya
Publisher: Rangacharya
Publication Year: 1912
Total Pages: 531
Language: English
Classification: Book_English
File Size: 24 MB

Page 411

CHAPTER VII-XBASUREMENT OF AREAR.
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Subject of treatment known as the Janya operation.
Hereafter we shall give out the junya operation in caloulations relating to measurement of areas. The rule for arriving at a longish quadrilateral figure with optionally chosen numbers as bijas :--
902. In the case of the optionally dorived longish quadrilateral figure the difference between the squares (of the bija numbers) constitutes the measure of the perpendicular-side, the product (of the bija numbers) multiplied by two becomos tho (other) side, and the sum of the squares (of the bija numbers) becomes the hypotenuse.
Examples in illustration thereof. 911. In relation to the geometrical figure to bo derived optionally, 1 and 2 are the bijas to be noted down. Toll (me) quiokly after calculation the moasurements of the perpendicular-side, tho othor side and the hypotenuso.
927. Having noted down, 0 friend, 2 and 3 as the bijax in rolation to a figure to be optionally derived, give out quickly, after caloulating, the measurements of the perpendicular-wido, tho other side and the hypotenuse.
Again another rule for constructing a longish quadrilateral figure with the aid of numbers denoted by the name of bijas:
937. The product of the sum and the difference of the bijas forms the measure of the perpon lioular-side. The sankramana of
201. Janya literally means "arining from" or "ant to be derived", hence it rofors here to trilateral and qundrilateral figuren that may be dorivo out of certain given data. The operation knowo 48 junya relates to the finding out of the length of the sides of trilateral and quadrilateral figuram to be no derived.
Bija, a given bere, generally happens to be a puitive integer. Two such are invariably given for the derivation of trilateral and quadrilateral tigures dependent on them.
The rationale of the role will be clear from the following algebraicei representation :
If a and bare the bija numbers, then a win the measure of tho perpendi. cular, 2 ab that of the other side, and a + b that of the hypotenone, of o oblong. From this it is evident that the bijas are norbers with the aid of the prodnot and the squares wheroof, w forming the measures of the eldes, right. angled triangle may be oonstructed.
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