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 425

CHAPTER VII-MEASUREMENT OP AKRAS.
228
The rule for arriving at the longish quadrilateral) figura associated with a diagonal having a numerioal value optionally determined :
1221. Each of the various figures that are derived with the aid of the given (bijas) is written down; and by means of the measure) of its diagonal the measure of the) givon diagonal is divided. The perpendioular-side, the base, and the diagonal (of this figure) as multiplied by the quotient (here) obtained, give rise to the perpendicular-side, the base and the diagonal (of the required figure).
An example in illustration thereof. 1231-1241.0 mathematician, quickly bring out with the aid of the given (bijas) the (value of the) perpendicular-sides and the bados of the four longish quadrilateral figures that havo respectivoly 1 and 2, 2 and 3, 4 and 7, and 1 and 8, for their bijas, and are also oharacterised by different basee. And, (in the problemn) boro, the diagonal is (in value) 65. Give out (the measures of) what may be the (required) geometrical figures in that caso).
The rule for arriving at the numerical values of the base and the perpendicular side of that derived longish quadrilateral figure, the numerical measures of the perimeter as also of the diagonal whereof are known :--
1251. Multiply the square of the diagonal by two; (from the resulting product), subtract the squaro of half the perimotor; (then) get at the square root of the resulting difference). If (this square root be thereafter) utilized in the performanco of the
1291. The rule is based on the principle that the sides of a right anglod triangle vary as the hypotonune, although for tho samo neanuro of the hypo. tangse there may be different sets of values for the sides.
1864. If a and 6 represont the sides of rectangle, then a+b in thu meagare of the dingonal, and 2a + 2b is the measuro of the perimotor. It can be been esily that
These two formales represent algebrsically the method donoribed in the rule hero,