Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

Page 480

CHAPTER IX-CALOULATIONS RELATING TO SHADOWS. 283 square of the (given) shadow. This (remainder) is to be multiplied by the sum of the square of the human shadow and one. (The quantity so arrived at) is to be subtracted from the square of the (given) shadow. The square root of this (resulting remainder) is to be subtracted from the (given) measure of the shadow; and, when (the quantity thus obtained is) divided by (the sum of) one and the square of the human shadow, there results exactly the measure of the inclination of the pillar.
An example in illustration thereof.
34. The human shadow (at the time) is twice (the human height). The shadow of a pillar, 13 hastas in height, is 29 (hastas). What is the measure of the slanting of the pillar here?
(General Examples).
35-37. A certain prince, staying in the interior of a palace, was, (at a certain moment) in the course of a forenoon, desirous of knowing the time elapsed in the course of the day, as also the measure of the human shadow (in terms of the human height). Then, the light of the sun coming through a window at a height of 32 hastas in the middle of the eastern wall fell at a place on the western wall at the height of 29 hastas. The distance between those two walls is 24 hastas. O mathematician, if you have taken pains (to acquaint yourself) with shadow-problems, calculate and give out the measure of the time elapsed then, on that day, and also the measure of the human shadow (at that time in terms of the human height).
381-39. At the time when, in the course of a forenoon, the human shadow is twice the human height, what, in relation to a (vertical excavation of) square (section) measuring 10 hastas in each dimension, will be the height of the shadow on the western wall caused by the eastern wall (thereof)? O mathematician, give out, if you know, how you may arrive at the value of the shadow that has ascended up (a perpendicular wall).
35-37. This example bears on the rules given in stanzas 8 and 23 above. 38-39. This example has to be worked out according to the rule given in stanza 21 above.