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 481

284
GANITASĀRASANGRAHA.
The rule for arriving at the shadow of a style due to (the light of) a lamp:
40. The height of the lamp as diminished by the height of the style is divided by the height of the style. If, by means of the quotient so obtained, the (horizontal) distance between the lamp and the style is divided, the measure of the shadow of the style is arrived at.
An example in illustration thereof.
413-42. The (horizontal) distance between a style and a lamp is in fact 96 angulas. The height of the flame of the lamp (above the floor) is 60 (angulas). O you who have gone to the other shore of the ocean of calculation, tell me quickly the measure of the shadow due to the flame of the lamp, in relation to a style which is 12 angulas (in height).
The rule for arriving at the (horizontal) distance between the lamp and the style :
43. The height of the lamp (above the floor) is diminished by the height of the style. The (resulting) quantity is divided by the height of the style. The measure of the shadow of the style, on being multiplied by the quotient so obtained, gives rise to the (horizontal) measure of the intervening distance between the style and the lamp.
An example in illustration thereof.
44. The shadow of the style is 8 angulas (in length). The height of the flame of the lamp (above the floor) is 60 (angulas).
40. Algebraically stated the rule.
is
b-a 8=0- ; where s is the length
a
of the shadow of the style whose height is represented by a, b is the height of the lamp above the ground, and c the horizontal distance between the lamp and the style. The formula may be seen to be correct by means of the diagram here given.
43. Using the same symbols, c = 8 x
b
b-a
a
44. The given measure of the height of the style is 12 angulas, vide stanzas 46-47 below.