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 473

276
GANITASĀRASANGRAHA.
drawn which will extend from north to south. The straight line ranning through the middle of the angles of this (fish-shaped figure) represents of itself the northern and the southern directions. The intermediate directions have to be ascertained as being derivable from half the interspace between these) directions.
47. The (measure of the) equinoctial shadow is indeed half of the sum of the measures of the shadows obtained at the middle of the day-time (or noon) on days when the sun enters the sign of Aries as also the sign of Libra.
52. In Larkā, Yavakāti, Siddhapurī, and Rūmakāpurī, there is no (such) equinoctial shadow at all; and, therefore, the day-time is of 30 ghatās.
63. In other regions, the day-time happens to be longer or shorter hy 30 ghatīs. On the days of the entrance of the sun) into Aries and into Libra, the day-time is everywhere of 30 ghatīs (in duration).
77. Having understood the measure of the duration of the day. time and also of the shadow at (noon or) the middle of the day according to the way described in astronomy, one should learn herein the calculations regarding shadows by means of the collection of rules hereafter to be given.
The rule for arriving at the time of day, on knowing the measure of the shadow of a given style at a given time in the forenoon or afternoon) in relation to a place where there is no equinoctial shadow :--
8}. One is added to the measure of the shadow (expressed in terms of the height of an object), and the sum 80 resulting)
8. If a be the height of the object and , the length of its shadow, then the time of the day that has elapsed or has to elapse is, &coording to the rule given here, equal to 1
, where A is the angle repre. 2 (cot. A + 1)
senting the altitude of the sun at the time. It may be seen that this formula gives only the approximate value of the time of the day in all cases except wben the altitude is 45', and that the approximation is very rough only in the case of large altitudes, pearing 90°. The forma la seems to be based on the fact that for small values the angles in a right-angled triangle are approximately proportional to the opposite sides.