278 GANITASARASANGRAHA. An example in illustration thereof. 13. A prize-fight between gymnasts began in the forenoon, when the shadow was cqual in measure to the style. (Its) conclusion took place in the afternoon, when (the measure of the shadow was) twice (that of the style) What is the duration of the fight? An example in illustration (of the rule) in the latter half (of the stunza). 14. The shadow of a pillar, 12 hastas (in height), is 24 hastas in measure. At that time, O arithmetician, of what measure will the human shadow be ? The rule for arriving, at the period (of the day elapsed or to elapse), in places having the equinoctial shadow, when the measure of the shadow at any time is known :- 15. To the measure of the known shadow (of the style) the measure of the style is added; (this sum is) diminished by the measure of the equinoctial shadow, and (the resulting difference is) doubled. The measure of the style divided by the quantity (so arrived at) gives rise to the value of the portion of the day (elapsed) in the forenoon, or (to elapse) in the afternoon, (as the case may be). An example in illustration thereof. 16-17. In the case of a style of 12 ungulas, the (equinoctial) noon-shadow is 2 angulus, and the known shadow (at the time of observation) is 8 angulas. What portion of the day is gone, or what portion (yet) remains? If the portion of the day (elapsed or to elapse) happens to be , what are the ghates (corresponding to it), the duration of the day being 30 ghatis? a 15. Algebraically the formula given here for the measure of the time of the day is 2 (s+ae) where e is the length of the equinoctial shadow of the style. The formula is obviously based on the formula given in the note to the rule in stanza 8 above.
पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/४७६
एतत् पृष्ठम् अपरिष्कृतम् अस्ति
