सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

277 Anya, we could put Anya = A² - H sin² a. As a matter of fact in verse 50, we are asked to take H sin² ~ A², as Bhāskara wanted that the second case also be included. Thus putting Anya = A² - H sin² a, equation I becomes K² (A² - H sin² a) - 2 AsRK = - (Adya) so that K = Anya ± √(Anya² - Adya) as given. Verse 52. The Bhuja is to be obtained through Karṇāgra from the equation a = b + s (already proved) and Rb / S = H sin a {ie. S = bR / H sin a as already proved}. This H sin a will be the same in the case of obtaining two values of K ie. two shadows one in the morning and the other in the afternoon, (the only difference being that they will be on alternate sides of the East-West line). Verses 53 and 54. Obtaining the shadow when time is given. In the two previous examples the magnitude of the shadow was obtained in a given direction ; now we shall obtain the same when time is given. The word unnata stands for the time that has elapsed after Sun-rise or that which is the balance of the day time. The unnata sub- tracted from half-the-day gives what is called Nata. The H sine of the unnata minus Chara or increased by the Chara according as the Sun's declination is north or south, is called Sūtra ; this multiplied by the H cos δ and divided by the radius, is called Kalā. Comm. (Ref fig. 51) The time measured by the arc MN, that is the time in between the moment when the Sun S is on the horizon and the moment when he is at L is called the unnata ie. the time measured after rising and the time measured by the arc NQ ie. the time in between