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

537 Let us consider the case of Vyatipāta. Suppose at the moment concerned, the declinations are of opposite direction. Find the sum of their numerical magnitudes. Suppose they are of the same direction; find their differ- ence. This sum or difference of the declinations gives the distance between the planes of the diurnal paths of the Sun and the Moon. This distance is to vanish in order that the diurnal paths may coincide. So we are asked first to find the above distance. Suppose we understand that the Vyatipātha has elapsed by noting the deolinations. This may be known easily by the criteria given previ- ously. Supposing 𝑥 and 𝑦 to be the declinatious of the Moon and the Sun and supposing that 𝑥 is on the decrease and approaching 𝑦, then the Vyatipātha is to occur. But suppose 𝑥 < 𝑦 and 𝑥 is on the decrease, then the Vyatipāta has taken place. Thus knowing whether the Vyatipātha has elapsed or is to occur, after an arbitrary time 𝑡, com- pute the declinations of the Sun and Moon and form their difference or sum as the case may be which gives the distance between the diurnal paths. Let the first distance found be called Ādya and the second distance the Anya. Then the Anya will be less than the Ādya because we have taken a time towards the occurrence of Vyatipāta when the distance is to get nullified. Find the difference of the Ādya and Anya. Then by the proportion “ If in time ‘𝑡’ taken in between the moments of the Ādya and Anya, the distance between the diurnal paths is reduced by Ādya — Anya, what time will be taken for the distance Ādya to vanish ?” we have the result T = (Ādya × 𝑡) / (Ādya — Anya) which gives approximately the time that has to elapse for the occurrence of the pāta. This will be approximate. After a lapse of time T from the Ādya moment concerned, again compute the declinations and repeat the procsss. We arrive at a particular point of time, which gives the moment of occurrence of the pāta. 68