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

446 latitude. The Vitribha then being in the zenith, and its latitude being 4½°, the Dṛk-kṣepa of the Moon according to Brahmagupta's formula will be 4½° and therefore the parallax in latitude obtained by the Dṛk kṣepa will be (790'-35 / 15) × (H sin 4½° / 3438) = (52'-42'' / 3438) 270 = 4'-8" which is not the case actually. Comm. Having thus shown the flaw in Brahma- gupta's approximate formula, Bhāskara proceeds to show how that formula could be justified in a particular way. Brahmagupta assumed the Moon's orbit to be the ecliptic because at the moment of an eclipse, the latitude of the Moon is very small so that he might be taken to be on the ecliptic. In figure 101 let the Ecliptic coincide with the prime-vertical ZE. Let EV be the Moon's orbit where V is the Vitribha of the Moon's orbit. The arc of the Sun's Dṛk-kṣepa is here zero and that of the Moon's Dṛk-kṣepa is ZV which is the sum of the arc of the Sun's Dṛk kṣepa namely zero and the latitude of the Moon's Vitribha namely ZV, since the pole of the ecliptic now coincides with the south point S, which means that ZV is the latitude of V. Let VV' be the nati which is equal to AB, since V'A is the so-called Vikṣepa Sadṛśamaṇḍala or the deflected position of VE on account of parallax in latitude. The four minutes of parallax in latitude is now VV'=AB. This parallax is obtained because, Bhāskara argues, the nati obtained by Brahmagupta is there because he took VE to be the Ecliptic and so obtained that nati with respect to VE. Now, Bhāskara says, this is to be corrected by the difference of the Moon's latitudes the original one and that obtained after the Moon is deflected by the parallax in longitude. This difference is 0-AB=BA. Correcting AB with BA, the result is AB+BA=0 so that ultimately