ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

118 INDIAN LUNI-SOLAR ASTRONOMY 160' R sin [θ – (a – 90°)] R vers (D – a) × R sin (D – θ) = ∓ ----------------------------------------------------------- R (H – R) × R 160' R cos(θ – a) × R sin(D – θ) R vers (D – a)¹ = ∓ ---------------------------------- × ----------------- R × R H – R This equation is a slightly modified one but practically the same in form as that of Mañjula, except that the constant here is 160', greater than his by 16'. The constant is 160' also in Candraśekhara's form as we shall see later on. We next consi- der the Moon's inequalities as given by Bhāskara II in his Bījo- panaya,* a special work on these inequalities composed in the Saka year 1074 (=1152A.D.) two years after he had composed the Siddhānta Śiromaṇi. Bhāskara II on Moon's Inequalities His preliminary statement runs thus .— 112' positive or negative representing the maximum difference. have been found by me in the daily obser- ved Moon (as calculated and as observed) at that point of the ecliptic where the arc from the kadamba (i.e., its pole) passing through the zenith cuts it.¹ Thus for observing the Moon he selected the nonagesimal as the suitable point where the uncertainty about her parallax is zero, and found ∓112' of arc to be the maximum difference bet- ween her calculated and observed places. Mallabhaṭṭa, perhaps a contemporary of Bhāskara II, ascribed this difference to a supposed Śīghrocca of the Moon. Bhāskara in stanzas 9-13, refutes the existence of the Śīghra in the case of the Moon, the substance of his argument begins (i) that it is against the teaching of the Sūrya-siddhānta and other accepted authorities, (ii) that there is no variation of the apparent angular diameter of the Moon corresponding to this alleged Śīghra, and (iii) that planets having a Śīghra have retrograde motion which is never the case with the Moon.

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*There is some uncertainty, about this new fraction introduced by Śrīpati.

1. लिप्ता विधोरर्के महीमिता मे दृग्गोचराः प्रत्यहमीक्षितस्य । कदम्ब गोलगत-सूत्रपाते क्रान्तौ धनर्णत्वजुषो भमध्यात् ॥ – Bijopanaya, stanza 8