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

493 180-MES, so that (1+ cos EMS) / 2 = (1 —cos MES) / 2 which may be taken to be an approximate truth. This ‘formula was indeed given by Lallācārya in the following verse, long before Bhāskara. “रविशीतकरान्तरांशजीवा विपरीता शशिखण्ड- ताडिता च, विहृता त्रिमजीवया सितं स्यात् शशलक्ष्माङ्कवदङ्गुलानि तस्मिन् ” verse 12 (Candra Sṛṅgonnatyadhikāra). Here विपरीता रविशीतकरान्तरांशजीवा mean Hvers ξ = |R—H cos ξ. शशिखण्डता- डिता = multiplied by the radius of the disc of the Moon. विहृता त्रिमजीवया = divided by R. Thus the formula given by Lallācārya amounts to r (R—H cos ξ) / R = d/2 (1—cos ξ) where r gives the angulas in the radius of the Moon's disc and d the diameter, and ξ = elongation of the Moon. Since the definition of phase in modern terms is a ratio, namely the ratio of the maximum width of the crescent to the diameter, phase × d = Sukla of the Hindu astronomers ∴ (1 — cos (elongation of the Moon)) / 2 × d = Sukla = r (1 —cos MES) as given by Lallācārya. So Lallā- cārya's formula is quite correct. We shall trace Lallā- cārya's steps in obtaining such an intricate correct formula which was overlooked by Bhāskara. (Refer fig. 118) Let E be the earth, S the Sun and M₁, M₂, M₃ etc. the positions of the Moon as the elongation gradually increases. No doubt the Sukla increases with elongation as known to all Hindu astronomers. But, the question is, does it increase with the sine or versine? We know both the sine and versine increase with the angle. Lallācārya noticed that Sm₁, Sm₂, Sm₃ as the Moon occupied positions M₁, M₂, M₃ etc., are the Hindu versines which are increasing. So he postulated that the Sukla increases with the Hindu versine. His formulation was thus correct. But why Bhāskara overlooked this correct formula was traceable to his getting prejudiced