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

188 stated in the ancient texts ; let people verify this by actual observation". Accepting an Ayanāṁsa which goes against the statement of this great astronomer, who said that he observed and called upon others to observe, is really unwarranted, especially when the adopted Ayanāṁsa of the Calendar reform committee goes on the basis of surmises and consensus. We shall deal with this topic in further detail in an appendix to this work, because it is a really important issue and has been wrongly solved. The importance of knowing the exact value of the arc is clear when we observe that from the correctly computed planetary positions of modern astronomy this ayanāṁsa is being subtracted to give the positions measured from the Zero-point of the Hindu Zodiac. An error in the Ayanāṁsa therefore vitiates the positions obtained by the above method. Coming to the point, the problem on hand is to obtain the rising times of the Sāyana Rāśis at a place of zero latitude i.e. what are called Laṅkōdaya times of Sāyana Rāśis (Ref. fig. 21). Let rS = 30° so that rA the equatorial arc gives the rising time of rS. We could have the magnitude of this arc by the formula derived from Napier's rules namely cos ω = tan α tan λ I. But as in Hindu trigonometry the tangent functions of angles are not used, Bhāskara gave the following formula Sin α = √(sin² λ − sin² δ) / cos δ II. This formula could be derived easily from formula I and the formulae cos λ = cos α cos δ III and sin δ = sin λ sin ω IV ; for multi- plying the right-hand sides of I and III we have cos ω cos λ = (sin α cos δ) / tan λ i.e. sin λ cos ω = cos δ sin α ∴ sin α = (sin λ cos ω) / cos δ V. But from IV sin ω =