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

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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 =