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

108
Fig. 7
In the Commentary under verses 1—25 ibid, Bhāskara
tells us how formulae I and II are used to construct the
table of 24 H sines. To start with, the four H sines of 30°,
45°, 60° and 90° which may be denoted by the symbol Hr
where r=8, 12, 16 and 24, are known. Now using the
formula II, H₄ is obtained from H₈, H₂ from H₄ and H₁
from H₂. Similarly from H₁₂, H₆ and H₃ are successively
obtained. Now using formula I, H₂₀, H₂₂, H₂₃, H₁₈, H₂₁ are
obtained respectively from H₄, H₂, H₁, H₆ and H₃. Now
again from H₂₀, H₂₂, H₁₈, we obtain using formula II H₁₀, and
H₅, H₁₁, H₉ respectively. Formula I gives again H₁₄, H₁₉, H₁₅,
H₁₃ from the above. H₁₄ gives H₇ and H₇ gives H₁₇ using
formula II and I respectively. Thus the table is Completed.
Then Bhāskara poses the problem as to how a table of
the H sines could be computed when a quadrant is divided
into 30 equal parts. He says that formula I and II do not
suffice in this behalf and shows how they do not, as follows