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

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Thus in the given problem where l = 100°,
H cos 100° = 7/12 × 21 (since H cos 100 = - H sin 10 =
120 × .1735 = - 21 approximately where R = 120')
= - 12′-15″ ∴ Δδ ± Δβ = 362 - 12′-15 = 349-45.
Now 123/4 H sin λ to be divided above = (123 × 118) / 4
= 3628′-30″,
so that 123/4 H sin λ × 1 / (Δδ ± Δβ) = (3628′-30″) / (349-45)
= 10°-22′-28″ =
= rQ. Now r's longitude from the zero point of the
Hindu zodiac is 11 Rāśis 19° so that Q's longitude =
11 R-19° minus 10°-22′-28″ = 11 Rāśis 8°-37′-32″. This
gives us the longitude of G which is called the Moon's
Goḷa Sandhi. Adding 3, 6, 9 Rāśis, we get successively
the first Āyana Sandhi, the other Goḷa Sandhi and the
second Āyana Sandhi of the Moon.
(1) Bhāskara overlooked a crudeness in his proce-
dure namely that Δβ is perpendicular to the ecliptic
whereas Δδ is perpendicular to the celestial Equator, but,
since Δβ is small, he overlooked the nicety. Strictly
speaking Δβ should have been corrected for Āyanavalana.
(2) There is also crudeness in computing Δδ and
Δβ for arcs of 15°, whereas they should have been done
for increase of every degree in the longitude. He could
have done that, because at the end of the Goḷādhyāya he
gave the method or computing the H sines for every degree
under the caption प्रतिभागज्यकाविधि.
We shall now give a modern method of computing
the value of rQ. From the spherical triangle RrA, where
⁀rR = 100°, R̂ = i = 4½°, we have
sin 100 = (tan rA) / (tan 4½)