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

530 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)