सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)
Siddhanta Shiromani Ganitadhyaya of Bhaskaracharya with Commentary
भास्कराचार्य द्वितीय द्वारा
पृष्ठ 259, कुल 573 में से
संदर्भ में पढ़ें239
(7) The seventh latitudinal triangle is D₁ S₁ B₁
where D₁ S₁ is the second segment of the Agrajyā, S₁ B₁ is
the Kujyā, and D₁ B₁ is the unmandala Sanku.
(8) The eighth latitudinal triangle is B₁ L₁ F₁
where B₁ L₁ is equal to the first segment of Agrajyā,
L₁ F₁ is the higher segment of Agrajyā, L₁ F₁ is the
higher segment of the Sama-Vritta-S'anku, and F₁B₁ is
the upper segment of Taddṛti mentioned before.
Comm. It was already mentioned that a latitudinal
triangle is such a right-angled tri-angle constituted by
the chords of the celestial sphere where the angles in the
triangle are ϕ, 90 − ϕ, 90°. The side opposite to ϕ is
called the Bhuja, that opposite to (90 − ϕ) is called
Koti and the third Karna. Such triangles are not only
eight as have been mentioned, but many more will be
there as mentioned by Bhāskara. They are all formed
as mentioned by him by the intersections of the diurnal
paths and the celestial equator with the circles of the
sphere namely horizon, prime vertical, meridian,
Equatorial horizon and declination circles. These
circles clearly intersect at ϕ or 90 − ϕ. The eight
triangles mentioned are those whose elements will be
entering computations. There is another important
latitudinal triangle with which we have to deal later
namely that formed by what is called Hriti, S'anku, and
S'ankutala (Fig. 39).
O₃K = Agrā ; O₃C = S'anku-tala ; CN = S'anku-bhuja
= CK ∴ Agrā = Sankutala + Sanku-bhuja
Agrā = R (H sin δ / H cos ϕ) ; S'ankutala = H cos Z tan ϕ
S'anku-bhuja = (H sin z H sin a) / R (Ref. fig. 40')
∴ R (H sin δ / H cos ϕ) = H cos z tan ϕ + (H sin z H sin a) / R I