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

line of intersection of the planes PCM a plane perpendi-
cular to the plane of the Equator, and ☉BD a plane per-
pendicular to the Ecliptic plane. Since ⚍C 11 ☉ B and
⚍N 11 ☉ D and BD☉ = CN⚍ = 90°, so the two tri-
angles are congruent
∴ ☉B / ⚍C = ☉D / ⚍N ie. H sin (λ + a) = (R × H sin δ) / (H sin ω)
∴ H sin δ = [H sin (λ + a) H sin ω] / R
NC = ⚍L = √(⚍C² — ⚍N²) = √(R² — H sin² δ) =
H cos δ. ⚍L is called Dyujyā as explained below in
note (3).
Another way of looking at the similarity of the tri-
angles C⚍N and B☉D is from the fact that they are
formed by the intersection of parallel planes, both of which
are perpendicular to the plane of the Equator. This idea will
be elaborated when we explain fig. 21, wherein the so-called
latitudinal triangles will be shown to be formed by the
intersection of the plane of the Equator and planes of
diurnal circles with the planes of the horizon and the
prime vertical. In fact, the plane of a great circle and
the parallel planes of the corresponding small circles form
the same dihedral angle with the planes of the celestial
sphere namely the planes of the meridian, horizon and
prime-vertical so that right-angled triangles formed by
their intersection will be all similar.
Formula II is derived from the formula H sin² δ +
H cos² δ = R² derived from fig. 6 from which formula,
formula III follows.