ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

BRAHMAGUPTA AND SINE RULE 103
Degrees of anomaly Equation of Phenomena
of conjunction conjunction
───────────────── ─────────── ─────────
60° 11+12=+23°
90° 23+10=+33°
121° 33+ 7=+40°
135° 40+ ½=+40°30'
148° 40°30'—3°=+37° 30'
164° 37°30'—12°=+25°30' Retrograde motion
begins.
173° 25°30'—13°=+12°30'
180° 12°30—12°30'=0°0'
187° —12°30'
196° —25°30' Direct motion begins.
212° —37°30'
225° —40°30'
239° —40°
270° —33°
300° —23°
332° —11° Sets in the west.
360° 0°
Now we come back to our discussion on the verse VI.1.
The Śīghra hypotenuse spoken of here is EP, when SP or
EM is taken to be R ; when ∠PEM is a maximum, PM is its
'sine'.
It would be seen from the figure that
R sin PMK × PM
EP = ────────────────────
Rsin PEM
This may again be written as
EP PM
───────────── = ──────────────
sin PMK sin PEM
This is equivalent to the sine rule for a triangle in plane
trigonometry. Brahmagupta is here seen to be the first person
to give it in Indian mathematics. This expression reminds us
of the famous relationship in respect to triangle ABC :
a b c
─────── = ─────────── = ───────
sin A sin B sin C