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