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

140 = Śaṅku, √(R² — Śaṅku²) = Drig-jyā. In all the cases cited above, the radins R happens to be the hypotenuse. Comm. The convention in verse 19 corresponds to saying in modern trigonometry that sin 90 + θ = cos θ sin (180 — θ) sin θ, sin 180 + θ = — sin θ, sin 270 — θ = — cos θ sin 270 + θ = — cos θ, sin 360 — θ = — sin θ. In Hindu trigonometry the sign is understood and not explicitly mentioned. Krāntijyā, Dyujyā, Drig-jyā and Śaṅku, are respecti- vely H sin δ, H cos δ, H sin Z, H cos Z where δ is decli- nation and Z the Zenith-distance of a celestial body. Taking the radius of the celertial equator to be R, the radius of the diurnal circle of a celestial would be equal to R × cos δ = H cos δ which is called Dyujyā because it is the radius of the diurnal circle. Verse 22. The lengths of the circumferences of the Manda—epicycles are respectively 13° — 40', 31° — 36', 70°, 38°, 33°, 50,* for the Sun, Moon, Mars, Mercury, Jupiter, Venus and Saturn. Comm. Bhāskara has given these measures reportedly on the basis of Āgama or ancient authority. The peculiarity of measuring the circumferences in degrees less than 360°, is due to the idea that these circumstances are measured in relation to that of the deferent or Kakshā Vritta taken to be 360°. In other words, circumference of the epicycle of a planet as given above : circumference of the mean orbit :: x : 360 = radius of the epicycle : radius of the mean orbit where x is the measure of the circumference of the planet- ary epicycle. It may be mentioned once again that the radius of a planetary epicycle is the measure of the greatest

• The printed book of Brahma Sphuta Siddhānta gives in the case of Saturn 30° only which might have been the mistake of the scribe (Vide verse 36, Spashtadhikāra B. S.). In the place of शून्यरामाः it ought to have been शून्यबाणाः.