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

49 εA is a tangent to the Moon's disc and M the centre of the Moon, Sin B = r' / d where B is the angular semi-dia- meter of the Moon's disc, r' = the spherical radius of the Moon's disc measured in yojanas, so that since Sin B = B' in Hindu trigonometry when the angle is small, 2πr' / 2πd = 2πr' / 324000 = 16 / 3438 ∴ 2πr' = (324000 × 16) / 3438 ; hence r' = (18000 × 16) / 191 × 7 / 44 = 504000 / 2101 = 240 yojanas. Bhaskara gives the semi-diameter of the Moon's disc to be 16'-0"-9"' so that the above r' is very approximately 240 yojanas as given by Bhaskara. Now with these constants pertaining to the Moon's distance, and his spherical radius, it was sought to find the spatial distance traversed by the Moon during a day. The rule of three used was " If 16'-0"-19"' of the Moon's angu- lar semi-diameter pertains to a spatial distance of 240 yoja- nas at his orbit, what does the mean daily motion of 790'-35" pertain to ? " The answer is 683064000 / 57609 = 11858¾ yojanas as given by Bhaskara elsewhere or taking the Moon's mean semi-angular diameter to be 16' only, and using the rule of three " If 16' at the lunar orbit correspond to 240 yojanas, what do 790'-35" correspond to " we have (790'-35" × 240) / 16' = 15 × 790 7/12 = 5/4 × 9487 = 9487 + 2371¾ = 11858¾ yojanas as given by Bhaskara. Thus having obtained the daily spatial motion, the Hindu Astronomers assumed all the other planets (includ- ing the Sun) to have the same daily mean spatial motion. On this assumption since the, Moon's orbit will be 27.3217 × 11858¾ = 324000 yojanas, and the circumference of the universe will be 324000 × 57753300000 = 18712069200000000 yojanas the Sun's orbit will be 7