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

367 Verse 8. An alternative method of obtaining the angular radii. The daily motion of the Sun increased by one-tenth of its value and halved, gives the angular diameter of the Sun. The Moon's daily motion multiplied by 3 and divided by 71, gives the angular diameter of the Moon. Or the daily motion of the Moon being decreased by 715 and divided by 25 and the result being added to 29 gives the angular diameter of the Moon. Comm. This method gives in an easy way the true angular radii. The formulae given are s' = ½s₁ (1+¹⁄₁₀) ; and m' = (3 m₁) / 74 = (m₁ - 715) / 25 + 29. This may be eluci- dated as follows. The argument used is "If the spherical diameter of 6522 Yojanas corresponds to a spatial daily motion of 11858¾ Yojanas, what angular diameter corres- ponds to the angular daily motion s₁?". The proportion- ality is clear and the result is (s₁ × 6522) / 11858¾ = 26088 / 47435 . Converting 26088 / 47435 , into a continued fraction, it is 1/(1+) 1/(1+) 1/(4+) 1/(1+) 1/(1+) 1/94 . The penultimate convergent is 11/20 = ½ (1+¹⁄₁₀). The formula follows. Similar calculation gives m'. Note. The advantage of these formulae is that they are not only easy but also adopting the true daily motion we have the true angular radii. This procedure was adopted by Bhāskara from Brahmagupta. The latter, how- ever, prescribes a nearer convergent namely 10/247 but actually 17/420 is the nearest convergent. The next formula namely m' = (m₁ - 715) / 29 + 29 is approximate. This may be elucidated as follows. Let the