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

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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