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

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daily motion be 715 ; then as per the previous formula the
angular diameter should be 3/74 × 715 = 2145/74 = 28 73/74 = 29'
very approximately. The mean daily motion is 790 which
corresponds to 32' of angular diameter. Taking advant-
age of this arithmetical correlation namely that the excess
of 3' over 29' corresponds to 75' of daily motion. Bhāskara
gives the formula m' = (m₁ - 715)/25 + 29. This formula
correctly holds good when m₁ = 740, for, equating
3x/74 = (x - 715)/25 + 29 = (x + 10)/25 , x will be equal to 740.
For other values between 715 and above it holds very
approximately. Thus, when m₁ = 715, m' = 28 73/74 ie. 29
when m₁ = 740, m' = 30, when m₁ = 765, m' = 31 1/75
(error 1/75) when m₁ = 790, m' = 32 1/37 (error 1/37) and so on.
Verse 9. An alternative method of finding the
angular diameter of the shadow cone.
2 ρ = 2/15 m₁ - 5/12 s, where m₁ and s₁ are the daily
motions of the Moon and the Sun respectively.
Comm. In the previous verse, we had formulae to
compute the diameters of the discs of the Sun and Moon,
knowing their daily motions. Since in practice we have
these daily motions computed for every day, so the compu-
tation based upon those daily motions conduces to ease in
the matter of calculation. Now in this verse, the radius
of the shadow cone is also calculated in terms of the daily
motions of the Sun and the Moon, which is more an
ingenious device adopted in practice. The elucidation of the
formula depends on the following technique as conceived
by the Hindu astronomers. In as much as the Sun's
sphere is far bigger than that of the Earth, the shadow of
the Earth assumes the form of a cone. From a knowledge
of the decrease in the diameter, as we proceed from the