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

366 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