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

55 = 1/160 of 1861/60 days = 1/160 of 31 days, one ghati. Hence per year the Kshayāhādya is 1 − 1/160 of (31ᵈ - 1ᵍ) so that for x years it would be {x − x/160 (31ᵈ - 1ᵍ)} d = x − x/160 (31 1/60) = x − 1/160 { 30x + x + x/60 } = x − 1/160 { 30x + x (1 + 1/60) } which is the formula given. Verse 4. Alternative method. The Dinādya obtained before multiplied by three, is to be diminished by 1/400th of the number of years; the result increased by 1/30th of the number of years gives the number of Kshayāhās. Comm. The Dinādya pertaining to one year is 0-15-30-22-30 and the Kshayāhādya is 0-48-22-7-30. Multiply the former by 3 and subtract from the latter; we have 0-1-51 = 0-1-51/60 = 0-1-17/20 = 0-37/20 = 37/20 × 1/60 = 37/1200 day Hence K−3D = 37/1200 day where K = Kshayāhādya and D = Dinādya ∴ K = 3D + 37/1200 hence per x years it will be 3D × x + 37x/1200 = 3D × x + (40 − 3) x / 1200 = 3D × x + x/30 − x/400 which is the formula given. Verse 4 contd. Alternative method. Or else K = K/160 (1 − 1/60) + x(1 − 1/5) Comm. The Kshayāhādya for an year is 0-48-22-7-30 48 ghatis = (1 − 1/5) day; hence for x years x (1 − 1/5).