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

accurate number should be (2 x / 65) - λ ie. a little less than (2 x / 65) . The question is now to find the value of λ. So, equating (2 x / 65) - λ to (A x / s), λ = (2 x / 65) - (A x / s) = x ((2 / 65) - (A / s)) = x ((2 s - 65 A) / (65 s)). Substituting for 2 s - 65 A namely 2 × 51840000 - 65 × 1593300 = 115500 λ = (x × 115500) / (65 × 51840000) = (x × 2 × 57750) / (65 × 51840000) = (2 x / 65) × 1 / (51840000 / 57750) = (2 x) / (65 × 898) ∴ (A x) / s = (2 x / 65) - λ = (2 x / 65) - (2 x) / (65 × 898) = (2 x / 65) (1 - 1 / 898) as given. The procedure, adopted as above, is in a way a short cut in Hindu Astronomy to obtaining a convenient con- vergent to a continued fraction. Let us use the method of continued fractions; the number of Adhikamāsas in x solar months is (A x / s) ie. x × A/s = (x × 1593300) / 51840000 = (x × 5311) / 172800 . Converting 172800 / 5311 into a continued fraction we have 32 + 1/(1+) 1/(1+) 1/(6+) 1/2 + 1/(1+) 1/(1+) 1/(18+) 1/4 to which 65/2 is a convergent but a good convergent is 245 / 69 . As this good convergent is unwieldy, Bhāskara used 2/65 and made amends for the roughness introduced by adopting it. Wherever a con- venient convergent is not available, an easy and rough convergent is used and amends will be made for the rough-