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-