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

54
Comm. Since the Dinādya per year is 0-15-30-22-30,
in x elapsed years it accrues to x × 0-15-30-22-30
= (x × 15)/60 days + (x × 30)/60 ghatis + x × 22½ palas = x/4 days +
x/2 g + (x × 45)/(2 × 60) palas = x/4 d + x/2 g + 3x/8 × 1/60 g = x/4 d +
x/2 (1 + 1/80) g = x/4 d + (x/2 (1 + 1/80))/60 d which is the given
formula.
Verse 2. Alternative method.
The number of elapsed years divided by respectively 4,
120, and 9600 and the Sum taken gives the Dinādya.
Comm. Let x be the number of elapsed years. The
Dinādya as before is x × 0-15-30-22-30 = x/4 d + (x × 30)/(60 × 60) d

• (x × 45)/(2 × 60) × d/(60 × 60) = (x/4 + x/120 + x/9600) d as given.
  Verse 3. To obtain what is known as Kshayāhādya.
  The number of elapsed Kshayāhās from the beginning of
  Kalpa upto the commencement of the year, is obtained as
  follows. Let x be the number of elapsed years; then
  x − (x (1 + 1/80) + 30x)/160 = Kshayāhās.
  Comm. The number of Kshayāhās in a Kalpa of
  4320000000 solar years is 25082550000 so that per year their
  number is 5-48-22-7-30. In this 0-48-22-7-30 is said to
  be Kshayāhādya per year = 1 − (0-11-37-52-30) putting
  the quantity within the brackets into a fraction, 52½ vipalas
  = 105/2 × 1/60 = 7/8 palas; (37 + 7/8) palas = 101/8 × 1/60
  ghatis = 101/160 ghatis ; 11 101/160 ghatis = 1861/(160 × 60) days