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

65
Comm. The first part is clear, because for every tithi,
there will be an increase of elongation of 12°. To get the
fractional part of the tithi in between the ending moment
of the tithi and the subsequent Sun-rise, the interval which
is Sāvana ie expressed in the unit of civil day has to be
converted into luni-Solar units. The rule of three is ‘ If for
63 Sāvana days there are 64 tithis, what will it be for the
above interval ?’ Here the approximate ratio of 64/63 is used
because the Ahargaṇa which is Laghu is small ie is less
than 365. The Kshaya-dina-Sesha which was got under
verses 12, 13, has a divisor of 64, and is of the form y/64 .
Hence the quantity to be added is (y × 64)/(64 × 63) = y/63 of a tithi
= y/63 × 12 × 60 minutes of arc = 8/7 × 10 y = 10 y (1 + 1/7)
minutes as given in the verse. This has to be added to
12t°, got before where t is the number of elapsed tithis.
Verse 17. Computation of Mars.
The mean daily motion of Mars is 0-31-26-28-7=0-30

• 0-0-90 minus 0-0-3-31-53. If x be the number of
  days x × 0-30' = x°/2 ; x × 0-0-90" = x/2 × 3' ; thus the
  rule prescribed is “ Half of the number of days gives the
  degrees ; half the number of days multiplied by 3 gives
  the number of minutes ” from this we have to subtract
  x × (0-0-3-31-53). The quantity within the brackets
  is approximately 1/17 of a minute for 1/17' = 0-0-3"-31"'-46"'.
  Since the Ahargaṇa is small the precision required is there.
  Thus the rule is x°/2 + x/2 × 3' + x'/17 + the Dhruvaka at the
  beginning of the Solar year.
  Verse 18. Computation of the S'īghroccha of Mercury.
  The mean daily motion of the Budha-S'īghra is
  4°-5'-32"-18"'-28"".
  9