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

stipulated finding the risings of smaller arcs like horas and
Dṛkkāṇas. Find (H sin l × H cos ω) / (H cos δ) ie. H sin α. Take
the asus in the arc of this H sine ie. find α in minutes.
Then l - α gives the number of asus for which the correct-
ion in the planetary position is to be effected, for, by
these asus the True Sun-rise is accelerated or belated. In
the middle of a quadrant these asus will be a little above
26 Vinadis. To obtain them at any point of the quadrant,
take H sin 2l as the argument so that the maximum correct-
ion will be had at the middle of the quadrant by this
argument. Then the rule of three is ‘ If by 120 as radius,
we have 26 Vinadis, what shall we have for H sin 2l ?’
The result is (H sin 2l × 26) / 120 = (H sin 2l) / 4½ approximately.
Then another rule of three. “ If by 60 Vinadis we have
m' of the planetary motion, where the daily motion of the
planet is m°, what shall we have for (H sin 2l) / 4½ ?” The
result is (H sin 2l × m) / (60 × 4½) minutes = (H sin 2l × m) / 270 . Then
the sign of the correction is clear.
(2) We shall now prove Bhāskara’s statement that
at the middle of the quadrant, the correction is 26 Vinadis.
We saw above that l - α = tan² ω/2 H sin 2l. It is really
creditable on the part of Bhāskara to have seen by intuit-
ion that the argument is H sin 2l. The maximum
correction is therefore tan² ω/2 expressed in asus or minu-
tes of arc. Let x = tan² ω/2
log x = 2 log tan ω/2. Take ω = 24
Then log x = 2 × 1̄.3275 = 2̄.6550
∴ x = ·04519 radian = 155 minutes of arc ie.
155 asus = 155 / 6 = 26 apply.