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

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the preceding from the succeeding, we have successively
the rising times. Thus the rising time of Mesha is
√3 sin² ω tan² ϕ + cos² ω (cos² ω + 3 − √3 sin ω tan ϕ II
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3 + cos² ω
That of Meṣa and Vṛṣabha put together, the rising
time is .
√sin² ω tan² ϕ + 3 cos² ω (cos² ω + ⅓) − sin ω tan ϕ III
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√3 (cos² ω + ⅓)
The combined rising time of the 3 Rasis Meṣa, Vṛṣa-
bha and Mithuna is from I using tables cos⁻¹ (tan ω tan ϕ)
= 5046 asus which exactly accords with what we have
found previously namely 1505+1659+1882 = 5046. Also
putting in I λ = 180°, we have sin x = 0 or x = 180° =
10800 asus ; subtracting 5046, we have the combined times
of rising of Karkataka, Simha ahd Kavya to be 5754 asus
as we have had. Putting again λ = 270, we have cos°⁻¹
(tan ω tan ϕ) = 2π − 5046 whioh signifies that the sum
of the rising times of the last three rasis is the same as
that of the first three which again means that the sum of
the rising times of Tula to Dhanus is equal to the sum of
the rising times of Karkaṭaka, Simha and Kanya establish-
ing Bhaskara's statement “विलोमसंस्थाः”.
Verse 60. Computations of Lagna, Udayāntara and
the like from the rising times of big arcs of the ecliptic
like Rasis will be approximate, whereas one desirous of
greater approximation has to find the same from the
rising times of smaller arcs likes Horas and Dṛkkāṇas, so
as to be more correct.
Comm. Rasis divided into halves are called horas
and if divided into one-third parts are called
Dṛkkāṇas. The meaning of the verse is that if after
having found the rising time of a particular Rāśi say
Meṣa, we say that one-third of that rising time is that of
one-third of that Rāśi, we will be making only an appro-