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

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Aries, Taurus etc. The names of the Rasis in Sanskrit
and the modern English words we use for them have the
same meaning, which raised a suspicion in the minds of
many orientalists that the Hindu Astronomy drew upon
the Greek. Many scholars of India assert that the Greeks
derived this knowledge from the ancient Hindus; but we
shall not enter into the controversy here. It may be noted
also that the Sanskrit names of week-days have the same
meaning as Sunday, Monday etc.
On the basis of taking trijyā equal to 3438', the other
H. sines or half-chords are also expressed in minutes.
Generally twenty-four H. Sines are given in a quadrant
and to obtain the H. sine of an angle intermediate, a for-
mula for interpolation also is given. Also the method of
calculating the H. sines for every degree is given, as we shall
see shortly. In the table of 24 H. sines, the first is H. sine
3°-45' or H. sine 225' and this is approximately taken
as 225' because in fig. 6 if AÔB=3°-45', the H. sine BC
will be almost equal to the arc AB. The H. Vers-sines
are also given to get the corresponding H. Cosines easily,
for, H. Vers sine 3°-45 = R — H. Cos 3°-45 = 7' means
H. Cosine 3°-45'=3431=H. sine (90°-3¾°) = H₂₃ where we
use the notation H r to mean the rth H. Sine.
Now we propose to give here some essential formulae
used by the Hindu astronomers, as given in the golādhyāya
by Bhāskara under the caption jyotpatti-krama. Inciden-
tally it may be noted that H. sine θ = R sine θ where sine θ
is the modern sine of the angle θ°. Similarly H. Cos θ=R
Cos θ and H vers θ = R vers θ. Thus when we have an equ-
ation of the type. Sin δ = Sin ϕ Cos z + Cos ϕ sin z sin a
in modern astronomy arising out of the famous spherical
triangle PZS where P is the Celestial Pole, Z the Zenith
and S the position of the Sun or a Star, the Correspond-
ing Hindu formula would be R³ H Sin δ = RH Sin ϕ
H cos Z + H cos ϕ H sin Z H sin a. Occasionally the