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

106 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