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

386 when his true motion equals the mean. It will be 32'- 0'' - 9'''. Note (4) Substituting the values of P, P' and σ in III ρ = 52'-42'' + 3'-57'' - 16'-16'' = 40'-23'' = Angular radius of the shadow-cone at the lunar orbit which almost accords with the modern value 41'-49''. Note (5) One may wonder as to how, taking wrong values for s and Ks, such a correct value could be obtained for P. In equation II, α, Km, e are all near the truth so that the terms effected are s/K and e/Ks; but both s and Ks being parameters s/Ks comes off alright, which is the angular radius of the Sun's disc which could be measured. The only vitiating term is e/Ks which is the horizontal parallax of the Sun which was overestimated unwittingly by a wrong supposition as indicated in the Kakshādhyāya. However e/Ks comes to be 3'-57'' and this overestimate is mitigated to some extent that the Earth has an atmos- phere which boosts the angular radius of the shadow cone by about 1' and the remainder of the overestimate makes amends for the smaller value of P taken. Verse 7. To convert spatial measures into angular measure. The diameters of the Sun, the Moon, and Rāhu in Yōjanas multiplied by R = 3438', and divided respectively by Ks, Km and Km give their angular measures. Comm. From fig. 69, (s/2) / Ks = sin Ê = Ê expressed in radians = E' / 3438 ∴ E' = (3438 × s) / (2 Ks) which means that the angular radius of the Sun is got by multiplying s/2 ie. the spherical radius of the Sun by R = 3438 and divid- ing by Ks as mentioned. Similar is the case with respect to the other two. Note. - The word Kalākaraṇa is used to signify To convert into angular measure.