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

345 the ecliptic, parallax appears to decrease the latitude so that we have to decrease the Sapātasūrya. The proportion that 70' of latitude correspond to 15° of Sapāta-chandra is due to the formula H sin 15° ✕ H sin 4½ —————————— = H sin β. Using logarithms, R log sin β = 9·4130 + 8·8946 = 8·3076 so that β = 1° - 10' = 70'. This proportion could be used because the Moon is within 15° of the Node. Hence when we are investigating the occurence of a solar eclipse, application of rule of three is not unjustified or crude. Herein, Bhāskara assumed the zenith-distance of the nonagesimal to be round about 45° and drew a conclusion that the effect in the longitude on account of parallax in latitude is one-sixth of the zenith-distance. Instead if the zenith-distance be assumed to be z, the result would be (48' - 43" ✕ sin z ✕ 15) / 70 = 21/2 sin z which may be taken as a better approximation. If, on the other hand the modern value of 57' of the lunar parallax be taken, the result would be (57 sin z ✕ 15) / 70 = 12 sin z approximately which is a better value. In this calculation, it is better to compute the zenith- distance of the nonagesinal using modern methods instead of assuming the nonagesimal to be on the meridian. 44