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

344 This declination of the culminating point being known, and the latitude being known, its meridian zenith-distance could be got. Take that to be roughly the zenith-distance of the Vitribha. Then an approximate estimate of the effect in latitude is obtained as follows. Let the zenith- distance of the Vitribha be x. Then if we have for H sin z = R, the maximum effect of 48′ — 46″ in the latitude, what shall we have for H sin 45° ? The result is (H sin 45 × 48′ — 46″) / 3438 = 2431 / 3438 × 48′ — 46″ = 34′ — 30″. Then again another approximate estimate is made as follows. Let the Sapātasūrya (Sapātasūrya = longitude of the Sun or what is the same of the Moon with respect to the Node) be λ. Then for λ = 15°, we have a latitude of 70′. That being so, for a variation of 34′ — 30″ in the latitude, what will be the corresponding variation in the longitude λ ? The result is = (69 / 2) × (15 / 70) = 207 / 28 = 7° 11/28 which is roughly one-sixth of 45°. Hence if the zenith-distance of the culminating point taken to be the Vitribha be 45° the variation in the Sapāta-sūrya (= Sapāta chandra) will be one-sixth thereof. Hence we are asked to increase or decrease as the may be, the Sapāta-sūrya by 1/6th. If the resulting Sapātasūrya be less than 7°. there may be an eclipse. When the lunar orbit lies north of the ecliptic, the culminating point of ecliptic being south of the zenith, the latitude of the Moon is decreased by parallax, so that, we have to decrease the Sapātasūrya; whereas when the lunar orbit is then south of the ecliptic, the effect of parallax is to increase the latitude and consequently, we have to increase the Sapātasūrya. Or again when the culminating point of the ecliptic is north of the zenith and the lunar orbit is north of the ecliptic, parallax appears to increase so that we have to increase the Sapātasūrya ; and when at that moment the lunar orbit is south of