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

443 an ambiguous sense. Ranganātha in his commentary takes the Madhya-Sthiti-khanda to mean that rectified for variation in β, and Spaṣṭa-Sthiti-khanda to mean that rectified for parallax. Some modern traditional commen- tators, for example pandit Sitha Ramajha commenting on the verse of the Sūryasiddhānta and the commentator of the verses of Brahma Sphutasiddhānta published under the editorship of Acharya Rama Swarupa Sharma, have ignored the variation in β and confined themselves only to the effect of parallax in longitude. Yet one more proof could be adduced in this behalf. Let D, be the moment of geocentric conjunction, t the time for a given grāsa in between D and T the moment of first geocentric contact. Then the times D, t and T are to be corrected both for parallax in longitude and that in latitude. Take the geocentric Sthiti-khanda, and geocentric Bhuja as the mean-values T and B and those corrected first for parallax in longitude as the True values T' and B'. Also take the time t corrected for parallax in longitude to be t'. We could write T' - T = δT, t' - t = δt and B' - B = δB. In the above, consider B expressed in time. Then D - T = S the mean Sthiti-khanda, D - t = B the mean Bhuja, D' - T' = S', the true Sthiti-khanda recti- fied for parallax in longitude, D' - t' = B' the Bhuja also rectified for the same. The δB = δD - δt, δI = δD - δT. Then using the proportion "If for D - T we have δD - δT as the variation what shall we have for D - t?" The result is ((D - t) (δD - δT)) / (D - T) = δB ∵ B + δB = B' = D - t + ((D - t) (δD - δT)) / (D - T) = (D - t) (1 + (δD - δT) / (D - T)) = (D - t) ((D + δD) - (T + δT)) / (D - T) = (D - t) (D' - T') / (D - T) = (Mean Bhuja × True Sthiti-khanda) / (Mean Sthiti-khanda)