ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

22 ASTRONOMY IN ANCIENT NATIONS Abu 'l Wefa and Ptolemy Therefore, Abu 'l Wefa did not know a single thing about the motion of the Moon which he had not borrowed from Ptolemy. But the prosneusis of Ptolemy is not the variation discovered by Tycho Brahe. The latter depends solely on the elongation of the Moon from the Sun, as it is = +39' .5 sin 2ε, while it is beyond the power of mortal man to express the effect of the prosneusis without the anomaly. Ptolemy's exprssion for all the inequalities in longitude assumed by him, when developed analytically, found to contain, in addition to terms represening the equation of the centre and the evection, the latter being +1°19'.5 sin (2ε—m), a very considerable term +17.8 sin 2ε [cos (2ε+m) +2 cos (2ε—m)], where ε is the elongation and m the mean anomaly.¹ Obviously this term has nothing in common with the varia- tion, except that it disappears in the syzygies and quadratures. Tycho Brahe did not hang his new term on to the unaltered lunar theory of Ptolemy, and by doing that we should in fact only spoil the latter and make its maximum error rise to more than a degree.² Owing to the insufficiency of the observations at his disposal, Ptolemy could only perceive that there was some out- standing inequality after allowing for the evection, only appearing outside the syzygies and quadratures, but he was neither able to find the law which governed the phenomenon, nor was he aware what a large quantity it represented; he could only tinker up his constructions a little, and in this he was most faithfully followed by the Arabs, who added nothing to what he had done and left it to the reviver of practical astronomy to discover the third lunar inequality. Al Fargani and others on Planets Passing to the five planets, we find that, generally speaking, very few attempts were made to improve the work of Ptolemy. But the Arabs were not content to consider the Ptolemaic system P. Tannery, Recherches, p. 213. Another expansion of Ptolemy's lunar inequalities in a series was given by Biot, Journal des Savants, 1843, p. 703 (Reprint, p. 49). P. Kempf, Untersuchungen uber die Ptolemaische Theorie der Mondbewegung, Berlin, 1878 (Inaug. Diss.), p. 37.