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

MOON AND ITS ORBIT 17 that Ptolemy's value had been found by himself,¹ and as he adopted 54" (or 1° in 66 years) as the annual amount of pre- cession, there remained (assuming that 760 years had passed since the time of Ptolemy) an outstanding error of 79"—54"=25" per annum. In reality the annual motion of the solar apsides is 11½"; still we may say that the discovery of this motion is due to Al Battani, though he did not announce it as such ; in fact he merely gives his own value as an improvement on that of Ptolemy. Even Ibn Junis (who found 86° 10') did not suspect that the apogee was steadily moving but merely says that it must be corrected for precession (1° in 70 years), and remarks that the longitude of the apogee is very difficult to determine accurately.² On the other hand, Al Zarkali found a smaller value, 77° 50' and as he also found a smaller value of the eccen- tricity he thought it necessary to let the centre of the Sun's eccentric orbit describe a smaller circle, after the example set by Ptolemy in the case of Mercury.³ The inclination of the ecliptic which the Greeks had found—23° 51 20" was by the astro- nomers of Al Mamun found—23° 33' (in 830), by Al Battani (in 879), and by Ibn Jūnis 23° 35'⁴. When Al Zarkali found 23° 33',he, and afterwards Abu 'l Hassan Ali of Morocco, concluded that the obliquity oscillated between 23° 53 and 23° 33', an idea to which the prevailing belief in the "trepidation" of the equi- noxes lent countenance.⁵ Moon and its orbit If we now turn to the Moon, we do not find that the Arabs made any advance on Ptolemy. Several of them noticed that the inclination of the lunar orbit was not exactly 5°, as stated by Hipparchus. Thus, Abu 'l Hassan Ali ben Amagiur early in the tenth century says that he had often measured the greatest latitude of the Moon and found results greater than that

1. Scient. Stell. Cap. xxviii. Bologna, 1645, p. 72; Nallino. p. 44. At the end of Cap. xlv. he says the apogees of the Sun and Venus are both in 82° 14,' and Ibn Junis also gives 82° 14' as the value found by Al Battani (Caussin, p. 154).
2. Caussin, pp. 232 and 238. Abu'l Faraj gives 89° 28' for the year 1279 (p. 22).
3. Sedillot, Prolegomenes aux tables astron. d' Olough Beg (1847), pp. lxxx-lxxxii. Riccioli, Almag. Novum, I. p. 157.
4. Caussin. p. 56. For A.D. 900 Newcomb gives 23° 34' 54", with a diminution of 46" per century, so that the Arabian astronomers erred less then 1'.
5. Aboul Hassan Ali, Traite des Instruments astron. des Arabes: T.I.p. 175; Sedillot, Memoire sur les instr. astr. des Arabes, p. 32.