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

ALKAZWINI—EXCENTRIC SPHERES 27 excentric sphere. The figure shows the excentric sphere enclosed in a sphere, al-mūdir or the turning one, which allows the upper apsis or apogee of the excentric or deferent sphere (3 in the figure) to move right round the outer surface of the mūdir. The inner surface of the mumaṭṭal sphere immediately surrounds the gauzahar sphere of the Moon. It was a necessary consequence of the large solar parallax of 3' accepted by Ptolemy, that Mercury and Venus must be very near the Earth, since they are assumed to be nearer than the Sun. Thus Abraham ben Chija says that the shadow of the Earth ex- tends beyond the orbit of Mercury but does not reach that of Venus.¹ Ptolemy never mentions the parallaxes of Mercury and Venus, as to which nothing was known, though they ought, of course, to be greater than 3'. But on the assumption that the smallest distance of Mercury is equal to the distance of the Moon at apogee, the parallax of Mercury ought to rise to 54', which must have been felt to be too large a quantity, though it does not seem to have struck Al Battani as anything surprising, per- haps because Mercury cannot be seen when in inferior conjunc- tion. It may have been this necessarily large parallax of Mercury, which induced Ibn Jūnis (without any explanation) to reduce the solar parallax from 3 to 2', or rather to 1' 57".² Geber³ blames Ptolemy for having said that the parallaxes of the planets are insensible, and remarks that he ought, therefore, logically to have placed Venus and Mercury above the Sun. He takes great pains to show that Venus may be exactly on the line joining the Sun and the Earth. Indeed, Geber neglects no opportunity of criticis- ing Ptolemy's methods of finding the elements of the orbits,⁴ and he is generally very unjust to him but he does not venture to

1. Sphaera mundi, ed. Osw. Schreckenfuchs, Basle, 1546 pp. 84, 86.
2. Unpublished chapters of Ibn Jūnis, reviewed by Delambre, Hist. de l'astr. du Moyen Age. p. 101.
3. Instrumentum primi mobilis a P. Apiano. Accedunt ijs Gebri filii Affla Hispalensis...libri IX. de astronomia. Norimbergæ, 1534, fol. (Introd. p. 3 and lib. VII. p. 104).
4. See the long indictment on pp. 2-3 of his introduction. He blames Ptolemy among other things for assuming that the centre of the deferent is half-way between the centres of the zodiac and of the equant, while he himself deduces this from the movements.