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

AL FARGANI AND OTHERS ON PLANETS 23 merely as a geometrical aid to computation; they required a real and physically true system of the world, and had therefore to assume solid crystal spheres after the manner of Aristotle. Above the Moon is the Alacir, the fifth essence, which is devoid of light- ness and heaviness, and is not perceptible to the human senses; of this substance the spheres and planets are formed.¹ Already in the book of Al Fargani we find the principle adopted which we have seen dates from the fifth century (Proklus) and which became universally accepted in the Middle Ages, that the greatest distance of a planet is equal to the smallest of the planet immediately above it, so that there are no empty spaces between the spheres.² The semidiameter of the Earth is by Al Fargani given as 3250 miles, which corresponds very nearly to Al Mamun's 56⅔ miles to a degree, if we put π = 3 1/7. Starting from Ptolemy's distances of

Greatest Distance of	Al Fargani	Al Battani	Abu 'l Faraj³
Moon	64⅙	64⅙	64⅙
Mercury	167	166	174
Venus	1,120	1,070	1,160
Sun	1,220	1,146⁴	1,260
Mars	8,876	8,022	8,820
Jupiter	14,405	12,924⁵	14,259
Saturn	20,110	18,094	19,963
the Moon and the Sun, it was easy to express the other distances
in semidiameters of the Earth, the ratios between the greatest and

1. Al Battani, cap. 50 (p. 195).
2. Al Fargani, cap. 21 (ed. Golius, p. 80). Much later, Maurolycus in his Cosmographia (Venice, 1543, f. 20a) proves that Mercury and Venus must be below the Sun, by pointing out that there would otherwise be a large vacant space between the Sun and the Moon.
3. pp. 189-191.
4. So in Nallino's ed. (Milan, 1903 p. 121) the ed. of 1645 has 1176.
5. The ed. of 1645 has 12, 420; obviously an error, as the ratio of greatest to smallest distance is given as 37:23 for Saturn 7:5 (misprinted 7:2), or "quan- titas unius et duarum quintarum ad unum" (p. 199). Nallino's ed (Milan

1903. has 12,924. Abraham ben Chija has 12,400.