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

40 ASTRONOMY IN ANCIENT NATIONS
Though the somewhat confused collection of essays entitled
the Libros del Saber would not, if published in the thirteenth
century, have advanced astronomical science, it cannot be denied
that the Alfonsine Tables were very useful in their day. The
actual elements are not given, nor is any thing said about any
observations by which somewhat more correct values of the
mean motions must have been found.¹
Arabs on motions of fixed stars.
Thus we finish our review of the planetary theories of the
Arabs. Now we shall say a few words about their ideas as to
the nature and motion of the fixed stars. The exaggerated
notion which prevailed before the invention of the telescope
with regard to the apparent angular diameters of the stars natu-
rally, led to erroneous estimates of their actual size, founded on
the assumption that the sphere of the fixed stars (the eighth
sphere) was immediately outside that of Saturn.² The stars of
the first magnitude were supposed to have an apparent diameter
equal to 1/20 of that of the Sun, from which it followed that their
actual diameters were about 4 1/2 times that of the Earth, or about
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propter motus supradictos non (ut in alijs planetis fit) circumferentiam
deferentis circularem, sed potius figuræ, habentis similitudinem cumplana
ovali peripheriam describere." Next by Albert of Brudzew in 1482 in his
Commentariolum super theoricas novas, printed at Milan in 1495 (ed.
Cracow, 1900, p. 124), where it is remarked that the centre of the lunar
epicycle describes a similar figure. This is also stated by E. Reinhold in
his commentary to Purbach, 1542, fol. p. 7 verso (ed. of Paris, 1558, fol. 78,)
by Vurstisius in his Questiones novae in theoricas, & c., Basle, 1573,
p. 233; and in Riccioli's Almagestum novum T. I, p. 564. The last three
writers (who give a figure) also take the equable angular motion round
the centre of the equant into account, which centre lies on the point of the
circumference of the small circle nearest the Earth. The curve described
by the centre of the epicycle thus becomes egg-shaped, and not like an
ellipse.

1. The tables in vol. v. of the Libros del Saber are quite different from the
   Alfonsine Tables, and are apparently only intended for astrological
   purposes.
2. Al Battani (cap. 50) gives the greatest distance of Saturn = 18,094, and the
   distance of the fixed stars = 19,000 semidiameters of the Earth. Al Fargani
   (p. 82) puts them exactly equal. Al Kusgi gives the diameters in parasangs,
   of the concavity of the stellar sphere = 33,509,180 of the ninth sphere
   33,524,309, of its convexity "no one but God knows" (Shah Cholgi, p. 97).