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

of astronomy.¹ Nor can any objection be raised to Abu'l Faraj
(Bar Hebraeus), and it would be impossible to explain more
clearly than he does the effect of the prosneusis. He says: "The
third inequality is the angle formed at the centre of the epicycle
by two lines which are drawn, one from the centre of the univ-
erse and the other from the point called the prosneusis, at the end
of which is the apogee of the epicycle, at which commences the
proper motion, and which is called the mean apogee. The apogee
which is at the end of the line drawn from the centre of the uni-
verse is called the apparent one. The point prosneusis is on the side
of the perigee of the eccentric, 10 parts 17 minutes from the centre
of the world² which is itself at the same distance from the centre
of eccentric. The maximum value of this angle is 13 parts 9 minutes
when the Moon is a crescent or ¾ gibbous, that is, near the hexagon
or trigon with the Sun. In fact, when the epicycle is four or
eight signs distant from the apogee of the eccentric, the Sun is
itself two or four signs distant from [the centre of the epicycle]
because it is half way between this centre and the apogee. In
the tables, this inequality of the two apogees is called the
first angle and is included in the motion of the centre."³ While
this describes the construction of Ptolemy as clrealy as
possible, at the same time the agreement of the account with
that of Abu'l Wefa is perfect. Abu'l Faraj even (like Nasir ed-
din) describes as a fourth inequality in longitude that caused
by the motion along an orbit inclined to the ecliptic, so that he
would not have neglected to describe the variation, if it had been
found by an astronomer of Baghdad. We may add that the
Jewish writer Abraham ben Chija (A. D. 1100), in his Sphaera
Mundi, also describes the "aberration" of the apside of the epi-
cycle, chiefly "in sexta et tertia parte mensis."⁴

1. Translated by Rudloff and Hochheim, Zeitschrift der Deutschen Morgen-
   land Ges. XLVII pp. 213–275. He describes (p. 249) how the line of
   apsides is directed to a point called "the corresponding point," and gives
   its position correctly. The inequality he calls the deviation.
2. Nasir ed-din gives 10° 9′.
3. Le livre de l' ascension, & c. T. II. PP. 29-30. Two codices add after the
   word prosneusis : "This is the point mohazat."
4. Sphaera Mundi (1546, ed. Schreckenfuchs), p. 75. Munster's commentary
   to the Hebrew text (p. 116) has "cum centrum est in sextili aut trino
   aspectu [id est, quando abest a sole duobus signis aut quatuor]"; • the words
   in brackets are not in the Hebrew original. The words "sixth" and "third"
   are unmistakable (shithith and shelishith). Apparently no one has hitherto
   thought of consulting Abraham ben Chija.