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

32 ASTRONOMY IN ANCIENT NATIONS
(the motion of the pole of the orbit being added to or subtracted
from the motion of the planet), so that the epicycle is hereby
rendered superfluous. The lengths of the radii of these small
circles are not given, except in the case of Saturn, where the
radius is 3° 3',¹ while the mean pole of the moon is 5° (the inclina-
tion of the lunar orbit) distant from the pole of the ecliptic,² and
the small circle is so exceedingly small as to produce no retrograde
motion, which is also the case with the Sun. The periods of the
poles of the outer planets are given by the following figures
Saturn makes 57 revolutions in 59 years and 1½+¼ days, in which
period the mean pole lags behind 2 revolutions 1½°+⅜°. Jupiter
makes 65 revolutions in 71 years, the mean pole lagging behind 6
revolutions. Mars makes 37 revolutions in 79 years and 3¼+¹/₁₈
days, the pole lagging behind 42 revolutions and 3⅙°³.
In other words, the motion on these small circles are com-
pleted in the synodic periods of planets. Similarly, the pole of Venus
makes 5 revolutions in the 8 years less 2¼d+¹/₂₀, lagging 1⅕ revo-
lutions in one year ; and Mercury 145 revolutions in 46 years
and 1¹/₃₀d⁴. It is curious that Alpetragius alters the order of the
planets, placing Venus between Mars and the Sun, because the
defectus (lagging) of Venus smaller than that of the Sun.⁵ He
also says that nobody has given any valid reason for accepting
the usually assumed order of the planets, and that Ptolemy is
wrong in stating that Mercury and Venus are never exactly in
a line with the Sun (a remark already made by Geber) ; and as
they shine by their own light they would not appear as dark
spots, if passing between us and the Sun. That they do not receive
their light from the Sun is proved, he thinks, by the fact that
they never appear crescent-shaped.⁶
There is no need to dwell any longer on this quaint theory

1. Fol. 16 a.
2. Fol. 25 a.
3. Fol. 16 a, 18 a, 19 b.
4. Fol. 21 b, 24 b.
5. "Nam reperimus defectum eius primum minorem defectu orbis solis et
   maiorem defectu orbis martis, et sequitur juxta radices nostras ut sit inter
   eos ambos."
6. Fol 21 a