by F.J. Ragep, Springer-Verlag New York Berlin Heidelberg, 1993
Book II. chap 11
[1] As for the first difficulty, which was cited [in connection] with the configuration
of the moon's orbs, no statement concerning it has reached me from
my predecessors. In this matter, I myself have devised what I shall now present.
[2] Let us set forth for that [purpose] a lemma, which is as follows: if two
coplanar circles, the diameter of one of which is equal to half the diameter of the
other, are taken to be internally tangent at a point, and if a point is taken on the
smaller circle-and let it be at the point of tangency-and if the two circles
move with simple motions
in opposite directions in such a way that the motion of the smaller [circle] is
twice that of the larger so the smaller completes two rotations for each rotation
of the larger, then that point will be seen to move on the diameter of the large
circle that initially passes through the point of tangency, oscillating between its
endpoints.
Let us illustrate this with four drawings so that one may conceive
from them how this [may occur], and they are these:
