bodies was that I knew that mathematicians by no means agree in their
investigations thereof. For, in the first place, they are so much in
doubt concerning the motion of the sun and the moon, that they can
not even demonstrate and prove by observation the constant length of
a complete year; and in the second place, in determining the motions
both of these and of the five other planets, they fail to employ
consistently one set of first principles and hypotheses, but use
methods of proof based only upon the apparent revolutions and motions.
For some employ concentric circles only; others, eccentric circles and
epicycles; and even by these means they do not completely attain the
desired end. For, although those who have depended upon concentric
circles have shown that certain diverse motions can be deduced from
these, yet they have not succeeded thereby in laying down any sure
principle, corresponding indisputably to the phenomena. These, on the
other hand, who have devised systems of eccentric circles, although
they seem in great part to have solved the apparent movements
by calculations which by these eccentrics are made to fit, have
nevertheless introduced many things which seem to contradict the first
principles of the uniformity of motion. Nor have they been able to
discover or calculate from these the main point, which is the shape of
the world and the fixed symmetry of its parts; but their procedure
has been as if someone were to collect hands, feet, a head, and other
members from various places, all very fine in themselves, but not
proportionate to one body, and no single one corresponding in its turn
to the others, so that a monster rather than a man would be formed
from them. Thus in their process of demonstration which they term a
"method," they are found to have omitted something essential, or to
have included something foreign and not pertaining to the matter in
hand. This certainly would never have happened to them if they had
followed fixed principles; for if the hypotheses they assumed were