1 The Birth of Science - MSRI

168 6. The Hellenistic Scientific Method
all that. . . . In many cases astronomers and physicists will set out to
demonstrate the same topics, for example the size of the sun or the
roundness of the earth, but they don’t follow the same route. The latter
will deduce whatever it may be from substance [] or powers
[], or from optimality arguments [ ], or
from generation or transformation, whereas the former will deduce it
from appropriate figures or magnitudes or the measurement of motion
and corresponding times. The physicist, with an eye towards
productive power, often touches on causes, whereas the astronomer,
when he is constructing proofs based on what comes from outside,
is a poor observer of causes[.]
Sometimes [an astronomer] through a “hypothesis” [©] finds page 215
a way to save the phainomena. For example, why do the sun, the
moon and the planets appear to move irregularly? If we suppose that
their round orbits are eccentric or that these bodies move on epicycles,
the apparent irregularities will be saved. One must investigate
in how many different ways the phainomena can be represented. . . 69
It should be remarked that in Simplicius’ time (early sixth century A.D.)
the terms “mathematician” and “astronomer” were often used synonymously,
in part through the influence of the title of Ptolemy’s work; just
before the passage cited, Simplicius contrasts physics with “mathematics
and astronomy”. 70
The astronomical example reported by Simplicius, namely the possibility
of explaining the same observable motions through an eccentric or an
epicycle, alludes to a theorem demonstrated by Apollonius of Perga and
then later by Ptolemy in the Almagest. 71 The result is the following. If a
point B has uniform circular motion around a point A and a third point
C has uniform circular motion around B (following a so-called epicycle),
then in the particular case that the two angular velocities are the same,
the resulting motion can still be uniform and circular, but around a center
distinct from A. Thus the motion of C can be described in two different
ways: by saying that C goes around a circular orbit eccentric relative to A,
or that it moves on an epicycle based on an orbit around A. From our point
of view these are two descriptions of the same motion, but for Posidonius
and Geminus they are two hypotheses about real motions.
The passage quoted on the previous page points out clearly the essential
feature of the “mathematician” (or “astronomer”): he limits himself
69
Simplicius, In Aristotelis physicorum libros commentaria (on II, 1, 193b), 64v, 34 – 65r, 1 = [CAG],
vol. IX, 291, 21 – 292, 19.
70
[CAG], vol. IX, 291, 19–20.
71
Ptolemy, Syntaxis mathematica, XII, i, 451–544 (ed. Heiberg).
Revision: 1.7 Date: 2002/09/14 23:17:37