1 The Birth of Science - MSRI

10.3 The Principle of Inertia 247
Any theory so based must allow as a consequence that the same gravity
can generate different motions (depending on initial velocity). Plutarch,
for the water near the center of the earth, does list three possible motions
for the same body subjected to the same fora toward the center: rest, uniform
circular motion around the center and unending oscillation about
the center. As we know now, these are indeed three possible motions for a
body in the conditions considered. In the case of a boulder, too, Plutarch
mentions not one but two possibilities: rest and oscillation.
Another very interesting statement made by Plutarch is that the moon
moves faster when closer to the earth. 59
The whole passage suggests that Plutarch’s source taught an inertial
theory of dynamics where what we call force (and gravity in particular)
does not determine motion uniquely, but only the variation in motion.
Therefore it is valuable from a history of science perspective to investigate
what that source may have been.
Lamprias, the De facie character who ridiculed the theory of the thrust
toward the center, had earlier told Apollonides (who typifies “mathematicians”
in the dialogue): “the deviations of visual rays are not in your
purview nor in that of Hipparchus.” 60 Thus Hipparchus is singled out as
a polemical target in the course of the same antiscientific polemic where
the supposed weirdnesses of our dynamical theory are highlighted. This
suggests the possibility that he was Plutarch’s source for the theory.
This conjecture gains plausibility in the light of several considerations.
First, the De facie alludes to other results certainly due to Hipparchus, such
as the observation that the moon has a measurable parallax61 and numerical
data from the Hipparchan lunar tables. 62
Second, the conjecture that the theory was due to Hipparchus is consistent
with the distribution and small number of the sources that hint at it.
It seems not to have been known to Philo of Byzantium when he wrote
the Belopoeica, 63 in the late third century B.C., so it probably belongs to the
second century. It also seems to have been unknown to many Alexandrian
scholars of the imperial period, which suggests that it had no time to sink
59 Plutarch, De facie. . . , 933B.
60 Plutarch, De facie. . . , 921D.
61 Hipparchus measured the lunar parallax (Ptolemy, Syntaxis mathematica, V, v, 369). In the De
facie, as Neugebauer notes, lunar parallax is mentioned just before Hipparchus is named (921D).
The passage was mistranslated by Cherniss, but the meaning was put to right in [Neugebauer:
HAMA], p. 661.
62 [Flacelière], p. 217; [Cherniss], p. 145.
63 The book discusses the motion of weights, but there is no trace of a reference to the principle
of inertia.
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