1 The Birth of Science - MSRI

10.3 The Principle of Inertia 249
[Hipparchus] recognizes the same cause also for bodies let fall from
above. 69
Thus Hipparchus’ theory treated identically the motion of a body thrown
up and of one dropped from on high. This unification suggests that the
astronomer, besides using the same terminology used by Plutarch, gave
it the same meaning. Only a theory that recognizes as essential variables
not just velocities but variations in velocity can unify the treatment of both
motions.
Simplicius offers us another highly valuable insight:
Hipparchus contradicts Aristotle regarding weight, as he says that
the further something is, the heavier it is. 70
Hipparchus’ statement seems inexplicable if regarded as referring to small
displacements from the surface of the earth: in normal experience, things
don’t get heavier the higher up they are. If anything, the fact that weights
accelerate as they fall may suggest the opposite idea, which was indeed
maintained by Aristotle. Therefore the weight change that Hipparchus
had in mind becomes manifest only when the distance to the center of
the earth changes appreciably. But if we think of bodies far away from the
earth, the statement is even odder. The only way to make it comprehensible
is to suppose that Hipparchus meant the weight of bodies inside the
earth, recognizing that it decreases as the body nears the center. (It can be page 311
seen from simple symmetry considerations that the weight vanishes at the
center, and it is natural to think that a small displacement from the center
will affect the weight but little. 71 )
We must conclude that Hipparchus’ work dealt also with the motion of
weights inside the earth, covering distances not negligible with respect to
the distance to the center. This is precisely the situation of the boulder and
the water in Plutarch’s passage. The other example Plutarch gives is the
moon, and Hipparchus was certainly the main source on the moon for this
69 © (Simplicius, In Aristotelis De Caelo
commentaria, [CAG], vol. VII, 265, 3–4).
70 ©
(ibid., 265, 9–11). This passage has been cited many times (in [Clagett: SM], for example)
in the translation given in [Cohen, Drabkin], which reads “. . . bodies are heavier the further removed
they are from their natural places” (p. 210). The last four words, added without bracketing,
have no correspondence in the original. It is true that specifying what the bodies are further from
makes the sentence more readable. It is also true that the reference point intended by Simplicius is
the center of the earth, which for him is indeed the natural place of a weight. None of this justifies
putting in Hipparchus’ mouth the Aristotelian notion of natural place.
71
Hipparchus may have used a more sophisticated reasoning than that. The reduction in weight
as the center of the earth is approached is naturally predicted by any theory that postulates that
gravity is a mutual attraction between bodies. In Section 10.7 we will analyze certain testimonia
that suggest that such a theory did arise in Hellenistic science.
Revision: 1.11 Date: 2003/01/06 02:20:46