1 The Birth of Science - MSRI

11.4 A Late Disciple of Archimedes 309
tors probably had access to the same sources, 71 one might conjecture that
the invariance of fall time was already mentioned in Hipparchus’ work on
gravity 72 — if only because it is hard to see how else it would be known
to Lucretius, 73 Hipparchus having been the last Hellenistic scientist who
studied motion under gravity, at least to our knowledge.
Suitable adaptation or alteration of experimental conditions to facilitate
measurements is customarily regarded as one of the fundamental features
of the Galilean method. For the study of motion under gravity, the object
of Galileo’s most important experiments, the key alteration was the use
of an inclined plane. His first consideration of inclined planes appears already
in the youthful De motu. Most interesting is a statement about the
particular case of horizontal planes:
And in this situation [i.e., in the absence of friction], any movable
body lying on a plane equidistant from the horizon will be moved by
a minimal force, that is, by a force smaller than any arbitrary force. 74
Though Galileo did not foresee all its consequences at the time, this
sentence marks the decisive step toward the supersession of Aristotelian
physics and the formulation of the principle of inertia. We have already
seen how Heron had introduced the subject:
We demonstrate that a weight in this situation [that is, on a horizontal,
frictionless plane] can be moved by a force less than any given
force. 75
Heron’s demonstration, treating a horizontal plane as the limiting case of
an inclined plane whose slope approaches zero, was to reappear in the
Dialogues. Now, the possible influence of Heron’s Mechanics on Galileo is page 382
71 For the connection between Philoponus and Simplicius, see pp. 289–290.
72 The real difficulty that must be overcome in reaching this invariance result is the need to set
aside the effects of air resistance. Thus the result is within reach of a theory based on the principle
of inertia and the notion of friction, and our earlier considerations (Section 10.3) make it plausible
that Hipparchus had gotten there. Philoponus (ibid., 642) says that a projectile receives at the
moment of launching a , which he calls “incorporeal” — an adjective that, as we
saw in Sextus Empiricus, had been used since imperial times to describe the entities of Hellenistic
scientific theories. Philoponus also uses for the same notion another name that was to have a bright
future: , kinetic energy.
73 Lucretius, De rerum natura, II, 225–239. Clagett writes that Philoponus’ passage “appears to
indicate that he had dropped bodies of different weight” ([Clagett: SM], p. 546). He continues: “It
is obvious, then, that neither Stevin nor Galileo was the first to perform such as experiment; nor in
all likelihood was Philoponus. But Philoponus does give us the first record of such an experiment
used to refute or confirm a dynamic law.” If we wish to attribute the experiment to the oldest
available source that mentions its result, credit should go to Lucretius, not Philoponus.
74 “Quae omnia si ita disposita fuerint, quodcumque mobile super planum horizonti aequidistans
a minima vi movebitur, imo et a vi minori quam quaevis alia vis” ([Galileo: Opere], vol. I,
p. 299).
75 Heron, Mechanica, I, iv, 20. We discussed this passage on page 244.
Revision: 1.11 Date: 2003/01/06 07:48:20