1 The Birth of Science - MSRI

244 10. Lost Science
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. 47
Heron proves this statement by taking arbitrarily close approximations to page 304
the horizontal plane with decreasing slope. Several other sources mention
the resistance a body in motion faces from the medium in which it moves,
vanishing only in the case of motion in the void. 48
Heron’s Mechanics has many overlaps with the homonymous pseudo-
Aristotelian work. In particular, the exposition of the parallelogram rule
for composing displacements is so similar in the two works that we may
suppose a common source. 49 The pseudo-Aristotelian Mechanics follows
this exposition with the remark that a point in uniform circular motion is
subjected simultaneously to two motions: one “according to nature” (
©) along the tangent and one “against nature” ( ©) directed
toward the center. 50 This suggests that only linear motions were regarded
as “according to nature”. Unfortunately, the text of this work is corrupt
and the quantitative analysis is not always clear.
It is worth recalling that already Aristotle recognized the acceleration
of falling weights, and that from statements of Simplicius we know that
Strato of Lampsacus made decisive progress in understanding the effect
of gravity. 51 He noticed that acceleration is easily provable (visualizable,
even) in the case of a trickle of water in free fall: after going down for a
while as a column, the water breaks up into drops. Simplicius, alas, does
not tell us by what argument Strato deduced from this that the water is
gaining speed. From the viewpoint of modern physics the separation into
drops comes from the cross-section of the trickle shrinking below a certain
critical value, and the decrease in the cross-section is what’s equivalent
to the increase in velocity (the rate of flow being of course constant). It is page 305
likely that Strato used just this argument to deduce the increase in velocity
from the decrease in cross-section. 52
47
Heron, Mechanica, I, iv, 20.
48
For example, Sextus Empiricus, Adversus mathematicos, I, 156: “It is characteristic of the vacuum
not to offer resistance.”
49
Heron, Mechanica, I, viii; Pseudo-Aristoteles, Mechanica, 848b, 14–30.
50
Pseudo-Aristoteles, Mechanics, 849a, 14–17.
51
Simplicius, In Aristotelis Physicorum libros commentaria, [CAG], vol. X, 916, 12–27.
52
That the cross-section shrinks cannot fail to be noticed by anyone who has observed with any
attention a water trickle in free fall. The conjecture that Strato connected the formation of drops
with the decrease in cross-section, coming up with an explanation similar to the “modern” one,
seems very plausible in the light of three circumstances. First, the notion of flow rate, on which
the explanation is based, is used in a completely analogous way by Heron in his Pneumatics, a
work for which Strato was probably one of the main sources (see page 114). Next, the thirteenth
century Liber de ratione ponderis, attributed to Jordanus Nemorarius and certainly based on classical
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