1 The Birth of Science - MSRI

308 11. The Age-Long Recovery
I will add another way in which one should understand that four
magnitudes are in proportion. It is the following. When the first is
neither more nor less than is necessary in order for it to have to the
second the same proportion that the third has to the fourth, we say
that the first magnitude has to the second the same proportion that
the third has to the fourth. 68
The circularity of this “definition” makes it clear that in Galileo’s time we
were still far from regaining the ability to build true scientific theories.
As to the seminal reestablishment of the experimental method, the common
attitude of denying any indebtedness to ancient science also denies
Galileo the merit of his hard, deliberate work in this direction. But a brief
recapitulation of the main phases of his experimental work can help set
the record straight.
Galileo’s first known experiments date from 1586, and tried to rebuild
the experimental basis for Archimedes’ On floating bodies. They culminated
with the construction of a hydrostatic balance, described in La bilancetta.
Galileo had already realized how important it was not just to read ancient
scientific texts, but to grapple with their concrete component. page 380
His second experimental scientific work, to our knowledge, is the first
on the motion of bodies, described in the De motu. Since the theory derived
therefrom by Galileo does not differ from the one that Simplicius
attributes to Hipparchus, 69 there is no reason to believe that the latter’s
theory was founded on a less solid experimental basis.
As to the momentous observation that the time a body takes to fall does
not depend on its weight (if one neglects air resistance), it was thought
for centuries that Galileo reached it by dropping weights from the tower
of Pisa. Surely a simpler way would have been to read it in Philoponus’
commentary to Aristotle’s Physics. 70 And it is not easy to maintain that the
experimental method, having eluded Hellenistic scientists, was invented
in the sixth century A.D. by a theologian and commentator of Aristotle.
Since some of Philoponus’ statements on motion under gravity are akin to
those that Simplicius attributes to Hipparchus, and since both commenta-
68 Galileo Galilei, Sopra le definizioni delle proporzioni d’Euclide, at Salviati’s seventh turn = [Galileo:
Opere], vol. VIII, p. 353. The passage caps Galileo’s critique of Euclid’s definition (on the grounds
that it is impossible to apply and is “more of a theorem to be proved than a definition to be given”).
This dialogue was first published by Vincenzio Viviani in his edition of Book V of the Elements
(Quinto libro degli Elementi d’Euclide, ovvero Scienza universale delle proporzioni spiegata colla dottrina
del Galileo. . . , Venice, 1674), with the subtitle: “To be added to the four Dialogues and mathematical
demonstrations concerning two new sciences.”
69 As observed in [Koyré: EG], pp. 70 and 100. In the De motu, Galileo cites the relevant Simplicius
passage on Hipparchus (which we discussed on page 248). He says he read it only after having
formulated the same theory independently ([Galileo: Opere], vol. I, pp. 319–320).
70 John Philoponus, In Aristotelis Physicorum libros commentaria, 683 in [CAG], vol. XVII.
Revision: 1.11 Date: 2003/01/06 07:48:20