1 The Birth of Science - MSRI

11.7 Newton’s Natural Philosophy 333
Newton was right in thinking that the law was very old (although he undoubtedly
overstates the case in throwing it as far back as Pythagoras).
Kepler believed that the sun’s “virtue” radiated out in straight lines and
gripped the planets, dragging them in circular orbits. 146 This is a far cry
from our modern idea of force, but it is close indeed to the passages of
Vitruvius and Pliny. It is hard to see why a hand-like “virtue” with which
the sun grips the planets should decrease with distance, if it were not the
case that this decay, too, had been suggested by classical sources.
Let’s turn to the passage of Vitruvius that immediately precedes the
ones studied in Section 10.6 (page 258). It reads:
. . . ergo potius ea ratio nobis constabit, quod, fervor quemadmodum
omnes res evocat et ad se ducit, ut etiam fructus e terra surgentes
in altitudinem per calorem videmus, . . . eadem ratione solis impetus
vehemens trigoni forma porrectis insequentes stellas ad se perducit.
. . 147
The Latin word ratio has multiple meanings: our “ratio” is one, and another
is “reason, argument”. The same is true of the Greek word logos, of
which the Latin ratio is often a direct translation. Now, recall that we have
established that Vitruvius used a Hellenistic scientific source for this discussion,
but disfigured it seriously. Thus we must inquire what lies behind
the “natural” meaning of the Latin, which is something like:
Therefore we find the following reasoning [ea ratio] stronger: in the
same way that heat calls and attracts everything to itself (as we see
the grain shoot up in height during the hot months. . . ), so for the
same reason [eadem ratione] the sun’s powerful force attracts to itself
the planets by means of rays projected in the shape of triangles[.]
To try to separate Vitruvius’ contribution from what was in the source,
we can start by imagining that both occurrences of ratio correspond to
logos, and that the original sense was that of our “ratio”. Then the juxtaposition
of “this ratio” (ea ratio) and “the same ratio” (eadem ratione) suggests
the idea of proportionality, which Vitruvius seems to have missed, as he
does not place these two expressions in parallel clauses. 147a The analogy page 409
with grain may be Vitruvius’; a scientific work would hardly have sandwiched
it between ratios and triangles, in the midst of a mathematical
argument.
146 See the last passage quoted on page 314 (footnote 93).
147 Vitruvius, De architectura, IX, i, 12.
147a However, if we read qua for quod, the two uses of ratio become parallel and the Latin lends
itself naturally to the proportionality interpretation. Vitruvius’ meaning may have been closer to
the original than what is attested by our manuscripts.
Revision: 1.11 Date: 2003/01/06 07:48:20