Routledge History of Philosophy Volume IV

118 SCIENCE AND MATHEMATICS UP TO DESCARTES
ambient medium which, in being rejoined at the rear of the mobile, is
continually pressing and pushing it; which fantasies and others like them it
would be appropriate to examine and resolve but with little gain. For now,
it suffices our Author that we understand that he wishes to investigate and
demonstrate to us some properties of a motion accelerated (whatever be the
cause of its acceleration) in such a way that…. 37
The structure of Day 3 is that Salviati reads aloud a Latin treatise by Galileo,
which the friends concurrently discuss in Italian.
The form of Galileo’s Latin text is mathematical. After a brief introduction,
there follow (without interruption for comment) one definition, four axioms and
six theorems concerning uniform motion. We then move on to accelerated
motion, for which ‘it is appropriate to search for and explicate a definition that
above all agrees with what nature employs’. 38 The basic criterion of choice was
simplicity.
When therefore I observe a stone falling from rest from on high to acquire
successively new increments of speed, why should I not believe these
increments to be made in the simplest way and that most accessible to
everyone? And, if we consider attentively, we shall find no addition and no
increment simpler than that which is applied always in the same way….
And so it seems in no way discordant with right reason if we accept
that intensification of speed is made according to extension of time, from
which the definition of the motion that will be our concern can be put thus:
I call an equably or uniformly accelerated motion one which proceeding
from rest adds to itself equal moments of swiftness in equal times. 39
An obvious point, and one that is made by Sagredo, is that it might be clearer to
say that speed increased proportionally with distance rather than with time.
Salviati reports that Galileo himself had once held this view, but that it was in
fact impossible, and indeed we may say that, if falling bodies did behave in this
way, they could not start naturally from rest but would remain suspended as it
were by skyhooks until given a push.
Galileo adds to the definition a principle that will allow him to draw into his
discussion of falling bodies the behaviour of balls rolled down inclined planes. ‘I
accept that the degrees of speed acquired by the same mobile on different
inclinations of planes are equal when the elevations of the planes are equal.’
After Salviati has adduced some experimental evidence from pendulums for this,
he proceeds to quote Galileo’s first two theorems on accelerated motion. The first
states that
The time in which a space is traversed by a mobile in uniformly
accelerated transference from rest is equal to the time in which the same
space would be traversed by the same mobile carried with a uniform