Galilei, Galileo, Discourse concerning the natation of bodies, 1663

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AXIOME II.
So that Weights abſolutely equall, but conjoyned with Velocity
unequall, are of Force, Moment and Vertue unequall: and the
more potent, the more ſwift, according to the proportion of the Ve­
locity of the one, to the Velocity of the other.
Of this we have a
very pertinent example in the Balance or Stiliard of unequall Arms,
at which Weights abſolutely equall being ſuſpended, they do not
weigh down, and gravitate equally, but that which is at a greater
diſtance from the Centre, about which the Beam moves, deſcends,
raiſing the other, and the Motion of this which aſcends is ſlow, and
the other ſwift: and ſuch is the Force and Vertue, which from the
Velocity of the Mover, is conferred on the Moveable, which receives
it, that it can exquiſitely compenſate, as much more Weight added to
the other ſlower Moveable: ſo that if of the Arms of the Balance,
one were ten times as long as the other, whereupon in the Beames
moving about the Centre, the end of that would go ten times as far
as the end of this, a Weight ſuſpended at the greater diſtance, may
ſuſtain and poyſe another ten times more grave abſolutely than it:
and that becauſe the Stiliard moving, the leſſer Weight ſhall move
ten times faſter than the bigger.
It ought alwayes therefore to be
underſtood, that Motions are according to the ſame Inclinations,
namely, that if one of the Moveables move perpendicularly to the
Horizon, then the other makes its Motion by the like Perpendicular;
and if the Motion of one were to be made Horizontally; that then
the other is made along the ſame Horizontall plain: and in ſumme,
alwayes both in like Inclinations.
This proportion between the
Gravity and Velocity is found in all Mechanicall Inſtruments: and
is conſidered by Ariſtotle, as a Principle in his Mechanicall Queſtions;
whereupon we alſo may take it for a true Aſſumption, That
AXIOME III.

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