Galilei, Galileo - Mechanics

Galilei, Galileo, Mechanics, 1665

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In the mean time, ſince I have hinted, that the benefit and help
derived from Machines is not, to be able with leſſe Force, by help
of the Machine to move thoſe weights, which, without it, could
not be moved by the ſame Force: it would not be beſides the
purpoſe to declare what the Commodities be which are derived to
us from ſuch like faculties, for if no profit were to be hoped for,
all endeavours employed in the acquiſt thereof will be but loſt
labour.

Proceeding therefore according to the nature of theſe Studies,
let us firſt propoſe four things to be conſidered. Firſt, the weight
to be transferred from place to place; and ſecondly, the Force
and Power which ſhould move it; thirdly, the Diſtance between
the one and the other Term of the Motion; Fourthly, the Time
in which that mutation is to be made: which Time becometh the
ſame thing with the Dexterity, and Velocity of the Motion; we
determining that Motion to be more ſwift then another, which in
leſſe Time paſſeth an equal Diſtance.

Now, any determinate Reſiſtance and limited Force whatſoever
being aſſigned, and any Diſtance given, there is no doubt to be
made, but that the given Force may carry the given Weight to the
determinate Diſtance; for, although the Force were extream
ſmall, yet, by dividing the Weight into many ſmall parts, none
of which remain ſuperiour to the Force, and by transferring them
one by one, it ſhall at laſt have carried the whole Weight to the
aſſigned Term: and yet one cannot at the end of the Work with
Reaſon ſay, that that great Weight hath been moved, and tranſ-
ported by a Force leſſe then it ſelf, howbeit indeed it was done
by a Force, that many times reiterated that Motion, and that
Space, which ſhall have been meaſured but only once by the whole
Weight. From whence it appears, that the Velocity of the Force
hath been as many times Superiour to the Reſiſtance of the weight,
as the ſaid Weight was ſuperiour to the Force; for that in the
ſame Time that the moving Force hath many times meaſured the
intervall between the Terms of the Motion, the ſaid Moveable
happens to have paſt it onely once: nor therefore ought we to
affirm a great Reſiſtance to have been overcome by a ſmall Force,
contrary to the conſtitution of Nature. Then onely may we ſay
the Natural Conſtitution is overcome, when the leſſer Force tranſ-
fers the greater Reſiſtance, with a Velocity of Motion like to that

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