Galilei, Galileo, Mechanics, 1665

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Returning now to our firſt Intention, which was to inveſtigate
the Nature of the Screw, we will conſider the Triangle A B C, of
which the Line A B is Horizontal, B C perpendicular to the ſaid
Horizon, and A C a Plane elevated; upon which the Moveable D
ſhall be drawn by a Force ſo much leſs than it, by how much the
Line B C is ſhorter than C A: But to elevate or raiſe the ſaid
Weight along the ſaid Plane A C, is as much as if the Triangle
C A B ſtanding ſtill, the Weight

Figure: /permanent/archimedes/galil_mecha_070_en_1665/figures/070.01.026.2.jpg not scanned
[Figure 23]

D be moved towards C, which is
the ſame, as if the ſame Weight
never removing from the Perpen-
dicular A E, the Triangle did
preſs forwards towards H.
For if
it were in the Site F H G, the
Moveable would be found to
have mounted the height A I.
Now, in fine, the primary Form and Eſſence of the Screw is no-
thing elſe but ſuch a Triangle A C B, which being forced for-
wards, ſhall work it ſelf under the Grave Body to be raiſed, and
lifteth it up, as we ſay, by the ^{*} head and ſhoulders.
And this was

its firſt Original: For its firſt Inventor (whoever he was) conſi-
dering how that the Triangle A B C going forwards raiſeth the
Weight D, he might have framed an Inſtrument like to the ſaid
Triangle, of a very ſolid Matter, which being thruſt forwards did
raiſe up the propoſed Weight: But afterwards conſidering better,
how that that ſame Machine might be reduced into a much leſſer
and more commodious Form, taking the ſame Triangle he twined
and wound it about the Cylinder A B C D in ſuch a faſhion, that
the height of the ſaid Triangle, that is the Line C B, did make the
Height of the Cylinder, and the Aſcending Plane did beget upon

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