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
23[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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