Galilei, Galileo - Mechanics

Galilei, Galileo, Mechanics, 1665

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the ſaid Cylinder the Helical Line deſcribed by the Line AEFGH,
which we vulgarly call the Wale of the Screw, which was produ-
ced by the Line A C. And in this manner is the Inſtrument made,
which is by the Greeks called Κόχλος, and by us a Screw; which

winding about
cometh to work

[Figure 24]

and inſinu-
ate with its
Wales under
the Weight, and
with facility rai-
ſeth it. And we
having demon-
ſtrated, That up-
on [or along]
the elevated Plane the Force hath the ſame proportion to the
Weight, that the perpendicular Altitude of the ſaid Plane hath to
its Length; ſo, ſuppoſing that the Force in the Screw A B C D is
multiplied according to the proportion by which the Length of the
whole Wale exceedeth the Altitude C B, from hence we come
to know that making the Screw with its Helix's more thick or cloſe
together, it becometh ſo much the more forceable, as being begot
by a Plane leſs elevated, and whoſe Length regards its own Per-
pendicular Altitude with greater proportion. But we will not
omit to advertiſe you, that deſiring to find the Force of a propo-
ſed Screw, it will not be needful that we meaſure the Length of
all its Wales, and the Altitude of the whole Cylinder, but it
will be enough if we ſhall but examine how many times the Di-
ſtance betwixt two ſingle and Contiguous terms do enter into one
ſole Turn of the ſame Wale, as for example, how many times
the Diſtance AF is contained in the Length of the Turn AEF:
For this is the ſame proportion that the Altitude CB hath to all
the Wale.

Levar in capo
ſignfieth to lift
on high by force

* Κόχλος, in La-
tine Cocblea, any
Screw winding
like the Shell of
a Snail.

If all that be underſtood which we have hitherto ſpoken touch-
ing the Nature of this Inſtrument, I do not doubt in the leaſt but
that all the other circumſtances may without difficulty be compre-
hended: as for inſtance, that inſteed of making the Weight to
mount upon the Screw if one accommodates its Nut with
the Helix incavated or made hollow, into which the Male Screw
that is the Wale entring, & then being turned round it raiſeth and
lifteth up the Nut or Male Screw together with the Weight which
was hanged thereat. Laſtly, we are not to paſs over that Conſidera-
tion with ſilence which at the beginning hath been ſaid to be neceſ-
ſary for us to have in all Mechanick Inſtruments, to wit, That
what is gained in Force by their aſſiſtance, is loſt again in Time,

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