Galilei, Galileo - Mechanics

Galilei, Galileo, Mechanics, 1665

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we will ſet before you the preſent Contemplation. Suppoſe, there-
fore, that A B, C D, and E F are three Leavers; and that on the
middle points of them G, H, and I the Weight K doth hang in
common, ſo that every one of them ſhall ſuſtain the third part of

[Figure 16]

it: And becauſe the Power in
B, ſuſtaining with the Leaver
B A thependent Weight in G,
hapneth to be the half of the
ſaid Weight, and it hath been
already ſaid, that it ſuſtaineth
the third part of the Weight
K: Therefore the Moment of
the Force B is equal to half of
the third part of the Weight K; that is, to the ſixth part of it:
And the ſame ſhall be demonſtrated of the other Forces D and F:
From whence we may eaſily gather, that putting three Gyrils or
Rundles into the inferiour Pulley, and two or three into the upper-

[Figure 17]

moſt, we may multiply the Force accor-

ding to our ^{*} Senarius. And if we would
encreaſe it according to any other even
Number, the Gyrils of the Pulley below
muſt be multiplyed according to the half
of that Number, according to which the
Force is to be multiplyed, circumpoſing
the Rope about the Pulleys, ſo as that one
of the ends be faſtned to the upper Pul-
ley, and let the Force be in the other; as
in this Figure adjoyning may manifeſtly
be gathered.

* Or in Sexcuple
proportion.

Now paſſing to the Declaration of the
manner how to multiply the Force ac-
cording to the odd Numbers, and begin-

[Figure 18]

ning at the triple proportion: firſt, let us
propoſe the preſent Contemplation, as
that, on the underſtanding of which the
knowledge of all the Work in hand
doth depend. Let therefore the Leaver
be A B, its Fulciment A, and from the
middle of it, that is, at the point C let
the Grave D be hanged; and let it be ſu-
ſtained by two equal Forces; and let one of them be applied to the
point C, and the other to the term B. I ſay, that each of thoſe Powers
have Moment equal to the third part of the Weight D. For the
Force in C ſuſtaineth a Weight equal to it ſelf, being placed in the
ſame Line in which the Weight D doth hang & Gravitate: But the

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