Galilei, Galileo - Mechanics

Galilei, Galileo, Mechanics, 1665

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Term of thoſe Diſtances, that is from the point of Suſpenſion, to
the ſame Center of the Earrh.

Theſe things determined and ſuppoſed, we come to the explica-
tion of a Principle, the moſt common and materiall of the greater
part of Mechanick Inſtruments: demonſtrating, that unequall
Weights weigh equally when ſuſpended by [or at] unequal Diſtan-
ces, which have contrary proportion to that which thoſe weights
are found to have, See the Demonſtration in the beginning of the
ſecond Dialogue of Local-Motions.

Some Adveriiſements about what hath been ſaid.

Now being that Weights unequall come to acquire equall
Moment, by being alternately ſuſpended at Diſtances that
have the ſame proportion with them; I think it not fit to
over paſſe with ſilence another congruicy and probability, which
may confirm the ſame truth; for let the Ballance A B, be conſide-
red, as it is divided into unequal parts in the point C, and let the
Weights be of the ſame propor-

[Figure 2]

tion that is between the Diſtan-
ces B C, and C A, alternately
ſuſpended by the points A, and
B: It is already manifeſt, that
the one will counterpoiſe the
other, and conſequently, that
were there added to one of them
a very ſmall Moment of Gravity, it would preponderate, raiſing
the other, ſo that an inſenſible Weight put to the Grave B, the
Ballance would move and deſcend from the point B towards E,
and the other extream A would aſcend into D, and in regard that
to weigh down B, every ſmall Gravity is ſufficient, therefore not
keeping any accompt of this inſenſible Moment, we will put no
difference between one Weights ſuſtaining, and one Weights
moving another. Now, let us conſider the Motion which the
Weight B makes, deſcending into E, and that which the other
A makes in aſcending into D, we ſhall without doubt find the
Space B E to be ſo much greater than the Space A D, as the Di-
ſtance B C is greater than C A, forming in the Center C two an-
gles D C A, and E C B, equall as being at the Cock, and conſe-
quently two Circumferences A D and B E alike; and to have the
ſame proportion to one another, as have the Semidiameters B C,
and C A, by which they are deſcribed: ſo that then the Velocity
of the Motion of the deſcending Grave B cometh to be ſo much
Superiour to the Velocity of the other aſcending Moveable A, as
the Gravity of this exceeds the Gravity of that; and it not being

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