Galilei, Galileo, Mechanics, 1665

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              Term of thoſe Diſtances, that is from the point of Suſpenſion, to
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              the ſame Center of the Earrh.</s>
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              <s>Theſe things determined and ſuppoſed, we come to the explica­
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              tion of a Principle, the moſt common and materiall of the greater
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              part of Mechanick Inſtruments: demonſtrating, that unequall
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              Weights weigh equally when ſuſpended by [or at] unequal Diſtan­
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              ces, which have contrary proportion to that which thoſe weights
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              are found to have, See the Demonſtration in the beginning of the
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              ſecond Dialogue of Local-Motions.</s>
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              Some Adveriiſements about what hath been ſaid.
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              <s>Now being that Weights unequall come to acquire equall
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              Moment, by being alternately ſuſpended at Diſtances that
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              have the ſame proportion with them; I think it not fit to
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              over paſſe with ſilence another congruicy and probability, which
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              may confirm the ſame truth; for let the Ballance A B, be conſide­
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              red, as it is divided into unequal parts in the point C, and let the
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              Weights be of the ſame propor­
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                <figure id="id.070.01.007.1.jpg" xlink:href="070/01/007/1.jpg" number="2"/>
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              tion that is between the Diſtan­
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              ces B C, and C A, alternately
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              ſuſpended by the points A, and
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              B: It is already manifeſt, that
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              the one will counterpoiſe the
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              other, and conſequently, that
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              were there added to one of them
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              a very ſmall Moment of Gravity, it would preponderate, raiſing
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              the other, ſo that an inſenſible Weight put to the Grave B, the
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              Ballance would move and deſcend from the point B towards E,
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              and the other extream A would aſcend into D, and in regard that
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              to weigh down B, every ſmall Gravity is ſufficient, therefore not
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              keeping any accompt of this inſenſible Moment, we will put no
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              difference between one Weights
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              ſuſtaining,
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              and one Weights
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                <emph type="italics"/>
              moving
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              another. </s>
              <s>Now, let us conſider the Motion which the
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              Weight B makes, deſcending into E, and that which the other
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              A makes in aſcending into D, we ſhall without doubt find the
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              Space B E to be ſo much greater than the Space A D, as the Di­
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              ſtance B C is greater than C A, forming in the Center C two an­
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              gles D C A, and E C B, equall as being at the Cock, and conſe­
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              quently two Circumferences A D and B E alike; and to have the
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              ſame proportion to one another, as have the Semidiameters B C,
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              and C A, by which they are deſcribed: ſo that then the Velocity
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              of the Motion of the deſcending Grave B cometh to be ſo much
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              Superiour to the Velocity of the other aſcending Moveable A, as
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              the Gravity of this exceeds the Gravity of that; and it not being </s>
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