Galilei, Galileo, Discourse concerning the natation of bodies, 1663

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            <p type="main">
              <s>
                <pb pagenum="407"/>
              this Weight ſhould deſcend more than that, or that more than this;
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              and therefore they make an
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              Equilibrium,
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              and their Moments continue
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              of ſemblable and equall Vertue.</s>
            </p>
            <p type="main">
              <s>The ſecond Principle is; That</s>
            </p>
            <p type="head">
              <s>AXIOME II.</s>
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            <p type="main">
              <s>
                <emph type="italics"/>
              The Moment and Force of the Gravity, is encreaſed by
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              the Velocity of the Motion.
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              </s>
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            <p type="main">
              <s>So that Weights abſolutely equall, but conjoyned with Velocity
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              unequall, are of Force, Moment and Vertue unequall: and the
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              more potent, the more ſwift, according to the proportion of the Ve­
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              locity of the one, to the Velocity of the other. </s>
              <s>Of this we have a
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              very pertinent example in the Balance or Stiliard of unequall Arms,
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              at which Weights abſolutely equall being ſuſpended, they do not
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              weigh down, and gravitate equally, but that which is at a greater
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              diſtance from the Centre, about which the Beam moves, deſcends,
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              raiſing the other, and the Motion of this which aſcends is ſlow, and
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              the other ſwift: and ſuch is the Force and Vertue, which from the
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              Velocity of the Mover, is conferred on the Moveable, which receives
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              it, that it can exquiſitely compenſate, as much more Weight added to
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              the other ſlower Moveable: ſo that if of the Arms of the Balance,
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              one were ten times as long as the other, whereupon in the Beames
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              moving about the Centre, the end of that would go ten times as far
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              as the end of this, a Weight ſuſpended at the greater diſtance, may
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              ſuſtain and poyſe another ten times more grave abſolutely than it:
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              and that becauſe the Stiliard moving, the leſſer Weight ſhall move
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              ten times faſter than the bigger. </s>
              <s>It ought alwayes therefore to be
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              underſtood, that Motions are according to the ſame Inclinations,
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              namely, that if one of the Moveables move perpendicularly to the
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              Horizon, then the other makes its Motion by the like Perpendicular;
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              and if the Motion of one were to be made Horizontally; that then
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              the other is made along the ſame Horizontall plain: and in ſumme,
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              alwayes both in like Inclinations. </s>
              <s>This proportion between the
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              Gravity and Velocity is found in all Mechanicall Inſtruments: and
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              is conſidered by
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              Ariſtotle,
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              as a Principle in his
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              Mechanicall Queſtions
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              ;
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              whereupon we alſo may take it for a true Aſſumption, That</s>
            </p>
            <p type="head">
              <s>AXIOME III.</s>
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            <p type="main">
              <s>
                <emph type="italics"/>
              Weights abſolutely unequall, do alternately counterpoyſe
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              and become of equall Moments, as oft as their Gravi­
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              ties, with contrary proportion, anſwer to the Velocity of
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              their Motions.
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              </s>
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          </chap>
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