Galilei, Galileo, Mechanics, 1665

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            <pb xlink:href="070/01/024.jpg" pagenum="294"/>
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              <s>The preſent Speculation hath been attempted by
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              Pappus Alex­
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              andrinus
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              in
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              Lib.
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              8.
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              de Collection. </s>
              <s>Mathemat.
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              but, if I be in the
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              right, he hath not hit the mark, and was overſeen in the Aſſumpti­
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              on that he maketh, where he ſuppoſeth that the Weight ought to
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              be moved along the Horizontal Line by a
                <emph type="italics"/>
              F
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              orce given; which is
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              falſe: there needing no ſenſible
                <emph type="italics"/>
              F
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              orce (removing the Accidental
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              Impediments, which in the Theory are not regarded) to move the
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              given Weight along the Horizon, ſo that he goeth about in vain
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              afterwards to ſeek with what
                <emph type="italics"/>
              F
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              orce it is to be moved along the
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              elevated Plane. </s>
              <s>It will be therefore better, the
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              F
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              orce that moveth
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              the Weight upwards perpendicularly, (which equalizeth the Gra­
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              vity of that Weight which is to be moved) being given, to
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              ſeek the
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              F
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              orce that moveth it along the Elevated Plane: Which
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              we will endeavour to do in a Method different from that of
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                <emph type="italics"/>
              Pappus.
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              </s>
            </p>
            <p type="main">
              <s>Let us therefore ſuppoſe the Circle A I C, and in it the Diame­
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              ter A B C, and the Center B, and two Weights of equal Moment
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              in the extreams B and C; ſo that the Line A C being a Leaver,
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              or Ballance moveable about the Center B, the Weight C ſhall
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              come to be ſuſtained by the Weight A. </s>
              <s>But if we ſhall imagine
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              the Arm of the Ballance B C to be inclined downwards according
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              to the Line B F, but yet in ſuch a manner that the two Lines
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              A B
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                <lb/>
              and
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              B F
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              do continue ſolidly conjoyned in the point
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              B,
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              in this caſe
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              the Moment of the Weight C ſhall not be equal to the Moment
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                <figure id="id.070.01.024.1.jpg" xlink:href="070/01/024/1.jpg" number="21"/>
                <lb/>
              of the Weight
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              A,
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              for that the Di­
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              ſtance of the point
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              F
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              from the Line
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              of Direction, which goeth accord­
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              ing to B I, from the
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              F
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              ulciment B un­
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              to the Center of the Earth, is dimi­
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              niſhed: But if from the point
                <emph type="italics"/>
              F
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              we
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              erect a Perpendicular unto B C, as is
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                <emph type="italics"/>
              F
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              K, the Moment of the Weight in
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                <emph type="italics"/>
              F
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              ſhall be as if it did hang by the
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              Line K
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              F,
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              and look how much the
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              Diſtance K B is diminiſhed by the
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              Diſtance B
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              A,
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              ſo much is the Moment of the Weight
                <emph type="italics"/>
              F
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              diminiſhed
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              by the Moment of the
                <emph type="italics"/>
              W
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              eight
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              A. A
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              nd in this faſhion inclining
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              the
                <emph type="italics"/>
              W
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              eight more, as for inſtance, according to B L, its Moment ſhall
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              ſtill diminiſh and ſhall be as if it did hang at the Diſtance
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              B
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              M, ac­
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              cording to the
                <emph type="italics"/>
              L
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              ine M
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              L,
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              in which point
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              it ſhall be ſuſtained by
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              a
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              W
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              eight placed in
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              A,
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              ſo much leſs than it ſelf, by how much the
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              Diſtance B
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              A
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              is greater than the Diſtance
                <emph type="italics"/>
              B
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              M. </s>
              <s>See therefore that
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              the
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              W
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              eight placed in the extream of the
                <emph type="italics"/>
              L
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              eaver B C, in inclining
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              downwards along the Circumference C
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              F L
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              I, cometh to diminiſh
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              its Moment and
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              Impetus
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              of going downwards from time to time, </s>
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