Galilei, Galileo, Mechanics, 1665

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              <s>
                <pb xlink:href="070/01/025.jpg" pagenum="295"/>
              more and leſs, as it is more or leſs ſuſtained by the Lines B F and
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              B L: But the conſidering that this Grave deſcending, and ſuſtained
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              by the Semidiameters B F and B L is one while leſs, and another
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              while more conſtrained to paſs along the Circumference C F L, is
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              no other, than if we ſhould imagine the ſame Circumference
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              C F L I to be a Superſicies ſo curved, and put under the ſame
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              Moveable: ſo that bearing it ſelf thereon it were conſtrained to
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              deſcend along thereby; for if in the one and other manner the
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              Moveable deſcribeth the ſame Courſe or Way, it will nothing im­
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              port whether, if ſuſpended at the Center B, it is ſuſtained by the
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              Semidiameter of the Circle, or elſe, whether that Fulciment being
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              taken away, it proceed along the Circumference C F L I: So that
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              we may confidently affirm, that the Grave deſcending downwards
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              from the point C along the Circumference C F L I, its Moment
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              of Deſcent in the point C is total and entire, becauſe it is not in
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              any part ſuſtained by the Circumference: And there is not in that
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              firſt point C, any indiſpoſition to Motion different from that, which
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              being at liberty, it would make along the Perpendicular and Con­
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              tingent Line D C E: But if the Moveable ſhall be placed in the
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              point F, then its Gravity is in part ſuſtained, and its Moment of
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              Deſcent is diminiſhed by the Circular Path or Way that is placed
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              under it, in that proportion wherewith the
                <emph type="italics"/>
              L
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              ine
                <emph type="italics"/>
              B
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              K is overcome
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              by
                <emph type="italics"/>
              B
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              C: But if when the Moveable is in F, at the firſt inſtant of
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              ſuch its Motion, it be as if it were in the Plane elevated according
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              to the Contingent
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              ine G F H, for that reaſon the inclination of the
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              Circumference in the point F differeth not from the inclination of
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              the Contingent
                <emph type="italics"/>
              L
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              ine F G any more ſave the inſenſible Angle of
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              the Contact. </s>
              <s>And in the ſame manner we ſhall find the Moment
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              of the ſaid Moveable to diminiſh in the point
                <emph type="italics"/>
              L,
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              as the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              ine BM
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              is diminiſhed by B C; ſo that in the Plane contingent to the Circle
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              in the point
                <emph type="italics"/>
              L,
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              as for inſtance, according to the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              ine N
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              O, the
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              Moment of Deſcent diminiſheth in the Moveable with the ſame
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              proportion. </s>
              <s>If therefore ^{*} upon the Plane HG the Moment of the
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                <arrow.to.target n="marg1117"/>
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              Moveable be diminiſhed by the total
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              Impetus
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              which it hath in its
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              Perpendicular D C E, according to the proportion of the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              ine K B
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              to the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              ine B C, and B F, being by the Solicitude of the Triangles
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              K B F and K F H the ſame proportion betwixt the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              ines K F and
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              F H, as betwixt the ſaid K B and
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              F, we will conclude that the
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              proportion of the entire and abſolute Moment, that the Moveable
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              hath in the Perpendicular to the Horizon to that which it hath up­
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              on the Inclined Plane H F, hath the ſame proportion that the
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                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              ine H F hath to the
                <emph type="italics"/>
              L
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              ine F K; that is, that the
                <emph type="italics"/>
              L
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              ength of the
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              Inclined Plane hath to the Perpendicular which ſhall fall from it
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              unto the Horizon. </s>
              <s>So that paſſing to a more diſtinct Figure, ſuch
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              as this here preſent, the Moment of Deſcending which the Move­</s>
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