Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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            <p type="main">
              <s>
                <pb xlink:href="040/01/874.jpg" pagenum="181"/>
                <emph type="italics"/>
              the ſaid Moveable doth naturally deſcend; whereupon there reſults a
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              mixture of certain contrary Affections, to wit, that degree of Celerity
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              acquired in the precedent Deſcent, which would of it ſelf carry the Move­
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              able uniformly
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              in infinitum,
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              and of Natural Propenſion to the Motion of
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              Deſcent according to that ſame proportion of Acceleration wherewith it
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              alwaies moveth. </s>
              <s>So that it will be but reaſonable, if, enquiring what
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              accidents happen when the Moveable after the Deſcent along any incli­
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              ned Plane is Reflected along ſome riſing Plane, we take that greateſt de­
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              gree acquired in the Deſcent to keep it ſelf perpetually the ſame in the
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              Aſcending Plane; But that there is ſuperadded to it in the Aſcent the
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              Natural Inclination downwards, that is the Motion from Reſt Accelerate
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              according to the received proportion: And leſt this ſhould, perchance, be
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              ſomewhat intricate to be underſtood, it ſhall be more clearly explained by a
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              Scheme.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let the Deſcent therefore be ſuppoſed to be made along the Declining
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              Plane A B, from which let the Reflex Motion be continued along another
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              Riſing Plane B C: And in the firſt place let the Planes be equal, and
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              elevated at equal Angles to the Horizon G H. </s>
              <s>Now it is manifeſt, that
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              the Moveable
                <emph.end type="italics"/>
              ex quiete
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              in A deſcending along A B acquireth degrees of
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              Velocity according to the increaſe of its Time, and that the degree in B
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              is the greateſt of thoſe acquired and by Nature immutably impreſſed, I
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              mean the Cauſes of new Acceleration or Retardation being removed:
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              of Acceleration, I ſay, if it ſhould paſſe any farther along the extended
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              Plane; and of Retardation, whilſt the Reflection is making along the
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              Acclivity B C: But along the Horizontal Plane G H the Equable Mo­
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              tion according to the de-
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.874.1.jpg" xlink:href="040/01/874/1.jpg" number="120"/>
                <lb/>
                <emph type="italics"/>
              gree of Velocity acquired
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              from A unto B would ex­
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              tend
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              in infinitum.
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              And
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              ſuch a Velocity would
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              that be which in a Time
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              equal to the Time of the
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              Deſcent along A B would paſſe a Space in double the Horizon to the ſaid
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              A B. </s>
              <s>Now let us ſuppoſe the ſame Moveable to be Equably moved with
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              the ſame degree of Swiftneſſe along the Plane B C, in ſuch ſort that alſo
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              in this Time equal to the Time of the Deſcent along A B a Space may be
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              paſſed a long B C extended double to the ſaid A B. </s>
              <s>And let us under­
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              ſtand that as ſoon as it beginneth to aſcend there naturally befalleth the
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              ſame that hapneth to it from A along the Plane A B, to wit, a certain
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              Deſcent
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              ex quiete
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              according to thoſe degrees of Acceleration, by vertue
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              of which, as it befalleth in A B, it may deſcend as much in the ſame
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              Time along the Reflected Plane as it doth along A B: It is manifeſt, that
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              by this ſame Mixture of the Equable Motion of Aſcent, and the Acce­
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              lerate of Deſcent the Moveable may be carried up to the Term C along
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              the Plane B C according to thoſe degrees of Velocity, which ſhall be
                <emph.end type="italics"/>
              </s>
            </p>
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