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

Table of figures

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                <pb xlink:href="040/01/873.jpg" pagenum="180"/>
                <emph type="italics"/>
              is to E F, as F E is to E C, that F C determineth the Time along C O:
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              And if a part of the Horizontal Line T C double to C A be divided in
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              two equal parts in V, the extenſion towards X ſhall be prolonged
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              in in­
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              finitum,
                <emph type="italics"/>
              whilſt it ſeeks to meet with the prolonged Line A E: And the
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              proportion of the Infinite Line T X to the Infinite Line V X, ſhall be
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              no other than the proportion of the Infinite Line V X to the Infinite
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              Line X C.
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              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              We may conclude the ſelf-ſame thing another way by reaſſuming the
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              ſame Reaſoning that we uſed in the Demonſtration of the firſt Propoſi­
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              tion. </s>
              <s>For reſuming the Triangle A B C, repreſenting to us by its Pa­
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              rallels to the Baſe B C the Degrees of Velocity continually encreaſed ac­
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              cording to the encreaſes of the Time; from which, ſince they are infi­
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              nite, like as the Points are infinite in the Line A C, and the Inſtants
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              in any Time, ſhall reſult the Superficies of that ſame Triangle, if we
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              underſtand the Motion to continue for ſuch another Time, but no far­
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              ther with an Accelerate, but with an Equable Motion, according to the
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              greateſt degree of Velocity acquired, which degree is repreſented
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              by the Line B C. </s>
              <s>Of ſuch degrees ſhall be made up an Aggregate like to
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              a Parallelogram A D B C, which is the double of
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.873.1.jpg" xlink:href="040/01/873/1.jpg" number="119"/>
                <lb/>
                <emph type="italics"/>
              the Triangle A B C. </s>
              <s>Wherefore the Space which
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              with degrees like to thoſe ſhall be paſſed in the ſame
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              Time, ſhall be double to the Space paſt with the de­
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              grees of Velocity repreſented by the Triangle A B C:
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              But along the Horizontal Plane the Motion is Equa­
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              ble, for that there is no cauſe of Acceleration, or Re­
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              tardation: Therefore it may be concluded that the
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              Space C D, paſſed in a Time equall to the Time A C is double to the
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              Space A C: For this Motion is made
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              ex quiete
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              Accelerate according
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              to the Parallels of the Triangle; and that according to the Parallels
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              of the Parallelogram, which, becauſe they are infinite, are donble to
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              the infinite Parallels of the Triangle.
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              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Moreover it may farther be obſerved, that what ever degree of
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              ſwiftneſs is to be found in the Moveable, is indelibly impreſſed upon it
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              of its own nature, all external cauſes of Acceleration or Retardation
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              being removed; which hapneth only in Horizontal Planes: for in de­
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              clining Planes there is cauſe of greater Acceleration, and in the riſing
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              Planes of greater Retardation. </s>
              <s>From whence in like manner it fol­
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              loweth that the Motion along the Horizontal Plane is alſo Perpetual:
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              for if it be Equable, it can neither be weakned nor retarded, nor much
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              leſſe deſtroyed. </s>
              <s>Farthermore, the degree of Celerity acquired by the
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              Moveable in a Natural Deſcent, being of its own Nature Indelible and
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              Penpetual, it is worthy conſideration, that if after the Deſcent along a
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              declining Plane a Reflexion be made along another Plane that is riſing,
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              in this latter there is cauſe of Retardation, for in theſe kind of Planes
                <emph.end type="italics"/>
              </s>
            </p>
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