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

Table of figures

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              <s>
                <pb xlink:href="040/01/911.jpg" pagenum="218"/>
                <emph type="italics"/>
              the
                <emph.end type="italics"/>
              Impetus,
                <emph type="italics"/>
              which it obtaineth in C, whoſe Meaſure is ſuppoſed to be
                <lb/>
              A C, Let A S be a Mean-proportional betwixt B A and A C. </s>
              <s>We will
                <lb/>
              demonſtrate that the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              in B is to the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              in C, as S A is to
                <lb/>
              A C. </s>
              <s>Let the Horizontal Line C D be double to the ſaid A C; and B E
                <lb/>
              double to B A. </s>
              <s>It appeareth by what hath been demonſtrated, That the
                <lb/>
              Cadent along A C being turned along the Horizon C D, and according
                <lb/>
              to the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              acquired in C, with an Equable Motion, ſhall paſs the
                <lb/>
              Space C D in a Time equal to that
                <lb/>
              in which the ſaid A C is paſſed
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.911.1.jpg" xlink:href="040/01/911/1.jpg" number="148"/>
                <lb/>
                <emph type="italics"/>
              with an Accelerate Motion; and
                <lb/>
              likewiſe that B E is paſſed in the
                <lb/>
              ſame time as A B: But the Time of
                <lb/>
              the Deſcent along A B is A S: There­
                <lb/>
              fore the Horizontal Line B E is
                <lb/>
              paſſed in A S. </s>
              <s>As the Time S A is
                <lb/>
              to the Time A C, ſo let E B be to
                <lb/>
              B L. </s>
              <s>And becauſe the Motion by
                <lb/>
              B E is Equable, the Space B L ſhall be paſſed in the Time A C ac­
                <lb/>
              cording to the Moment of Celerity in B: But in the ſame Time A C
                <lb/>
              the Space C D is paſſed, according to the Moment of Velocity in C:
                <lb/>
              the Moments of Velocity therefore are to one another as the Spaces
                <lb/>
              which according to the ſame Moments are paſſed in the ſame Time:
                <lb/>
              Therefore the Moment of Velocity in C is to the Moment of Celerity in
                <lb/>
              B, as D C is to B L. </s>
              <s>And becauſe as D C is to B E, ſo are their halfs,
                <lb/>
              to wit, C A to A B: but as E B is to B L, ſo is B A to A S: Therefore,
                <emph.end type="italics"/>
                <lb/>
              exæquali,
                <emph type="italics"/>
              as D C is to B L, ſo is C A to A S: that is, as the Moment
                <lb/>
              of Velocity in C is to the Moment of Velocity in B, ſo is C A to A S; that
                <lb/>
              is, the Time along C A to the Time along A B. </s>
              <s>I he manner of Meaſu­
                <lb/>
              ring the
                <emph.end type="italics"/>
              Impetus,
                <emph type="italics"/>
              or the Moment of Velocity upon a Line along which it
                <lb/>
              makes a Motion of Deſcent is therefore manifeſt; which
                <emph.end type="italics"/>
              Impetus
                <lb/>
                <emph type="italics"/>
              is indeed ſuppoſed to encreaſe according to the Proportion of the
                <lb/>
              Time.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              But this, before we proceed any farther, is to be premoniſhed, that in
                <lb/>
              regard we are to ſpeak for the future of the Motion compounded of the
                <lb/>
              Equable Horizontal, and of the Naturally Accelerate downwards, (for
                <lb/>
              from this Mixtion reſults, and by it is deſigned the Line of the Project,
                <lb/>
              that is a Parabola;) it is neceſſary that we define ſome common meaſure
                <lb/>
              according to which we may meaſure the Velocity,
                <emph.end type="italics"/>
              Impetus,
                <emph type="italics"/>
              or Moment
                <lb/>
              of both the Motions. </s>
              <s>And ſeeing that of the Equable Motion the de­
                <lb/>
              grees of Velocity are innumerable, of which you may not take any
                <lb/>
              promiſcuouſly, but one certain one which may be be compared and con­
                <lb/>
              joyned with the Degree of Velocity naturally Accelerate. </s>
              <s>I can think of
                <lb/>
              no more eaſie way for the electing and determining of that, than by aſ­
                <lb/>
              ſuming another of the ſame kind. </s>
              <s>And that I may the better expreſs
                <lb/>
              my meaning; Let A C be Perpendicular to the Horizon C B; and A C
                <emph.end type="italics"/>
              </s>
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