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

Table of figures

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        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/914.jpg" pagenum="221"/>
                <emph type="italics"/>
              an Horizontal Line, and parallel to C D. </s>
              <s>And if the Amplitude C D
                <lb/>
              be equal to the whole Altitude D A, B I ſhall be equal to B A and B D.
                <lb/>
              </s>
              <s>And if the Time of the Fall along A B, and the Moment of Velocity
                <lb/>
              acquired in B along the Deſcent A B
                <emph.end type="italics"/>
              ex quiete
                <emph type="italics"/>
              in A be ſuppoſed to be
                <lb/>
              meaſured by the ſaid A B, then D C (that is twice B I) ſhall be the
                <lb/>
              Space which ſhall be paſſed by the
                <emph.end type="italics"/>
              Impetus A
                <emph type="italics"/>
              B turned along the Hori­
                <lb/>
              zontal Line in the ſame Time: But in the ſame Time falling along B D
                <lb/>
              out of Reſt in B, it ſhall paſs the Altitude B D: Therefore the Movea­
                <lb/>
              ble falling out of Reſt in A along A B,
                <lb/>
              being converted with the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              A B
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.914.1.jpg" xlink:href="040/01/914/1.jpg" number="150"/>
                <lb/>
                <emph type="italics"/>
              along the Horizontal Parallel ſhall
                <lb/>
              paſs a Space equal to D C. </s>
              <s>And the
                <lb/>
              Fall along B D ſupervening, it paſſeth
                <lb/>
              the Altitude B D, and deſcribes the
                <lb/>
              Parabola B C; whoſe
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              in the
                <lb/>
              Term C is compounded of the Equable
                <lb/>
              Tranſverſal whoſe Moment is as A B,
                <lb/>
              and of another Moment acquired in the
                <lb/>
              Fall B D in the Term D or C; which
                <lb/>
              Moments are Equal. </s>
              <s>If therefore we
                <lb/>
              ſuppoſe A B to be the Meaſure of one of them, as ſuppoſe of the Equa­
                <lb/>
              ble Tranſverſal; and B I, which is equal to B D, to be the Meaſure of
                <lb/>
              the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              acquired in D or C; then the Subtenſe I A ſhall be the
                <lb/>
              quantity of the Moment compound of them both: Therefore it ſhall be
                <lb/>
              the quantity or Meaſure of the whole Moment which the Project deſcend­
                <lb/>
              ing along the Parabola B C ſhall acquire of
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              in C. </s>
              <s>This pre­
                <lb/>
              miſed, take in the Parabola any point E, in which we are to determine
                <lb/>
              of the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              of the Project. </s>
              <s>Draw the Horizontal Parallel E F,
                <lb/>
              and let B G be a Mean-proportional between B D and B F. </s>
              <s>And foraſ­
                <lb/>
              much as A B or B D is ſuppoſed to be the Meaſure of the Time, and of
                <lb/>
              the Moment of the Velocity in the Fall B D
                <emph.end type="italics"/>
              ex quiete
                <emph type="italics"/>
              in B: B G ſhall
                <lb/>
              be the Time, or the Meaſure of the Time, and of the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              in F, coming
                <lb/>
              out of B. </s>
              <s>If therefore B O be ſuppoſed equal to B G, the Diagonal
                <lb/>
              drawn from A to O ſhall be the quantity of the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              in E; for
                <lb/>
              A B hath been ſuppoſed the determinator of the Time, and of the
                <emph.end type="italics"/>
              Impe­
                <lb/>
              tus
                <emph type="italics"/>
              in B, which turned along the Horizontal Parallel doth alwaies
                <lb/>
              continue the ſame: And B O determineth the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              in F or in E
                <lb/>
              along the Deſcent
                <emph.end type="italics"/>
              ex quiete
                <emph type="italics"/>
              in B in the Altitude B F: But theſe two
                <lb/>
              A B and B O are
                <emph.end type="italics"/>
              potentia
                <emph type="italics"/>
              equal to the Power A O. </s>
              <s>Therefore that is
                <lb/>
              manifeſt which was ſought.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>The Contemplation of the Compoſition of theſe diffe­
                <lb/>
              rent
                <emph type="italics"/>
              Impetus's,
                <emph.end type="italics"/>
              and of the quantity of that
                <emph type="italics"/>
              Impetus
                <emph.end type="italics"/>
              which reſults
                <lb/>
              from this mixture, is ſo new to me, that it leaveth my mind in no
                <lb/>
              ſmall confuſion. </s>
              <s>I do not ſpeak of the mixtion of two Motions </s>
            </p>
          </chap>
        </body>
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