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

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            <p type="main">
              <s>
                <pb xlink:href="040/01/903.jpg" pagenum="210"/>
                <emph type="italics"/>
              tion of the Squares of C B, D B, E B, or, if you will, in the doubled
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              proportion of the Lines. </s>
              <s>And if unto the Moveable moved beyond B
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              towards C with the Equable Lation we ſuppoſe the Perpendicular
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              Deſcent to be ſuperadded according to the quantity C I, in the Time
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              B C it ſhall be found conſtituted in the Term I. </s>
              <s>And proceeding farther,
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                <figure id="id.040.01.903.1.jpg" xlink:href="040/01/903/1.jpg" number="146"/>
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                <emph type="italics"/>
              in the Time D B, namely,
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              in the double of B C, the
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              Space of the Deſcent down­
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              wards ſhall be quadruple to
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              the firſt Space C I: For
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              it hath beendemonſtrated in
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              the firſt Trastate, that the
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              Spaces paſſed by GraveBo­
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              dies with a Motion Natu­
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              rally Accelerate are in du­
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              plicate proportion of their Times. </s>
              <s>And it likewiſe followeth, that the
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              Space E H paſſed in the Time B E, ſhall be as G. </s>
              <s>So that it is manifeſtly
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              proved, that the Spaces E H, D F, C I, are to one another as the Squares
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              of the Lines E B, D B, C B. </s>
              <s>Now from the points I, F, and H draw
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              the Right Lines I O, F G, H L, Parallel to the ſaid E B; and each of
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              the Lines H L, F G, and I O ſhall be equal to each of the other Lines
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              E B, D B, and C B; as alſo each of thoſe B O, B G, and B L, ſhall be
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              equal to each of thoſe C I, D F, and E H: And the Square H L ſhall
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              be to the Square F G, as the Line L B to B G: And the Square F G
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              ſhall be to the Square I O, as G B to B O: Therefore the Points I, F,
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              and H are in one and the ſame Parabolical Line. </s>
              <s>And in like manner
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              it ſhall be demonſtrated, any equalparticles of Time of whatſoever Mag­
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              nitude being taken, that the place of the Moveable whoſe Motion is
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              compounded of the like Lations, is in the ſame Times to be found in the
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              ſame Parabolick Line: Therefore the Propoſition is manifeſt.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>This Concluſion is gathered from the Converſion of the
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              firſt of thoſe two Propoſitions that went before, for the Parabola
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              being, for example, deſcribed by the points B H, if either of the
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              two F or I were not in the deſcribed Parabolick Line, it would be
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              within, or without; and by conſequence the Line F G would be
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              either greater or leſſer than that which ſhould determine in the Pa­
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              rabolick Line; Wherefore the Square of HL would have, not to
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              the Square of F G, but to another greater or leſſer, the ſame pro­
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              portion that the Line L B hath to BG, but it hath the ſame propor­
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              tion to the Square of F G: Therefore the point F is in the Parabo­
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              lick Line: And ſo all the reſt,
                <emph type="italics"/>
              &c.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>It cannot be denied but that the Diſcourſe is new, in­
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              genious and concludent, arguing
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              ex ſuppoſitione,
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              that is, ſuppoſing
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              that the Tranſverſe Motion doth continue alwaies Equable, and </s>
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