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

Table of figures

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            <p type="main">
              <s>
                <pb xlink:href="040/01/845.jpg" pagenum="152"/>
              ſuppoſe that the Moveable G is to the Moveable H, as F
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              is to
                <lb/>
              F C; and then the
                <emph type="italics"/>
              Equilibrium
                <emph.end type="italics"/>
              ſhall follow, that is, the Moveables
                <lb/>
              H and G ſhall have equal Moments, and the Motion of the ſaid
                <lb/>
              Moveables ſhall ceaſe.
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              nd becauſe we ſee that the
                <emph type="italics"/>
              Impetus,
                <emph.end type="italics"/>
                <lb/>
              Energy, Moment, or Propenſion of a Moveable to Motion is the
                <lb/>
              ſame as is the Force or ſmalleſt Reſiſtance that ſufficeth to ſtop it;
                <lb/>
              and becauſe it hath been concluded, that the Grave Body H is ſuf.
                <lb/>
              </s>
              <s>ficient to arreſt the Motion of
                <lb/>
                <figure id="id.040.01.845.1.jpg" xlink:href="040/01/845/1.jpg" number="88"/>
                <lb/>
              the Grave Body G: Therefore
                <lb/>
              the leſſer Weight H, which in
                <lb/>
              the Perpendicular F C imploy­
                <lb/>
              eth its total Moment, ſhall be
                <lb/>
              the preciſe meaſure of the par­
                <lb/>
              tial Moment that the greater
                <lb/>
              Weight G exerciſeth along the
                <lb/>
              inclined Plane F
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              : But the
                <lb/>
              meaſure of the total Moment of
                <lb/>
              the ſaid Grave Body G, is the
                <lb/>
              ſelf ſame, (ſince that to impede
                <lb/>
              the Perpendicular Deſcent of a
                <lb/>
              Grave Body there is required the oppoſition of ſuch another Grave
                <lb/>
              Body, which likewiſe is at liberty to move Perpendicularly:)
                <lb/>
              Therefore the partial
                <emph type="italics"/>
              Impetus
                <emph.end type="italics"/>
              or Moment of G along the inclined
                <lb/>
              Plane F A ſhall be to the grand and total
                <emph type="italics"/>
              Impetus
                <emph.end type="italics"/>
              of the ſame G
                <lb/>
              along the Perpendicular F C, as the Weight H to the Weight G:
                <lb/>
              that is, by Conſtruction, as the ſaid Perpendicular F C, the Eleva­
                <lb/>
              tion of the inclined Plane, is to the ſame inclined Plane F A:
                <lb/>
              Which is that that by the
                <emph type="italics"/>
              Lemma
                <emph.end type="italics"/>
              was propoſed to be demon­
                <lb/>
              ſtrated, and which by our Author, as we ſhall ſee, is ſuppoſed as
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              known in the ſecond part of the Sixth Propoſition of the preſent
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              Treatiſe.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1092"/>
              * Or inclined
                <lb/>
              Plane.</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>From this that you have already concluded I conceive
                <lb/>
              one may eaſily deduce, arguing
                <emph type="italics"/>
              ex æquali
                <emph.end type="italics"/>
              by perturbed Proportion,
                <lb/>
              that the Moments of the ſame Moveable, along Planes variouſly
                <lb/>
              inclined (as F A and F I) that have the ſame Elevation, are to each
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              other in Reciprocal proportion to the ſame Planes.</s>
            </p>
            <p type="main">
              <s>SALV.
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              moſt certain Concluſion. </s>
              <s>This being agreed on, we
                <lb/>
              will paſs in the next place to demonſtrate the
                <emph type="italics"/>
              Theoreme,
                <emph.end type="italics"/>
              namely,
                <lb/>
              that</s>
            </p>
          </chap>
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