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

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        <body>
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            <p type="main">
              <s>
                <pb xlink:href="040/01/842.jpg" pagenum="149"/>
                <figure id="id.040.01.842.1.jpg" xlink:href="040/01/842/1.jpg" number="86"/>
                <lb/>
                <emph type="italics"/>
              as VS is to SX. </s>
              <s>For it is demonſtrated, that Spaces
                <lb/>
              paſſed are in duplicate proportion to the Times, or, (which
                <lb/>
              is the ſame) are as the Squares of the Times: But the pro­
                <lb/>
              portion of the Space VS to the Space ST is double to the
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              proportion of V S to SX, or is the ſame that V S, and S X
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              ſquared have to one another: Therefore, the proportion of
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              the Times of the Motion by V S, and ST, is as the Spaces or
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              Lines V S to S X.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>SCHOLIUM.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              That which is demonſtrated in Motions that are made Perpendicu­
                <lb/>
              larly, may be underſtood alſo to hold true in the Motions made along
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              Planes of any whatever Inclination; for it is ſuppoſed, that in them
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              the degree of Acceleration encreaſeth in the ſame proportion; that
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              is, according to the encreaſe of the Time; or, if you will, according
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              to the ſimple and primary Series of Numbers.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Here I deſire
                <emph type="italics"/>
              Sagredus,
                <emph.end type="italics"/>
              that I alſo may be allowed, al­
                <lb/>
              beit perhaps with too much tediouſneſſe in the opinion of
                <emph type="italics"/>
              Simplici­
                <lb/>
              us,
                <emph.end type="italics"/>
              to defer for a little time the preſent Reading, untill I may have
                <lb/>
              explained what from that which hath been already ſaid and de­
                <lb/>
              monſtrated, and alſo from the knowledge of certain Mechanical
                <lb/>
              Concluſions heretofore learnt of our
                <emph type="italics"/>
              Academick,
                <emph.end type="italics"/>
              I now remember
                <lb/>
              to adjoyn for the greater confirmation of the truth of the Princi­
                <lb/>
              ple, which hath been examined by us even now with probable
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              Reaſons and Experiments: and, which is of more importance, for
                <lb/>
              the Geometrical proof of it, let me firſt demonſtrate one ſole Ele­
                <lb/>
              mental
                <emph type="italics"/>
              Lemma
                <emph.end type="italics"/>
              in the Contemplation of
                <emph type="italics"/>
              Impetus's.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>If our advantage ſhall be ſuch as you promiſeus, there
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              is no time that I would not moſt willingly ſpend in diſcourſing
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              about the confirmation and thorow eſtabliſhing theſe Sciences of
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              Motion: and as to my own particular, I not only grant you liber­
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              ty to ſatisfie your ſelf in this particular, but moreover entreat you
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              to gratifie, as ſoon as you can, the Curioſity which you have begot
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              in me touching the ſame: and I believe that
                <emph type="italics"/>
              Simplicius
                <emph.end type="italics"/>
              alſo is of the
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              ſame mind.</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>I cannot deny what you ſay.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              S
                <emph.end type="italics"/>
              ALV. </s>
              <s>Seeing then that I have your permiſſion, I will in the
                <lb/>
              firſt place conſider, as an Effect well known, That</s>
            </p>
          </chap>
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