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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="040/01/030.jpg" pagenum="14"/>
            <p type="main">
              <s>SAGR. </s>
              <s>I do not very well underſtand the queſtion.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>I will expreſs it better by drawing a Figure: therefore
                <lb/>
              I will ſuppoſe the line A B [in
                <emph type="italics"/>
              Fig.
                <emph.end type="italics"/>
              3.] parallel to the Horizon,
                <lb/>
              and upon the point B, I will erect a perpendicular B C; and after
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              that I adde this ſlaunt line C A. </s>
              <s>Underſtanding now the line C
                <lb/>
              A to be an inclining plain exquiſitely poliſhed, and hard, upon
                <lb/>
              which deſcendeth a ball perfectly round and of very hard matter,
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              and ſuch another I ſuppoſe freely to deſcend by the perpendicular
                <lb/>
              C B: will you now confeſs that the
                <emph type="italics"/>
              impetus
                <emph.end type="italics"/>
              of that which
                <lb/>
              ſcends by the plain C A, being arrived to the point A, may be
                <lb/>
              equal to the
                <emph type="italics"/>
              impetus
                <emph.end type="italics"/>
              acquired by the other in the point B, after
                <lb/>
              the deſcent by the perpendicular C
                <lb/>
                <arrow.to.target n="marg44"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg44"/>
                <emph type="italics"/>
              The impetuoſity of
                <lb/>
              moveables equally
                <lb/>
              approaching to the
                <lb/>
              centre, are equal.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>I reſolutely believe ſo: for in effect they have both the
                <lb/>
              ſame proximity to the centre, and by that, which I have already
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              granted, their impetuoſities would be equally ſufficient to re-carry
                <lb/>
              them to the ſame height.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Tell me now what you believe the ſame ball would do
                <lb/>
              put upon the Horizontal plane A B?</s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg45"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg45"/>
                <emph type="italics"/>
              Vpon an
                <lb/>
              tall plane the
                <lb/>
              able lieth ſtill.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>It would lie ſtill, the ſaid plane having no declination.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>But on the inclining plane C A it would deſcend, but
                <lb/>
              with a gentler motion than by the perpendicular C B?</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>I may confidently anſwer in the affirmative, it
                <lb/>
              ing to me neceſſary that the motion by the perpendicular C B
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              ſhould be more ſwift, than by the inclining plane C A; yet
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              vertheleſs, iſ this be, how can the Cadent by the inclination
                <lb/>
              rived to the point A, have as much
                <emph type="italics"/>
              impetus,
                <emph.end type="italics"/>
              that is, the ſame
                <lb/>
              gree of velocity, that the Cadent by the perpendicular ſhall have
                <lb/>
              in the point B? theſe two Propoſitions ſeem contradictory.</s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg46"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg46"/>
                <emph type="italics"/>
              The veloeity by the
                <lb/>
              inclining plane
                <lb/>
              qual to the
                <lb/>
              ty by the
                <lb/>
              oular, and the
                <lb/>
              tion by the
                <lb/>
              dicular ſwifter
                <lb/>
              than by the
                <lb/>
              nation.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Then you would think it much more falſe, ſhould I
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              ſay, that the velocity of the Cadents by the perpendicular, and
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              inclination, are abſolutely equal: and yet this is a Propoſition
                <lb/>
              moſt true, as is alſo this that the Cadent moveth more ſwiftly by
                <lb/>
              the perpendicular, than by the inclination.</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>Theſe Propoſitions to my ears ſound very harſh: and
                <lb/>
              I believe to yours
                <emph type="italics"/>
              Simplicius
                <emph.end type="italics"/>
              ?</s>
            </p>
            <p type="main">
              <s>SIMPL. </s>
              <s>I have the ſame ſenſe of them.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>I conceit you jeſt with me, pretending not to
                <lb/>
              hend what you know better than my ſelf: therefore tell me
                <emph type="italics"/>
                <lb/>
              plicius,
                <emph.end type="italics"/>
              when you imagine a moveable more ſwift than
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              ther, what conceit do you fancy in your mind?</s>
            </p>
            <p type="main">
              <s>SIMPL. </s>
              <s>I fancie one to paſs in the ſame time a greater ſpace
                <lb/>
              than the other, or to move equal ſpaces, but in leſſer time.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Very well: and for moveables equally ſwift, what's
                <lb/>
              your conceit of them?</s>
            </p>
            <p type="main">
              <s>SIMPL. </s>
              <s>I fancie that they paſs equal ſpaces in equal times.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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