Galilei, Galileo, The systems of the world, 1661

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="065/01/021.jpg" pagenum="15"/>
            <p type="main">
              <s>SALV. </s>
              <s>And have you no other conceit thereof than this?</s>
            </p>
            <p type="main">
              <s>SIMPL. </s>
              <s>This I think to be the proper definition of equal
                <lb/>
              tions.</s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg47"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg47"/>
                <emph type="italics"/>
              Velocities are ſaid
                <lb/>
              to be equal, when
                <lb/>
              the ſpaces paſſed
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              are proportionate to
                <lb/>
              their time.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>We will add moreover this other: and call that equal
                <lb/>
              velocity, when the ſpaces paſſed have the ſame proportion, as the
                <lb/>
              times wherein they are paſt, and it is a more univerſal definition.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>It is ſo: for it comprehendeth the equal ſpaces paſt in
                <lb/>
              equal times, and alſo the unequal paſt in times unequal, but
                <lb/>
              portionate to thoſe ſpaces. </s>
              <s>Take now the ſame Figure, and
                <lb/>
              ing the conceipt that you had of the more haſtie motion, tell me
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              why you think the velocity of the Cadent by C B, is greater
                <lb/>
              than the velocity of the Deſcendent by C A?</s>
            </p>
            <p type="main">
              <s>SIMPL. </s>
              <s>I think ſo; becauſe in the ſame time that the Cadent
                <lb/>
              ſhall paſs all C B, the Deſcendent ſhall paſs in C A, a part leſs
                <lb/>
              than C B.</s>
            </p>
            <p type="main">
              <s>SALV. True; and thus it is proved, that the moveable moves
                <lb/>
              more ſwiftly by the perpendicular, than by the inclination. </s>
              <s>Now
                <lb/>
              conſider, if in this ſame Figure one may any way evince the
                <lb/>
              ther conceipt, and finde that the moveables were equally ſwift
                <lb/>
              by both the lines C A and C B.</s>
            </p>
            <p type="main">
              <s>SIMPL. </s>
              <s>I ſee no ſuch thing; nay rather it ſeems to contradict
                <lb/>
              what was ſaid before.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>And what ſay you,
                <emph type="italics"/>
              Sagredus
                <emph.end type="italics"/>
              ? </s>
              <s>I would not teach you
                <lb/>
              what you knew before, and that of which but juſt now you
                <lb/>
              duced me the definition.</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>The definition I gave you, was, that moveables may
                <lb/>
              be called equally ſwift, when the ſpaces paſſed are proportional
                <lb/>
              to the times in which they paſſed; therefore to apply the
                <lb/>
              tion to the preſent caſe, it will be requiſite, that the time of
                <lb/>
              ſcent by C A, to the time of falling by C B, ſhould have the
                <lb/>
              ſame proportion that the line C A hath to the line C B; but I
                <lb/>
              underſtand not how that can be, for that the motion by C B is
                <lb/>
              ſwifter than by C A.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>And yet you muſt of neceſſity know it. </s>
              <s>Tell me a little,
                <lb/>
              do not theſe motions go continually accelerating?</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>They do; but more in the perpendicular than in the
                <lb/>
              inclination.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>But this acceleration in the perpendicular, is it yet
                <lb/>
              withſtanding ſuch in compariſon of that of the inclined, that
                <lb/>
              two equal parts being taken in any place of the ſaid
                <lb/>
              lar and inclining lines, the motion in the parts of the
                <lb/>
              lar is alwaies more ſwift, than in the part of the inclination?</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>I ſay not ſo: but I could take a ſpace in the
                <lb/>
              on, in which the velocity ſhall be far greater than in the like ſpace
                <lb/>
              taken in the perpendicular; and this ſhall be, if the ſpace in the </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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