Galilei, Galileo, The systems of the world, 1661

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="065/01/019.jpg" pagenum="13"/>
              ſhall be an eaſie task; for I reply, that the moveable paſſeth by
                <lb/>
              the aforeſaid degrees, but the paſſage is made without ſtaying in </s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg42"/>
                <lb/>
              any of them; ſo that the paſſage requiring but one ſole inſtant
                <lb/>
              of time, and every ſmall time containing infinite inſtants, we ſhall
                <lb/>
              not want enough of them to aſſign its own to each of the infinite
                <lb/>
              degrees of tardity; although the time were never ſo ſhort.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg42"/>
                <emph type="italics"/>
              The moveable
                <lb/>
              parting from reſv
                <lb/>
              paſſeth thorow all
                <lb/>
              degrees of velocity
                <lb/>
              without ſtaying in
                <lb/>
              any.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>Hitherto I apprehend you; nevertheleſs it is very much
                <lb/>
              that that Ball ſhot from a Cannon (for ſuch I conceive the
                <lb/>
              dent moveable) which yet we ſee to fall with ſuch a precipice,
                <lb/>
              that in leſs than ten pulſes it will paſs two hundred yards of
                <lb/>
              titude; ſhould in its motion be found conjoyned with ſo ſmall a
                <lb/>
              degree of velocity, that, ſhould it have continued to have moved
                <lb/>
              at that rate without farther acceleration, it would not have paſt
                <lb/>
              the ſame in a day.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>You may ſay, nor yet in a year, nor in ten, no nor in a
                <lb/>
              thouſand; as I will endeavour to ſhew you, and alſo happily
                <lb/>
              out your contradiction, to ſome ſufficiently ſimple queſtions that
                <lb/>
              I will propound to you. </s>
              <s>Therefore tell me if you make any
                <lb/>
              ſtion of granting that, that that ball in deſcending goeth
                <lb/>
              ſing its
                <emph type="italics"/>
              impetus
                <emph.end type="italics"/>
              and velocity.</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>I am moſt certain it doth.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>And if I ſhould ſay that the
                <emph type="italics"/>
              impetus
                <emph.end type="italics"/>
              acquired in any
                <lb/>
              place of its motion, is ſo much, that it would ſuffice to re-carry
                <lb/>
              it to that place from which it came, would you grant it?</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>I ſhould conſent to it without contradiction, provided
                <lb/>
              waies, that it might imploy without impediment its whole
                <emph type="italics"/>
              impetus
                <emph.end type="italics"/>
                <lb/>
              in that ſole work of re-conducting it ſelf, or another equal toit, to
                <lb/>
                <arrow.to.target n="marg43"/>
                <lb/>
              that ſelf-ſame height as it would do, in caſe the Earth were bored
                <lb/>
              thorow the centre, and the Bullet fell a thouſand yards from the
                <lb/>
              ſaid centre, for I verily believe it would paſs beyond the centre,
                <lb/>
              aſcending as much as it had deſcended; and this I ſee plainly in
                <lb/>
              the experiment of a plummet hanging at a line, which removed
                <lb/>
              from the perpendicular, which is its ſtate of reſt, and afterwards
                <lb/>
              let go, falleth towards the ſaid perpendicular, and goes as far
                <lb/>
              yond it; or onely ſo much leſs, as the oppoſition of the air, and
                <lb/>
              line, or other accidents have hindred it. </s>
              <s>The like I ſee in the
                <lb/>
              ter, which deſcending thorow a pipe, re-mounts as much as it had
                <lb/>
              deſcended.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg43"/>
                <emph type="italics"/>
              The ponderous
                <lb/>
              ver deſcending
                <lb/>
              quireth
                <emph.end type="italics"/>
              impetus
                <lb/>
                <emph type="italics"/>
              ſufficient to
                <lb/>
              carry it to the like
                <lb/>
              height.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>You argue very well. </s>
              <s>And for that I know you will not
                <lb/>
              ſcruple to grant that the acquiſt of the
                <emph type="italics"/>
              impetus
                <emph.end type="italics"/>
              is by means of the
                <lb/>
              receding from the term whence the moveable departed, and its
                <lb/>
              proach to the centre, whither its motion tendeth; will you ſtick
                <lb/>
              to yeeld, that two equal moveables, though deſcending by divers
                <lb/>
              lines, without any impediment, acquire equal
                <emph type="italics"/>
              impetus,
                <emph.end type="italics"/>
              provided
                <lb/>
              that the approaches to the centre be equal?</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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