Galilei, Galileo, The systems of the world, 1661

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="065/01/153.jpg" pagenum="145"/>
              compoſition of the two motions do go alwayes receding with
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              greater and greater proportion from the circumference of that
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              cle, which the centre of the ſtones gravity would have deſigned,
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              if it had alwayes ſtaid upon the Tower; it followeth of neceſſity
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              that this receſſion at the firſt be but little, yea very ſinall, yea,
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              more, as ſmall as can be imagined, ſeeing that the deſcending
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              grave body departing from reſt, that is, from the privation of
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              motion, towards the bottom and entring into the right motion
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              downwards, it muſt needs paſſe through all the degrees of
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              ty, that are betwixt reſt, and any aſſigned velocity; the which
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              degrees are infinite; as already hath been at large diſcourſed and
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              proved.</s>
            </p>
            <p type="main">
              <s>It being ſuppoſed therefore, that the progreſſe of the
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              ration being after this manner, and it being moreover true, that
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              the deſcending grave body goeth to terminate in the centre of the
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              Earth, it is neceſſary that the line of its mixt motion be ſuch, that
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                <arrow.to.target n="marg329"/>
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              it go continually receding with greater and greater proportion
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              from the top of the Tower, or to ſpeak more properly, from
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              the circumference of the circle deſcribed by the top of the Tower,
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              by means of the Earths converſion; but that ſuch receſſions be
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              leſſer and leſſer
                <emph type="italics"/>
              in infinitum
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              ; by how much the moveable finds it
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              ſelf to be leſſe and leſſe removed from the firſt term where it
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              reſted. </s>
              <s>Moreover it is neceſſary, that this line of the
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              ed motion do go to terminate in the centre of the Earth. </s>
              <s>Now
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              having preſuppoſed theſe two things, I come to deſcribe about
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              the centre A [
                <emph type="italics"/>
              in Fig. </s>
              <s>1. of this ſecond Dialogue
                <emph.end type="italics"/>
              ;] with the ſemi­
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              diameter A B, the circle B I, repreſenting to me the Terreſtrial
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              Globe, and prolonging the ſemidiameter A B to C, I have
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              ſcribed the height of the Tower B C; the which being carried
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              about by the Earth along the circumference B I, deſcribeth with
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              its top the arch C D: Dividing, in the next place, the line C A
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              in the middle at E; upon the centre E, at the diſtance E C, I
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              ſcribe the ſemicircle C I A: In which, I now affirm, that it is very
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              probable that a ſtone falling from the top of the Tower C, doth
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              move, with a motion mixt of the circular, which is in common,
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              and of its peculiar right motion. </s>
              <s>If therefore in the circumference
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              C D, certain equal parts C F, F G, G H, H L, be marked, and
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              from the points F, G, H, L, right lines be drawn towards the
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              centre A, the parts of them intercepted between the two
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              cumferences C D and B I, ſhall repreſent unto us the ſame
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              Tower C B, tranſported by the Terreſtrial Globe towards D I;
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              in which lines the points where they come to be interſected by the
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              arch of the ſemicircle C I, are the places by whichfrom time to
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              time the falling ſtone doth paſſe; which points go continually
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              with greater and greater proportion receding from the top of the </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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