Baliani, Giovanni Battista, De motv natvrali gravivm solidorvm et liqvidorvm

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    <archimedes>
      <text>
        <body>
          <chap type="bk">
            <subchap1 n="2" type="proposition">
              <subchap2 n="2" type="proof">
                <p type="main">
                  <s id="s.000420">
                    <pb xlink:href="064/01/062.jpg"/>
                  Fiat EH aequalis AC, et ab AG abla­
                    <lb/>
                  ta AH, residuo HG fiat aequalis EI.</s>
                </p>
                <p type="main">
                  <s id="s.000421">Dico EI esse portionem quaesitam.</s>
                </p>
                <p type="main">
                  <s id="s.000422">Quoniam AE est casus gravis A tempore ae per
                    <lb/>
                  supp. & AE, AC sunt in dupl. ratione tem­
                    <lb/>
                  porum ae, ac per constr. </s>
                  <s id="s.000423">AC est casus gravis
                    <lb/>
                  tempore ac
                    <arrow.to.target n="marg99"/>
                  , & proinde EH aequalis AC est
                    <lb/>
                  casus tempore eg aequali ipsi ab si grave du­
                    <lb/>
                  ceretur per EH eadem prorsus virtute qua
                    <lb/>
                  ductum fuit per AC
                    <arrow.to.target n="marg100"/>
                  .</s>
                </p>
                <p type="margin">
                  <s id="s.000424">
                    <margin.target id="marg99"/>
                  Per 3. pr. huius.</s>
                </p>
                <p type="margin">
                  <s id="s.000425">
                    <margin.target id="marg100"/>
                  Per axioma primum.</s>
                </p>
                <p type="main">
                  <s id="s.000426">Item quia AG, AE sunt in duplicata ratione tem­
                    <lb/>
                  porum ag, ae per constr., AG est casus tempo­
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                  re ag
                    <arrow.to.target n="marg101"/>
                  , & proinde residuum EG est casus re­
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                  sidui eg
                    <arrow.to.target n="marg102"/>
                  , dum tamen motus proveniat tam
                    <lb/>
                  e gravitate quam a quolibet impetu superaddi­
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                  to, at EH probatum est esse casum itidem, eg
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                  dum tamen grave ducatur ea solum virtute
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                  qua ductum fuit per AC
                    <arrow.to.target n="marg103"/>
                  , ig, residuum HG
                    <lb/>
                  est spatium quod perficitur eodem tempore eg,
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                  a solo impetu acquisito in E
                    <arrow.to.target n="marg104"/>
                  , quod est aequa­
                    <lb/>
                  le EI per constr., unde EI est spatium quaesitum.</s>
                </p>
                <p type="margin">
                  <s id="s.000427">
                    <margin.target id="marg101"/>
                  Per 3. primi huius.</s>
                </p>
                <p type="margin">
                  <s id="s.000428">
                    <margin.target id="marg102"/>
                  Per 19. Quinti.</s>
                </p>
                <p type="margin">
                  <s id="s.000429">
                    <margin.target id="marg103"/>
                  Per axioma primum.</s>
                </p>
                <p type="margin">
                  <s id="s.000430">
                    <margin.target id="marg104"/>
                  Per axioma secundum.</s>
                </p>
                <p type="main">
                  <s id="s.000431">Sit deinde portio temporis eb disiuncta ab ae, puta
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                  gK, & sit rursus reperienda portio spatij EB
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                  per quod grave A ducatur vi solius impetus
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                  in E acquisiti in dicta portione temporis gk:
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                  reperto prius spatio EC respondenti tempori eg
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                  immediato ipsi ae modo quo supra dictum
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                  fuit; fiat ac tempus aequale tempori gK, & ut</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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