Monantheuil, Henri de, Aristotelis Mechanica, 1599

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      <text>
        <body>
          <chap>
            <subchap1>
              <pb xlink:href="035/01/128.jpg" pagenum="88"/>
              <p type="head">
                <s id="id.001388">Propoſitionis conuerſio. </s>
              </p>
              <p type="main">
                <s id="id.001389">
                  <emph type="italics"/>
                Naui æqualiter prouecta, atque palmula retroceßit: motus capitis
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                remi proprius duplus eſt motus nauis.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="id.001390">
                  <emph type="italics"/>
                Si enim C H æqualis ponatur B D, quoniam eidem B D æqua­
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                lis eſt H E in parallelogrammo, æquales igitur erunt C H &
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                H E ax. 1. </s>
                <s id="id.001391">Et ſic dupla erit C E ipſius H E: & eadem C E
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                dupla ipſius B D. </s>
                <s>æquales porro ſunt C E & A E prop 26. lib. 1.
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                </s>
                <s>Dupla ergo erit A E rectæ B D. </s>
                <s>ſed recta A E decurſa eſt à ca­
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                pite remi, & B D à ſcalmo, quantùm autem prouehitur ſcalmus,
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                tantùm & nauis. </s>
                <s id="id.001392">Igitur ſi nauis tantùm fuerit prouecta, quantùm
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                remi palmula retroceßit, duplum conficit caput remi motu proprio
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                eius interualli, quod nauis conficit. </s>
                <s id="id.001393">quod fuit demonſtrandum.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="head">
                <s id="id.001394">Propoſitio quarta. </s>
              </p>
              <p type="main">
                <s id="id.001395">
                  <emph type="italics"/>
                Nauis decurrens minus ſpatium: quam caput remi decurrat: maius
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                tamen eius dimidio: magis prouehitur: quam palmula retrocedat:
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                minus autem dimidio: minus.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="id.001396">
                  <emph type="italics"/>
                In poſtremo diagrammate ponatur B D minor, quam A E:
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                ſed eius dimidio maior. </s>
                <s id="id.001397">Dico quod ipſa B D maior eſt, quam C H.
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                </s>
                <s id="id.001398">Nam B D & H E æquales ſunt, ad hæc A E & C E æqua­
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                les ſunt. </s>
                <s id="id.001399">maior igitur erit H E dimidio ipſius A E. </s>
                <s>quapropter
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                reliqua C H minor dimidio erit eiuſdem A E. </s>
                <s id="id.001400">Et minor igitur
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                erit C H quam B D. </s>
                <s id="id.001401">Interuallum autem B D, id eſt quod nauis
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                confecit, interuallum vero C H remi palmula in contrarium de­
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                currit. </s>
                <s id="id.001402">Ideo prior pars theorematis vera. </s>
                <s id="id.001403">Poſterior autem ſimiliter
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                oſtendetur. </s>
                <s id="id.001404">Si enim B D minor eſt dimidio ipſius A E, minor
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                igitur erit & H E dimidio eiuſdem A E. </s>
                <s id="id.001405">Et quoniam A E &
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                C E æquales ſunt. </s>
                <s id="id.001406">Reliqua igitur C H dimidio eiuſdem A E
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                maior erit. </s>
                <s id="id.001407">Et proinde minor erit B D quam C H. </s>
                <s id="id.001408">Nauis igitur
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                minus interuallum decurret in anteriora: quam remi palmula in
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                contrarium. </s>
                <s id="id.001409">quod fuit demonſtrandum.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="head">
                <s id="id.001410">Corollarium. </s>
              </p>
              <p type="main">
                <s id="id.001411">
                  <emph type="italics"/>
                Hinc & ex præcedenti infertur, quod ſi caput remi motu pro­
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                prio decurrat interuallum maius, quam nauis, ſiue duplum, ſiue du­
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                plo minus, ſiue maius: ſemper interuallum nauis adiuncto ei quod
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                palmula retroceſſerit, æquale erit ei, quod à capite remi motu proprio
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                conficitur.
                  <emph.end type="italics"/>
                </s>
              </p>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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