Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
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        <div type="section" level="1" n="23">
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              <pb file="0036" n="36" rhead="ARCHIMEDIS"/>
            angulus b n f œqualis angulo o g f: </s>
            <s xml:space="preserve">quòd cum ſit g o perpendi-
              <lb/>
              <anchor type="note" xlink:label="note-0036-01a" xlink:href="note-0036-01"/>
            cularis ad e f, & </s>
            <s xml:space="preserve">h n ad eandem perpendicularis erit. </s>
            <s xml:space="preserve">quod de-
              <lb/>
            monstrare oportebat.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="7">
            <note position="right" xlink:label="note-0035-01" xlink:href="note-0035-01a" xml:space="preserve">cor. 8. ſe-
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            xti.</note>
            <figure xlink:label="fig-0035-01" xlink:href="fig-0035-01a">
              <image file="0035-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0035-01"/>
            </figure>
            <note position="right" xlink:label="note-0035-02" xlink:href="note-0035-02a" xml:space="preserve">17. ſextĩ.</note>
            <note position="right" xlink:label="note-0035-03" xlink:href="note-0035-03a" xml:space="preserve">14. ſexti.</note>
            <note position="right" xlink:label="note-0035-04" xlink:href="note-0035-04a" xml:space="preserve">32. primi</note>
            <note position="right" xlink:label="note-0035-05" xlink:href="note-0035-05a" xml:space="preserve">4. primi.</note>
            <note position="right" xlink:label="note-0035-06" xlink:href="note-0035-06a" xml:space="preserve">28</note>
            <note position="left" xlink:label="note-0036-01" xlink:href="note-0036-01a" xml:space="preserve">29, primi</note>
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          <p>
            <s xml:space="preserve">Et quod in humido eſt ſurſum ſeretur ſecundum per-
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              <anchor type="note" xlink:label="note-0036-02a" xlink:href="note-0036-02"/>
            pendicularem, quæ per b ducta eſtipſi rt æquidiſtans.</s>
            <s xml:space="preserve">]
              <lb/>
            _Cur hoc quidem ſurſum, illud uero deorſum per lineam perpen-_
              <lb/>
            _dicularem feratur, diximus ſupra in octauam primi libri buius. </s>
            <s xml:space="preserve">qua_
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            _re neque in hac, neque in alijs, quæ ſequuntur, eadem iterare neceſſa_
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            _rium exiſtimauimus._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="8">
            <note position="left" xlink:label="note-0036-02" xlink:href="note-0036-02a" xml:space="preserve">G</note>
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        </div>
        <div type="section" level="1" n="24">
          <head xml:space="preserve">PROPOSITIO III.</head>
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              <emph style="sc">Recta</emph>
            portio conoidis rectanguli quando
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            axem habuerit minorem, quam ſeſquialterum
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            eius, quæ uſque ad axem, quamcunque propor-
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            tionem habens ad humidum in grauitate; </s>
            <s xml:space="preserve">demiſ-
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            ſa in humidum, ita ut baſis ipſius tota ſit in humi
              <lb/>
            do; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">poſita inclinata, non manebit inclinata, ſed
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            ita reſtituetur, ut axis ipſius ſecundum perpendi
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            cularem fiat.</s>
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          </p>
          <p>
            <s xml:space="preserve">DEMITTATVR enim aliqua portio in humidum,
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            qualis dicca eſt: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">ipſius baſis in humido: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecta ipſa
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            plano per axẽ, recto ad ſuperficiẽ humidi, ſit ſectio a p ol
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            rectanguli coniſectio: </s>
            <s xml:space="preserve">axis portionis, & </s>
            <s xml:space="preserve">ſectionis diame-
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            ter p f: </s>
            <s xml:space="preserve">ſuperficiei autem humidi ſectio ſit is. </s>
            <s xml:space="preserve">Quòd ſi incli
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            nata iaceat portio, non erit axis ſecundum perpendicula-
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            rem. </s>
            <s xml:space="preserve">ergo p f cum is angulos rectos non faciet. </s>
            <s xml:space="preserve">Itaque
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            ducatur linea quædã k ω æquidiſtans ipſi is; </s>
            <s xml:space="preserve">contingensq;
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            </s>
            <s xml:space="preserve">ſectionẽ ap ol in o: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſolidæ quidẽ magnitudinis a p o l
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            ſit r grauitatis centrum: </s>
            <s xml:space="preserve">ipſius autem i p o s centrum ſit</s>
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