Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s706" xml:space="preserve">
              <pb file="0036" n="36" rhead="ARCHIMEDIS"/>
            angulus b n f œqualis angulo o g f: </s>
            <s xml:id="echoid-s707" xml:space="preserve">quòd cum ſit g o perpendi-
              <lb/>
              <note position="left" xlink:label="note-0036-01" xlink:href="note-0036-01a" xml:space="preserve">29, primi</note>
            cularis ad e f, & </s>
            <s xml:id="echoid-s708" xml:space="preserve">h n ad eandem perpendicularis erit. </s>
            <s xml:id="echoid-s709" xml:space="preserve">quod de-
              <lb/>
            monstrare oportebat.</s>
            <s xml:id="echoid-s710" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s711" xml:space="preserve">Et quod in humido eſt ſurſum ſeretur ſecundum per-
              <lb/>
              <note position="left" xlink:label="note-0036-02" xlink:href="note-0036-02a" xml:space="preserve">G</note>
            pendicularem, quæ per b ducta eſtipſi rt æquidiſtans.</s>
            <s xml:id="echoid-s712" 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:id="echoid-s713" xml:space="preserve">qua_
              <lb/>
            _re neque in hac, neque in alijs, quæ ſequuntur, eadem iterare neceſſa_
              <lb/>
            _rium exiſtimauimus._</s>
            <s xml:id="echoid-s714" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div53" type="section" level="1" n="24">
          <head xml:id="echoid-head29" xml:space="preserve">PROPOSITIO III.</head>
          <p>
            <s xml:id="echoid-s715" xml:space="preserve">
              <emph style="sc">Recta</emph>
            portio conoidis rectanguli quando
              <lb/>
            axem habuerit minorem, quam ſeſquialterum
              <lb/>
            eius, quæ uſque ad axem, quamcunque propor-
              <lb/>
            tionem habens ad humidum in grauitate; </s>
            <s xml:id="echoid-s716" xml:space="preserve">demiſ-
              <lb/>
            ſa in humidum, ita ut baſis ipſius tota ſit in humi
              <lb/>
            do; </s>
            <s xml:id="echoid-s717" xml:space="preserve">& </s>
            <s xml:id="echoid-s718" xml:space="preserve">poſita inclinata, non manebit inclinata, ſed
              <lb/>
            ita reſtituetur, ut axis ipſius ſecundum perpendi
              <lb/>
            cularem fiat.</s>
            <s xml:id="echoid-s719" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s720" xml:space="preserve">DEMITTATVR enim aliqua portio in humidum,
              <lb/>
            qualis dicca eſt: </s>
            <s xml:id="echoid-s721" xml:space="preserve">ſitq; </s>
            <s xml:id="echoid-s722" xml:space="preserve">ipſius baſis in humido: </s>
            <s xml:id="echoid-s723" xml:space="preserve">& </s>
            <s xml:id="echoid-s724" xml:space="preserve">ſecta ipſa
              <lb/>
            plano per axẽ, recto ad ſuperficiẽ humidi, ſit ſectio a p ol
              <lb/>
            rectanguli coniſectio: </s>
            <s xml:id="echoid-s725" xml:space="preserve">axis portionis, & </s>
            <s xml:id="echoid-s726" xml:space="preserve">ſectionis diame-
              <lb/>
            ter p f: </s>
            <s xml:id="echoid-s727" xml:space="preserve">ſuperficiei autem humidi ſectio ſit is. </s>
            <s xml:id="echoid-s728" xml:space="preserve">Quòd ſi incli
              <lb/>
            nata iaceat portio, non erit axis ſecundum perpendicula-
              <lb/>
            rem. </s>
            <s xml:id="echoid-s729" xml:space="preserve">ergo p f cum is angulos rectos non faciet. </s>
            <s xml:id="echoid-s730" xml:space="preserve">Itaque
              <lb/>
            ducatur linea quædã k ω æquidiſtans ipſi is; </s>
            <s xml:id="echoid-s731" xml:space="preserve">contingensq;
              <lb/>
            </s>
            <s xml:id="echoid-s732" xml:space="preserve">ſectionẽ ap ol in o: </s>
            <s xml:id="echoid-s733" xml:space="preserve">& </s>
            <s xml:id="echoid-s734" xml:space="preserve">ſolidæ quidẽ magnitudinis a p o l
              <lb/>
            ſit r grauitatis centrum: </s>
            <s xml:id="echoid-s735" xml:space="preserve">ipſius autem i p o s centrum </s>
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