Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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              <pb o="26" file="0063" n="63" rhead="DE IIS QVAE VEH. IN AQVA."/>
            _humidi ſuperficiem.</s>
            <s xml:id="echoid-s1517" xml:space="preserve">]_ Est enim t ω æqualis κ r, hoc eſt ei, quæ
              <lb/>
            uſque ad axem. </s>
            <s xml:id="echoid-s1518" xml:space="preserve">quare ex ijs, quæ ſuperius demonſtrata ſunt, linea
              <lb/>
            t h ducta erit ad humidi ſuperficiem perpendicularis.</s>
            <s xml:id="echoid-s1519" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1520" xml:space="preserve">_Minorem igitur proportionem habet quadratum p i_
              <lb/>
              <note position="right" xlink:label="note-0063-01" xlink:href="note-0063-01a" xml:space="preserve">O</note>
            _ad quadratum i y, quàm quadratum e ψ ad ψ b quadratũ]_
              <lb/>
            Hæc & </s>
            <s xml:id="echoid-s1521" xml:space="preserve">alia, quæ ſequuntur, tum in hac, tum in ſequenti propoſitio-
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            ne non alio, quàm quo ſupra modo demonstrabimus.</s>
            <s xml:id="echoid-s1522" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1523" xml:space="preserve">_Itaque per z g ductis perpendicularibus ad humidi ſu-_
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              <note position="right" xlink:label="note-0063-02" xlink:href="note-0063-02a" xml:space="preserve">P</note>
            _perficiem, quæ i pſi t h æ quidiftent; </s>
            <s xml:id="echoid-s1524" xml:space="preserve">ſequitur portionem ip_
              <lb/>
            _ſam non manere, ſed reuolui adeo, ut axis cum ſuperſicie_
              <lb/>
            _humidi angulum faciat maiorem eo, quem nunc facit.</s>
            <s xml:id="echoid-s1525" xml:space="preserve">]_
              <lb/>
            Nam cum perpendicularis, quæ per g, ducitur ad eas partes cadat,
              <lb/>
            in quibus eſt l; </s>
            <s xml:id="echoid-s1526" xml:space="preserve">quæ autem per Z ad eis in quibus a: </s>
            <s xml:id="echoid-s1527" xml:space="preserve">neceſſarium eſt
              <lb/>
            centrum g deorſum ferri, & </s>
            <s xml:id="echoid-s1528" xml:space="preserve">Z ſurſum. </s>
            <s xml:id="echoid-s1529" xml:space="preserve">quare partes ſolidi, quæ
              <lb/>
            ſunt ad l deorſum; </s>
            <s xml:id="echoid-s1530" xml:space="preserve">quæ uero ad a ſurſum ferentur, ut axis cum ſu-
              <lb/>
            perficie humidi maiorem angulum contineat.</s>
            <s xml:id="echoid-s1531" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1532" xml:space="preserve">Sic enim erit i o æ qualis ψ b, itẽq; </s>
            <s xml:id="echoid-s1533" xml:space="preserve">ω i æ qualis ψ r, & </s>
            <s xml:id="echoid-s1534" xml:space="preserve">p h
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              <note position="right" xlink:label="note-0063-03" xlink:href="note-0063-03a" xml:space="preserve">Q</note>
            ipſi f.</s>
            <s xml:id="echoid-s1535" xml:space="preserve">] _Hoc in tertia figura, quam nos addidimus, perſpicue apparet_.</s>
            <s xml:id="echoid-s1536" xml:space="preserve"/>
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        <div xml:id="echoid-div111" type="section" level="1" n="38">
          <head xml:id="echoid-head43" xml:space="preserve">PROPOSITIO IX.</head>
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            <s xml:id="echoid-s1537" xml:space="preserve">
              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
              <lb/>
            axem habuerit maiorem quidem, quàm ſeſquial-
              <lb/>
            terum eius, quæ uſque ad axem; </s>
            <s xml:id="echoid-s1538" xml:space="preserve">minorem uero,
              <lb/>
            quàm ut ad eam, quæ uſque ad axem proportio-
              <lb/>
            nem habeat, quam quindecim ad quatuor; </s>
            <s xml:id="echoid-s1539" xml:space="preserve">& </s>
            <s xml:id="echoid-s1540" xml:space="preserve">in
              <lb/>
            grauitate ad humidum proportionem habeat ma
              <lb/>
            iorem, quàm exceſſus, quo quadratum, quod fit
              <lb/>
            ab axe maius eſt quadrato, quod ab exceſſu, quo
              <lb/>
            axis eſt maior, quàm ſeſquialter eius, quæ uſq; </s>
            <s xml:id="echoid-s1541" xml:space="preserve">ad
              <lb/>
            axem, habet ad quadratum, quod ab axe: </s>
            <s xml:id="echoid-s1542" xml:space="preserve">in </s>
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