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="39">
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              <pb file="0068" n="68" rhead="ARCHIMEDIS"/>
            _erit conuertendo tota portio ad partem ipſius demerſam, ut quadrd-_
              <lb/>
            _tum b d ad exceſſum, quo quadratum f q excedit. </s>
            <s xml:space="preserve">quare per conuer-_
              <lb/>
            _ſionem rationis tota portio ad eam, quæ extra humidum est ut_
              <lb/>
            _qu.</s>
            <s xml:space="preserve">idratum b d ad quadratum f q: </s>
            <s xml:space="preserve">nam quadratum b d tanto maius_
              <lb/>
            _est exceſſu, quo excedit quadratum f q, quantum est ipſum f q qua-_
              <lb/>
            _dratum_.</s>
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          </p>
          <div type="float" level="2" n="4">
            <note position="right" xlink:label="note-0067-08" xlink:href="note-0067-08a" xml:space="preserve">E</note>
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          <p style="it">
            <s xml:space="preserve">_Quoniam quæ ex parte 1 deorſum, quæ uero ex parte a_
              <lb/>
              <anchor type="note" xlink:label="note-0068-01a" xlink:href="note-0068-01"/>
            _ſurſum ferentur.</s>
            <s xml:space="preserve">]_ Hæc nos ita correximus, nam in translatione
              <lb/>
            mendoſe, ut opinor, legebatur, quoniam quæ ex parte l ad ſuperiora
              <lb/>
            ferentur, perpendicularis enim quæ tranſit per z ad partes l, & </s>
            <s xml:space="preserve">quæ
              <lb/>
            per g ad partes a cadit. </s>
            <s xml:space="preserve">quare centrum z unà cum p. </s>
            <s xml:space="preserve">trtibus ijs, quæ
              <lb/>
            ſunt ad l deorſum feretur, centrum uero g unà cum partibus quæ ad
              <lb/>
            a ſurſum.</s>
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          <div type="float" level="2" n="5">
            <note position="left" xlink:label="note-0068-01" xlink:href="note-0068-01a" xml:space="preserve">F</note>
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          <p>
            <s xml:space="preserve">Similiter demonſtrabitur non manere portionem, ſed
              <lb/>
              <anchor type="note" xlink:label="note-0068-02a" xlink:href="note-0068-02"/>
            inclinari, donec utique axis cum ſuperficie humidi faciat
              <lb/>
            angulum angulo b æqualem.</s>
            <s xml:space="preserve">] _Illud uero tum ex ijs, quæ in an_
              <lb/>
            _tecedenti dicta ſunt, tum ex figuris, quas appoſuimus, facile demon-_
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            _strari potest._</s>
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            <note position="left" xlink:label="note-0068-02" xlink:href="note-0068-02a" xml:space="preserve">G</note>
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        </div>
        <div type="section" level="1" n="40">
          <head xml:space="preserve">PROPOSITIO X.</head>
          <p>
            <s xml:space="preserve">
              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
              <lb/>
            leuior humido axem habuerit maiorem, quàm
              <lb/>
            ut ad eam, quæ uſque ad axem proportionem ha-
              <lb/>
            beat, quam quindecim ad quatuor: </s>
            <s xml:space="preserve">in humidum
              <lb/>
            demiſſa, ita ut baſis ipſius non contingat humi-
              <lb/>
            dum: </s>
            <s xml:space="preserve">non nunquam quidem recta conſiſtet; </s>
            <s xml:space="preserve">non
              <lb/>
              <anchor type="note" xlink:label="note-0068-03a" xlink:href="note-0068-03"/>
            nunquam inclinata: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">interdum adeo inclinata,
              <lb/>
              <anchor type="note" xlink:label="note-0068-04a" xlink:href="note-0068-04"/>
            ut baſis ipſius in uno puncto contingat ſuperfi-
              <lb/>
            ciem humidi: </s>
            <s xml:space="preserve">idq; </s>
            <s xml:space="preserve">in duabus diſpoſitionibus:</s>
            <s xml:space="preserve"/>
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