Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIME DIS
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        <div type="section" level="1" n="28">
          <p style="it">
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            dam non minor est proportio, quàm tertiæ & </s>
            <s xml:space="preserve">quartæ ad quartam;
              <lb/>
            </s>
            <s xml:space="preserve">est enim quadratum m o unà cum exceſſu, quo quadratum n o exce
              <lb/>
            dit quadratum m o æquale ipſi n o quadrato. </s>
            <s xml:space="preserve">quare per conuerſio
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            nem rationis ex 30 eiuſdem, primæ & </s>
            <s xml:space="preserve">ſecundæ ad primam non ma-
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            ior proportio erit, quàm tertiæ & </s>
            <s xml:space="preserve">quartæ ad tertiam: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco to-
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            ta portio ad portionem eam, quæ est extra bumidum non maiorem
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            proportionem babebit, quàm quadratum n o ad quadratum mo. </s>
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              <lb/>
            quod demonstrandum proponebatur.</s>
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          <div type="float" level="2" n="1">
            <note position="right" xlink:label="note-0043-03" xlink:href="note-0043-03a" xml:space="preserve">A</note>
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          <p>
            <s xml:space="preserve">Habet autem tota portio ad eam, quæ extra humidum
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              <anchor type="note" xlink:label="note-0044-01a" xlink:href="note-0044-01"/>
            proportionem eandem, quam quadratum n o ad quadra
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            tum p f.</s>
            <s xml:space="preserve">] _Ex uigeſimaſexta libri de conoidibus, & </s>
            <s xml:space="preserve">ſpbæroi-_
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            _dibus._</s>
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            <note position="left" xlink:label="note-0044-01" xlink:href="note-0044-01a" xml:space="preserve">B</note>
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          <p>
            <s xml:space="preserve">Ex quo eſſicitur, ut p ſ non ſit minor ipſa o m; </s>
            <s xml:space="preserve">neque
              <lb/>
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            pb ipſa o h.</s>
            <s xml:space="preserve">] _Sequitur illud ex decima & </s>
            <s xml:space="preserve">decimaquarta quinti,_
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            _& </s>
            <s xml:space="preserve">ex uigeſimaſecunda ſexti elementorum, ut ſuperius dictum eſt._</s>
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            <note position="left" xlink:label="note-0044-02" xlink:href="note-0044-02a" xml:space="preserve">C</note>
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          <p>
            <s xml:space="preserve">Quæ ergo ab h ducitur ad rectos angulos ipſi n o coi-
              <lb/>
              <anchor type="note" xlink:label="note-0044-03a" xlink:href="note-0044-03"/>
            bit cum p b inter p & </s>
            <s xml:space="preserve">b.</s>
            <s xml:space="preserve">] _Cur boc ita contingat, nos proxi-_
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            _me explicauimus._</s>
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            <note position="left" xlink:label="note-0044-03" xlink:href="note-0044-03a" xml:space="preserve">D</note>
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        <div type="section" level="1" n="29">
          <head xml:space="preserve">PROPOSITIO VI.</head>
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              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
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            leuior humido axem habuerit maiorem quidem
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            quàm ſeſquialterum eius, quæ uſque ad axem,
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            minorem nero, quàm ut ad eam, quæ uſque ad
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            axem proportionem habeat, quam quindecim
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            ad quatuor; </s>
            <s xml:space="preserve">in humidum demiſſa adeo, ut baſis
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            ipſius contingat humidum, nunquam conſiſtet
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            inclinata ita, ut baſis in uno puncto humidum
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            contingat.</s>
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