Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <p style="it">
            <s xml:id="echoid-s932" xml:space="preserve">
              <pb file="0044" n="44" rhead="ARCHIME DIS"/>
            dam non minor est proportio, quàm tertiæ & </s>
            <s xml:id="echoid-s933" xml:space="preserve">quartæ ad quartam;
              <lb/>
            </s>
            <s xml:id="echoid-s934" 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:id="echoid-s935" xml:space="preserve">quare per conuerſio
              <lb/>
            nem rationis ex 30 eiuſdem, primæ & </s>
            <s xml:id="echoid-s936" xml:space="preserve">ſecundæ ad primam non ma-
              <lb/>
            ior proportio erit, quàm tertiæ & </s>
            <s xml:id="echoid-s937" xml:space="preserve">quartæ ad tertiam: </s>
            <s xml:id="echoid-s938" xml:space="preserve">& </s>
            <s xml:id="echoid-s939" xml:space="preserve">idcirco to-
              <lb/>
            ta portio ad portionem eam, quæ est extra bumidum non maiorem
              <lb/>
            proportionem babebit, quàm quadratum n o ad quadratum mo. </s>
            <s xml:id="echoid-s940" xml:space="preserve">
              <lb/>
            quod demonstrandum proponebatur.</s>
            <s xml:id="echoid-s941" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s942" xml:space="preserve">Habet autem tota portio ad eam, quæ extra humidum
              <lb/>
              <note position="left" xlink:label="note-0044-01" xlink:href="note-0044-01a" xml:space="preserve">B</note>
            proportionem eandem, quam quadratum n o ad quadra
              <lb/>
            tum p f.</s>
            <s xml:id="echoid-s943" xml:space="preserve">] _Ex uigeſimaſexta libri de conoidibus, & </s>
            <s xml:id="echoid-s944" xml:space="preserve">ſpbæroi-_
              <lb/>
            _dibus._</s>
            <s xml:id="echoid-s945" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s946" xml:space="preserve">Ex quo eſſicitur, ut p ſ non ſit minor ipſa o m; </s>
            <s xml:id="echoid-s947" xml:space="preserve">neque
              <lb/>
              <note position="left" xlink:label="note-0044-02" xlink:href="note-0044-02a" xml:space="preserve">C</note>
            pb ipſa o h.</s>
            <s xml:id="echoid-s948" xml:space="preserve">] _Sequitur illud ex decima & </s>
            <s xml:id="echoid-s949" xml:space="preserve">decimaquarta quinti,_
              <lb/>
            _& </s>
            <s xml:id="echoid-s950" xml:space="preserve">ex uigeſimaſecunda ſexti elementorum, ut ſuperius dictum eſt._</s>
            <s xml:id="echoid-s951" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s952" xml:space="preserve">Quæ ergo ab h ducitur ad rectos angulos ipſi n o coi-
              <lb/>
              <note position="left" xlink:label="note-0044-03" xlink:href="note-0044-03a" xml:space="preserve">D</note>
            bit cum p b inter p & </s>
            <s xml:id="echoid-s953" xml:space="preserve">b.</s>
            <s xml:id="echoid-s954" xml:space="preserve">] _Cur boc ita contingat, nos proxi-_
              <lb/>
            _me explicauimus._</s>
            <s xml:id="echoid-s955" xml:space="preserve"/>
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        <div xml:id="echoid-div72" type="section" level="1" n="29">
          <head xml:id="echoid-head34" xml:space="preserve">PROPOSITIO VI.</head>
          <p>
            <s xml:id="echoid-s956" xml:space="preserve">
              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
              <lb/>
            leuior humido axem habuerit maiorem quidem
              <lb/>
            quàm ſeſquialterum eius, quæ uſque ad axem,
              <lb/>
            minorem nero, quàm ut ad eam, quæ uſque ad
              <lb/>
            axem proportionem habeat, quam quindecim
              <lb/>
            ad quatuor; </s>
            <s xml:id="echoid-s957" xml:space="preserve">in humidum demiſſa adeo, ut baſis
              <lb/>
            ipſius contingat humidum, nunquam conſiſtet
              <lb/>
            inclinata ita, ut baſis in uno puncto humidum
              <lb/>
            contingat.</s>
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