Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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        <div xml:id="echoid-div272" type="section" level="1" n="92">
          <p>
            <s xml:id="echoid-s4831" xml:space="preserve">
              <pb file="0192" n="192" rhead="FED. COMMANDINI"/>
            grauitatis eſſe punctum m. </s>
            <s xml:id="echoid-s4832" xml:space="preserve">patetigitur totius dodecahe-
              <lb/>
            dri, centrum grauitatis idẽ eſſe, quod & </s>
            <s xml:id="echoid-s4833" xml:space="preserve">ſphæræ ipſum com
              <lb/>
            prehendentis centrum. </s>
            <s xml:id="echoid-s4834" xml:space="preserve">quæ quidem omnia demonſtraſſe
              <lb/>
            oportebat.</s>
            <s xml:id="echoid-s4835" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div278" type="section" level="1" n="93">
          <head xml:id="echoid-head100" xml:space="preserve">PROBLEMA VI. PROPOSITIO XX VIII.</head>
          <p>
            <s xml:id="echoid-s4836" xml:space="preserve">
              <emph style="sc">Data</emph>
            qualibet portione conoidis rectangu
              <lb/>
            li, abſciſſa plano ad axem recto, uel non recto; </s>
            <s xml:id="echoid-s4837" xml:space="preserve">fie-
              <lb/>
            ri poteſt, ut portio ſolida inſcribatur, uel circum-
              <lb/>
            ſcribatur ex cylindris, uel cylindri portionibus,
              <lb/>
            æqualem habentibus altitudinem, ita ut recta li-
              <lb/>
            nea, quæ inter centrum grauitatis portionis, & </s>
            <s xml:id="echoid-s4838" xml:space="preserve">
              <lb/>
            figuræ inſcriptæ, uel circumſcriptæ interiicitur,
              <lb/>
            ſit minor qualibet recta linea propoſita.</s>
            <s xml:id="echoid-s4839" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4840" xml:space="preserve">Sit portio conoidis rectanguli a b c, cuius axis b d, gra-
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            uitatisq; </s>
            <s xml:id="echoid-s4841" xml:space="preserve">centrum e: </s>
            <s xml:id="echoid-s4842" xml:space="preserve">& </s>
            <s xml:id="echoid-s4843" xml:space="preserve">fit g recta linea propoſita. </s>
            <s xml:id="echoid-s4844" xml:space="preserve">quam ue
              <lb/>
            ro proportionem habet linea b e ad lineam g, eandem ha-
              <lb/>
            beat portio conoidis ad ſolidum h: </s>
            <s xml:id="echoid-s4845" xml:space="preserve">& </s>
            <s xml:id="echoid-s4846" xml:space="preserve">circumſcribatur por
              <lb/>
            tioni figura, ſicuti dictum eſt, ita ut portiones reliquæ ſint
              <lb/>
            ſolido h minores: </s>
            <s xml:id="echoid-s4847" xml:space="preserve">cuius quidem figuræ centrum grauitatis
              <lb/>
            ſit punctum
              <emph style="sc">K</emph>
            . </s>
            <s xml:id="echoid-s4848" xml:space="preserve">Dico lineã k e minorem eſſe linea g propo-
              <lb/>
            ſita. </s>
            <s xml:id="echoid-s4849" xml:space="preserve">niſi enim ſit minor, uel æqualis, uel maior erit. </s>
            <s xml:id="echoid-s4850" xml:space="preserve">& </s>
            <s xml:id="echoid-s4851" xml:space="preserve">quo-
              <lb/>
            niam figura circumſcripta ad reliquas portiones maiorem
              <lb/>
              <note position="left" xlink:label="note-0192-01" xlink:href="note-0192-01a" xml:space="preserve">8. quĭnti.</note>
            proportionem habet, quàm portio conoidis ad ſolidum h;
              <lb/>
            </s>
            <s xml:id="echoid-s4852" xml:space="preserve">hoc eſt maiorem, quàm b c ad g: </s>
            <s xml:id="echoid-s4853" xml:space="preserve">& </s>
            <s xml:id="echoid-s4854" xml:space="preserve">b e ad g non minorem
              <lb/>
            habet proportionem, quàm ad _k_ e, propterea quod k e non
              <lb/>
            ponitur minor ipſa g: </s>
            <s xml:id="echoid-s4855" xml:space="preserve">habebit figura circumſcripta ad por
              <lb/>
            tiones reliquas maiorem proportionem quàm b e ad e k: </s>
            <s xml:id="echoid-s4856" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0192-02" xlink:href="note-0192-02a" xml:space="preserve">29. quĭnti
                <lb/>
              ex tradi-
                <lb/>
              tione Cã-
                <lb/>
              ſàni.</note>
            & </s>
            <s xml:id="echoid-s4857" xml:space="preserve">diuidendo portio conoidis ad reliquas portiones habe-
              <lb/>
            bit maiorem, quàm b
              <emph style="sc">K</emph>
            ad K e. </s>
            <s xml:id="echoid-s4858" xml:space="preserve">quare ſi fiat ut portio </s>
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