Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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FED. COMMANDINI
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        <div type="section" level="1" n="92">
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              <pb file="0192" n="192" rhead="FED. COMMANDINI"/>
            grauitatis eſſe punctum m. </s>
            <s xml:space="preserve">patetigitur totius dodecahe-
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            dri, centrum grauitatis idẽ eſſe, quod & </s>
            <s xml:space="preserve">ſphæræ ipſum com
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            prehendentis centrum. </s>
            <s xml:space="preserve">quæ quidem omnia demonſtraſſe
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            oportebat.</s>
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            <figure xlink:label="fig-0191-01" xlink:href="fig-0191-01a">
              <image file="0191-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0191-01"/>
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            <note position="right" xlink:label="note-0191-01" xlink:href="note-0191-01a" xml:space="preserve">corol. pri
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            mæ ſphæ
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            ricorum
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            Theod.</note>
            <note position="right" xlink:label="note-0191-02" xlink:href="note-0191-02a" xml:space="preserve">6. primi
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            phærico
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            rum.</note>
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        <div type="section" level="1" n="93">
          <head xml:space="preserve">PROBLEMA VI. PROPOSITIO XX VIII.</head>
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              <emph style="sc">Data</emph>
            qualibet portione conoidis rectangu
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            li, abſciſſa plano ad axem recto, uel non recto; </s>
            <s xml:space="preserve">fie-
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            ri poteſt, ut portio ſolida inſcribatur, uel circum-
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            ſcribatur ex cylindris, uel cylindri portionibus,
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            æqualem habentibus altitudinem, ita ut recta li-
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            nea, quæ inter centrum grauitatis portionis, & </s>
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            figuræ inſcriptæ, uel circumſcriptæ interiicitur,
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            ſit minor qualibet recta linea propoſita.</s>
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          </p>
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            <s xml:space="preserve">Sit portio conoidis rectanguli a b c, cuius axis b d, gra-
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            uitatisq; </s>
            <s xml:space="preserve">centrum e: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">fit g recta linea propoſita. </s>
            <s xml:space="preserve">quam ue
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            ro proportionem habet linea b e ad lineam g, eandem ha-
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            beat portio conoidis ad ſolidum h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">circumſcribatur por
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            tioni figura, ſicuti dictum eſt, ita ut portiones reliquæ ſint
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            ſolido h minores: </s>
            <s xml:space="preserve">cuius quidem figuræ centrum grauitatis
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            ſit punctum
              <emph style="sc">K</emph>
            . </s>
            <s xml:space="preserve">Dico lineã k e minorem eſſe linea g propo-
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            ſita. </s>
            <s xml:space="preserve">niſi enim ſit minor, uel æqualis, uel maior erit. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quo-
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            niam figura circumſcripta ad reliquas portiones maiorem
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              <anchor type="note" xlink:label="note-0192-01a" xlink:href="note-0192-01"/>
            proportionem habet, quàm portio conoidis ad ſolidum h;
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            </s>
            <s xml:space="preserve">hoc eſt maiorem, quàm b c ad g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">b e ad g non minorem
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            habet proportionem, quàm ad _k_ e, propterea quod k e non
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            ponitur minor ipſa g: </s>
            <s xml:space="preserve">habebit figura circumſcripta ad por
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            tiones reliquas maiorem proportionem quàm b e ad e k: </s>
            <s xml:space="preserve">
              <lb/>
              <anchor type="note" xlink:label="note-0192-02a" xlink:href="note-0192-02"/>
            & </s>
            <s xml:space="preserve">diuidendo portio conoidis ad reliquas portiones habe-
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            bit maiorem, quàm b
              <emph style="sc">K</emph>
            ad K e. </s>
            <s xml:space="preserve">quare ſi fiat ut portio co-</s>
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