Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE CENTRO GRAVIT. SOLID.
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              <pb o="3" file="0117" n="117" rhead="DE CENTRO GRAVIT. SOLID."/>
            cta b d in g puncto, ducatur c g; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">protrahatur ad circuli
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            uſque circumferentiam; </s>
            <s xml:space="preserve">quæ ſecet a e in h. </s>
            <s xml:space="preserve">Similiter conclu
              <lb/>
            demus c g per centrum circuli tranſire: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">bifariam ſecare
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            lineam a e; </s>
            <s xml:space="preserve">itemq́; </s>
            <s xml:space="preserve">lineas b d, a e inter ſe æquidiſtantes eſſe.
              <lb/>
            </s>
            <s xml:space="preserve">Cumigitur c g per centrum circuli tranſeat; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ad punctũ
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            f perueniat neceſſe eſt: </s>
            <s xml:space="preserve">quòd c d e f ſit dimidium circumfe
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            rentiæ circuli. </s>
            <s xml:space="preserve">Quare in eadem
              <lb/>
              <anchor type="figure" xlink:label="fig-0117-01a" xlink:href="fig-0117-01"/>
            diametro c f erunt centra gra
              <lb/>
              <anchor type="note" xlink:label="note-0117-01a" xlink:href="note-0117-01"/>
            uitatis triangulorum b c d,
              <lb/>
            a f e, & </s>
            <s xml:space="preserve">quadrilateri a b d e, ex
              <lb/>
              <anchor type="note" xlink:label="note-0117-02a" xlink:href="note-0117-02"/>
            quibus conſtat hexagonum a b
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            c d e f. </s>
            <s xml:space="preserve">perſpicuum eſt igitur in
              <lb/>
            ipſa c f eſſe circuli centrum, & </s>
            <s xml:space="preserve">
              <lb/>
            centrum grauitatis hexagoni.
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            </s>
            <s xml:space="preserve">Rurſus ducta altera diametro
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            a d, eiſdem rationibus oſtende-
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            mus in ipſa utrumque cẽtrum
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            ineſſe. </s>
            <s xml:space="preserve">Centrum ergo grauita-
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            tis hexagoni, & </s>
            <s xml:space="preserve">centrum circuli idem erit.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="4">
            <figure xlink:label="fig-0117-01" xlink:href="fig-0117-01a">
              <image file="0117-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0117-01"/>
            </figure>
            <note position="right" xlink:label="note-0117-01" xlink:href="note-0117-01a" xml:space="preserve">13. Archi
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            medis.</note>
            <note position="right" xlink:label="note-0117-02" xlink:href="note-0117-02a" xml:space="preserve">9. @iuſdé.</note>
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          <p>
            <s xml:space="preserve">Sit heptagonum a b c d e f g æquilaterum atque æquian
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            gulum in circulo deſcriptum:
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            </s>
            <s xml:space="preserve">
              <anchor type="figure" xlink:label="fig-0117-02a" xlink:href="fig-0117-02"/>
            & </s>
            <s xml:space="preserve">iungantur c e, b f, a g: </s>
            <s xml:space="preserve">di-
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            uiſa autem c e bifariam in pũ
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            cto h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta d h produca-
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            tur in k. </s>
            <s xml:space="preserve">non aliter demon-
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            ſtrabimus in linea d k eſſe cen
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            trum circuli, & </s>
            <s xml:space="preserve">centrum gra-
              <lb/>
            uitatis trianguli c d e, & </s>
            <s xml:space="preserve">tra-
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            peziorum b c e f, a b f g, hoc
              <lb/>
            eſt centrum totius heptago-
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            ni: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">rurſus eadem centra in
              <lb/>
            alia diametro cl ſimiliter du-
              <lb/>
            cta contineri. </s>
            <s xml:space="preserve">Quare & </s>
            <s xml:space="preserve">centrum grauitatis heptagoni, & </s>
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              <lb/>
            centrum circuli in idem punctum conucniunt. </s>
            <s xml:space="preserve">Eodem mo</s>
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