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="64">
          <p>
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            quæ quidem in centro conueniunt. </s>
            <s xml:space="preserve">idem igitur eſt centrum
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            grauitatis quadrati, & </s>
            <s xml:space="preserve">circuli centrum.</s>
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          </p>
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            <figure xlink:label="fig-0115-02" xlink:href="fig-0115-02a">
              <image file="0115-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0115-02"/>
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            <note position="right" xlink:label="note-0115-04" xlink:href="note-0115-04a" xml:space="preserve">51. tortil.</note>
          </div>
          <p>
            <s xml:space="preserve">Sit pentagonum æquilaterum, & </s>
            <s xml:space="preserve">æquiangulum in circu-
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            lo deſcriptum a b c d e: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iun-
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              <anchor type="figure" xlink:label="fig-0116-01a" xlink:href="fig-0116-01"/>
            cta b d, bifariamq́; </s>
            <s xml:space="preserve">in ſ diuiſa,
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            ducatur c f, & </s>
            <s xml:space="preserve">producatur ad
              <lb/>
            circuli circumferentiam in g;
              <lb/>
            </s>
            <s xml:space="preserve">quæ lineam a e in h ſecet: </s>
            <s xml:space="preserve">de-
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            inde iungantur a c, c e. </s>
            <s xml:space="preserve">Eodem
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            modo, quo ſupra demonſtra-
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            bimus angulum b c f æqualem
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            eſſe angulo d c f; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">angulos
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            ad f utroſque rectos: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcir-
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            colineam c f g per circuli cen
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            trum tranſire. </s>
            <s xml:space="preserve">Quoniam igi-
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            tur latera c b, b a, & </s>
            <s xml:space="preserve">c d, d e æqualia ſunt; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">æquales anguli
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            c b a, c d e: </s>
            <s xml:space="preserve">erit baſis c a baſi c e, & </s>
            <s xml:space="preserve">angulus b c a angulo
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              <anchor type="note" xlink:label="note-0116-01a" xlink:href="note-0116-01"/>
            d c e æqualis. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">reliquus a c h, reliquo e c h. </s>
            <s xml:space="preserve">eſt au-
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            tem c h utrique triangulo a c h, e c h communis. </s>
            <s xml:space="preserve">quare
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            baſis a h æqualis eſt baſi h e: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">anguli, quiad h recti: </s>
            <s xml:space="preserve">ſuntq́;
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            </s>
            <s xml:space="preserve">recti, qui ad f. </s>
            <s xml:space="preserve">ergo lineæ a e, b d inter ſe ſe æquidiſtant. </s>
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              <lb/>
              <anchor type="note" xlink:label="note-0116-02a" xlink:href="note-0116-02"/>
            Itaque cum trapezij a b d e latera b d, a e æquidiſtantia à li
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            nea fh bifariam diuidantur; </s>
            <s xml:space="preserve">centrum grauitatis ipſius erit
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            in linea f h, ex ultima eiuſdem libri Archimedis. </s>
            <s xml:space="preserve">Sed trian-
              <lb/>
              <anchor type="note" xlink:label="note-0116-03a" xlink:href="note-0116-03"/>
            guli b c d centrum grauitatis eſt in linea c f. </s>
            <s xml:space="preserve">ergo in eadem
              <lb/>
            linea c h eſt centrum grauitatis trapezij a b d e, & </s>
            <s xml:space="preserve">trian-
              <lb/>
            guli b c d: </s>
            <s xml:space="preserve">hoc eſt pentagoni ipſius centrum & </s>
            <s xml:space="preserve">centrum
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            circuli. </s>
            <s xml:space="preserve">Rurſus ſi iuncta a d, bifariamq́; </s>
            <s xml:space="preserve">ſecta in k, duca-
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            tur e k l: </s>
            <s xml:space="preserve">demonſtrabimus in ipſa utrumque centrum in
              <lb/>
            eſſe. </s>
            <s xml:space="preserve">Sequitur ergo, ut punctum, in quo lineæ c g, e l con-
              <lb/>
            ueniunt, idem ſit centrum circuli, & </s>
            <s xml:space="preserve">centrum grauitatis
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            pentagoni.</s>
            <s xml:space="preserve"/>
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            <figure xlink:label="fig-0116-01" xlink:href="fig-0116-01a">
              <image file="0116-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0116-01"/>
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            <note position="left" xlink:label="note-0116-01" xlink:href="note-0116-01a" xml:space="preserve">4. Primi.</note>
            <note position="left" xlink:label="note-0116-02" xlink:href="note-0116-02a" xml:space="preserve">08. primi.</note>
            <note position="left" xlink:label="note-0116-03" xlink:href="note-0116-03a" xml:space="preserve">13. Archi-
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            medis.</note>
          </div>
          <p>
            <s xml:space="preserve">Sit hexagonum a b c d e f æquilaterum, & </s>
            <s xml:space="preserve">æquiangulum
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            in circulo deſignatum: </s>
            <s xml:space="preserve">iunganturq́; </s>
            <s xml:space="preserve">b d, a c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">bifariam ſe-</s>
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