Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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        <div xml:id="echoid-div192" type="section" level="1" n="64">
          <p>
            <s xml:id="echoid-s2839" xml:space="preserve">
              <pb o="2" file="0115" n="115" rhead="DE CENTRO GRAVIT. SOLID."/>
            tur, centrum grauitatis eſt idem, quod circuli cen
              <lb/>
            trum.</s>
            <s xml:id="echoid-s2840" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2841" xml:space="preserve">Sit primo triangulum æquilaterum a b c in circulo de-
              <lb/>
            ſcriptum: </s>
            <s xml:id="echoid-s2842" xml:space="preserve">& </s>
            <s xml:id="echoid-s2843" xml:space="preserve">diuiſa a c bifariam in d, ducatur b d. </s>
            <s xml:id="echoid-s2844" xml:space="preserve">erit in li-
              <lb/>
            nea b d centrum grauitatis triãguli a b c, ex tertia decima
              <lb/>
            primi libri Archimedis de centro grauitatis planorum. </s>
            <s xml:id="echoid-s2845" xml:space="preserve">Et
              <lb/>
            quoniam linea a b eſt æqualis
              <lb/>
              <figure xlink:label="fig-0115-01" xlink:href="fig-0115-01a" number="70">
                <image file="0115-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0115-01"/>
              </figure>
            lineæ b c; </s>
            <s xml:id="echoid-s2846" xml:space="preserve">& </s>
            <s xml:id="echoid-s2847" xml:space="preserve">a d ipſi d c; </s>
            <s xml:id="echoid-s2848" xml:space="preserve">eſtq́;
              <lb/>
            </s>
            <s xml:id="echoid-s2849" xml:space="preserve">b d utrique communis: </s>
            <s xml:id="echoid-s2850" xml:space="preserve">trian-
              <lb/>
            gulum a b d æquale erit trian
              <lb/>
              <note position="right" xlink:label="note-0115-01" xlink:href="note-0115-01a" xml:space="preserve">8. primi.</note>
            gulo c b d: </s>
            <s xml:id="echoid-s2851" xml:space="preserve">& </s>
            <s xml:id="echoid-s2852" xml:space="preserve">anguli angulis æ-
              <lb/>
            quales, qui æqualibus lateri-
              <lb/>
            bus ſubtenduntur. </s>
            <s xml:id="echoid-s2853" xml:space="preserve">ergo angu
              <lb/>
              <note position="right" xlink:label="note-0115-02" xlink:href="note-0115-02a" xml:space="preserve">13. primi.</note>
            li ad d utriq; </s>
            <s xml:id="echoid-s2854" xml:space="preserve">recti ſunt. </s>
            <s xml:id="echoid-s2855" xml:space="preserve">quòd
              <lb/>
            cum linea b d ſecet a c biſa-
              <lb/>
            riam, & </s>
            <s xml:id="echoid-s2856" xml:space="preserve">ad angulos rectos; </s>
            <s xml:id="echoid-s2857" xml:space="preserve">in
              <lb/>
              <note position="right" xlink:label="note-0115-03" xlink:href="note-0115-03a" xml:space="preserve">corol. p@@
                <lb/>
              mæ tertii</note>
            ipſa b d eſt centrum circuli.
              <lb/>
            </s>
            <s xml:id="echoid-s2858" xml:space="preserve">quare in eadem b d linea erit
              <lb/>
            centrum grauitatis trianguli, & </s>
            <s xml:id="echoid-s2859" xml:space="preserve">circuli centrum. </s>
            <s xml:id="echoid-s2860" xml:space="preserve">Similiter
              <lb/>
            diuiſa a b bifariam in e, & </s>
            <s xml:id="echoid-s2861" xml:space="preserve">ducta c e, oſtendetur in ipſa utrũ
              <lb/>
            que centrum contineri. </s>
            <s xml:id="echoid-s2862" xml:space="preserve">ergo ea erunt in puncto, in quo li-
              <lb/>
            neæ b d, c e conueniunt. </s>
            <s xml:id="echoid-s2863" xml:space="preserve">trianguli igitur a b c centrum gra
              <lb/>
            uitatis eſt idem, quod circuli centrum.</s>
            <s xml:id="echoid-s2864" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2865" xml:space="preserve">Sit quadratum a b c d in cir-
              <lb/>
              <figure xlink:label="fig-0115-02" xlink:href="fig-0115-02a" number="71">
                <image file="0115-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0115-02"/>
              </figure>
            culo deſcriptum: </s>
            <s xml:id="echoid-s2866" xml:space="preserve">& </s>
            <s xml:id="echoid-s2867" xml:space="preserve">ducantur
              <lb/>
            a c, b d, quæ conueniant in e. </s>
            <s xml:id="echoid-s2868" xml:space="preserve">er-
              <lb/>
            go punctum e eſt centrum gra
              <lb/>
            uitatis quadrati, ex decima eiuſ
              <lb/>
            dem libri Archimedis. </s>
            <s xml:id="echoid-s2869" xml:space="preserve">Sed cum
              <lb/>
            omnes anguli ad a b c d recti
              <lb/>
            ſint; </s>
            <s xml:id="echoid-s2870" xml:space="preserve">erit a b c femicirculus:
              <lb/>
            </s>
            <s xml:id="echoid-s2871" xml:space="preserve">
              <note position="right" xlink:label="note-0115-04" xlink:href="note-0115-04a" xml:space="preserve">51. tortil.</note>
            itemq́; </s>
            <s xml:id="echoid-s2872" xml:space="preserve">b c d: </s>
            <s xml:id="echoid-s2873" xml:space="preserve">& </s>
            <s xml:id="echoid-s2874" xml:space="preserve">propterea li-
              <lb/>
            neæ a c, b d diametri circuli:</s>
            <s xml:id="echoid-s2875" xml:space="preserve"/>
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