Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <pb o="35" file="0181" n="181" rhead="DE CENTRO GRAVIT. SOLID."/>
          <p>
            <s xml:id="echoid-s4500" xml:space="preserve">Sit ſruſtum a e a pyramide, quæ triangularem baſim ha-
              <lb/>
            beat abſciſſum: </s>
            <s xml:id="echoid-s4501" xml:space="preserve">cuius maior baſis triangulum a b c, minor
              <lb/>
            d e f; </s>
            <s xml:id="echoid-s4502" xml:space="preserve">& </s>
            <s xml:id="echoid-s4503" xml:space="preserve">axis g h. </s>
            <s xml:id="echoid-s4504" xml:space="preserve">ducto autem plano per axem & </s>
            <s xml:id="echoid-s4505" xml:space="preserve">per lineã
              <lb/>
            d a, quod ſectionem faciat d a k l quadrilaterum; </s>
            <s xml:id="echoid-s4506" xml:space="preserve">puncta
              <lb/>
            K l lineas b c, e f bifariam ſecabunt. </s>
            <s xml:id="echoid-s4507" xml:space="preserve">nam cum g h ſit axis
              <lb/>
            ſruſti: </s>
            <s xml:id="echoid-s4508" xml:space="preserve">erit h centrum grauitatis trianguli a b c: </s>
            <s xml:id="echoid-s4509" xml:space="preserve">& </s>
            <s xml:id="echoid-s4510" xml:space="preserve">g
              <lb/>
            centrum trianguli d e f: </s>
            <s xml:id="echoid-s4511" xml:space="preserve">cen-
              <lb/>
              <figure xlink:label="fig-0181-01" xlink:href="fig-0181-01a" number="134">
                <image file="0181-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0181-01"/>
              </figure>
              <note position="right" xlink:label="note-0181-01" xlink:href="note-0181-01a" xml:space="preserve">3. diffi. hu
                <lb/>
              ius.</note>
            trum uero cuiuslibet triangu
              <lb/>
            li eſt in recta linea, quæ ab an-
              <lb/>
            gulo ipſius ad dimidiã baſim
              <lb/>
            ducitur ex decimatertia primi
              <lb/>
            libri Archimedis de cẽtro gra
              <lb/>
            uitatis planorum. </s>
            <s xml:id="echoid-s4512" xml:space="preserve">quare cen-
              <lb/>
              <note position="right" xlink:label="note-0181-02" xlink:href="note-0181-02a" xml:space="preserve">Vltima e-
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              auſdẽ libri
                <lb/>
              Archime-
                <lb/>
              dis.</note>
            trũ grauitatis trapezii b c f e
              <lb/>
            eſt in linea _K_ l, quod ſit m: </s>
            <s xml:id="echoid-s4513" xml:space="preserve">& </s>
            <s xml:id="echoid-s4514" xml:space="preserve">à
              <lb/>
            puncto m ad axem ducta m n
              <lb/>
            ipſi a k, uel d l æquidiſtante;
              <lb/>
            </s>
            <s xml:id="echoid-s4515" xml:space="preserve">erit axis g h diuiſus in portio-
              <lb/>
            nes g n, n h, quas diximus: </s>
            <s xml:id="echoid-s4516" xml:space="preserve">ean
              <lb/>
            dem enim proportionem ha-
              <lb/>
            bet g n ad n h, quã l m ad m _k_. </s>
            <s xml:id="echoid-s4517" xml:space="preserve">
              <lb/>
            At l m ad m K habet eam, quã
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            duplum lateris maioris baſis
              <lb/>
            b c una cum latere minoris e f
              <lb/>
            ad duplum lateris e f unà cum
              <lb/>
            later b c, ex ultima eiuſdem
              <lb/>
            libri Archimedis. </s>
            <s xml:id="echoid-s4518" xml:space="preserve">Itaque à li-
              <lb/>
            nea n g abſcindatur, quarta
              <lb/>
            pars, quæ ſit n p: </s>
            <s xml:id="echoid-s4519" xml:space="preserve">& </s>
            <s xml:id="echoid-s4520" xml:space="preserve">ab axe h g abſcindatur itidem
              <lb/>
            quarta pars h o: </s>
            <s xml:id="echoid-s4521" xml:space="preserve">& </s>
            <s xml:id="echoid-s4522" xml:space="preserve">quam proportionem habet fruſtum ad
              <lb/>
            pyramidem, cuius maior baſis eſt triangulum a b c, & </s>
            <s xml:id="echoid-s4523" xml:space="preserve">alti-
              <lb/>
            tudo ipſi æqualis; </s>
            <s xml:id="echoid-s4524" xml:space="preserve">habeat o p ad p q. </s>
            <s xml:id="echoid-s4525" xml:space="preserve">Dico centrum graui-
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            tatis fruſti eſſe in linea p o, & </s>
            <s xml:id="echoid-s4526" xml:space="preserve">in puncto q. </s>
            <s xml:id="echoid-s4527" xml:space="preserve">namque ipſum
              <lb/>
            eſſe in linea g h manifeſte conſtat. </s>
            <s xml:id="echoid-s4528" xml:space="preserve">protractis enim fruſti </s>
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