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."/>
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            <s xml:id="echoid-s4500" xml:space="preserve">Sit ſruſtum a e a pyramide, quæ triangularem baſim ha-
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            beat abſciſſum: </s>
            <s xml:id="echoid-s4501" xml:space="preserve">cuius maior baſis triangulum a b c, minor
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            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
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            d a, quod ſectionem faciat d a k l quadrilaterum; </s>
            <s xml:id="echoid-s4506" xml:space="preserve">puncta
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            K l lineas b c, e f bifariam ſecabunt. </s>
            <s xml:id="echoid-s4507" xml:space="preserve">nam cum g h ſit axis
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            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
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            centrum trianguli d e f: </s>
            <s xml:id="echoid-s4511" xml:space="preserve">cen-
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              <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"/>
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              <note position="right" xlink:label="note-0181-01" xlink:href="note-0181-01a" xml:space="preserve">3. diffi. hu
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              ius.</note>
            trum uero cuiuslibet triangu
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            li eſt in recta linea, quæ ab an-
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            gulo ipſius ad dimidiã baſim
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            ducitur ex decimatertia primi
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            libri Archimedis de cẽtro gra
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            uitatis planorum. </s>
            <s xml:id="echoid-s4512" xml:space="preserve">quare cen-
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              <note position="right" xlink:label="note-0181-02" xlink:href="note-0181-02a" xml:space="preserve">Vltima e-
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              auſdẽ libri
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              Archime-
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              dis.</note>
            trũ grauitatis trapezii b c f e
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            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
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            puncto m ad axem ducta m n
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            ipſi a k, uel d l æquidiſtante;
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            </s>
            <s xml:id="echoid-s4515" xml:space="preserve">erit axis g h diuiſus in portio-
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            nes g n, n h, quas diximus: </s>
            <s xml:id="echoid-s4516" xml:space="preserve">ean
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            dem enim proportionem ha-
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            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
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            b c una cum latere minoris e f
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            ad duplum lateris e f unà cum
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            later b c, ex ultima eiuſdem
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            libri Archimedis. </s>
            <s xml:id="echoid-s4518" xml:space="preserve">Itaque à li-
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            nea n g abſcindatur, quarta
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            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
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            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
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            pyramidem, cuius maior baſis eſt triangulum a b c, & </s>
            <s xml:id="echoid-s4523" xml:space="preserve">alti-
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            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
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            eſſe in linea g h manifeſte conſtat. </s>
            <s xml:id="echoid-s4528" xml:space="preserve">protractis enim fruſti </s>
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