Valerio, Luca, De centro gravitatis solidorvm libri tres

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/070.jpg" pagenum="62"/>
              ipſius OR; ſed & AO erat dupla ipſius OR; æqualis
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              igitur AO erit ipſi ON. quare vt AK, ad KD, ita erit
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              AO, ad ON: igitur in triangulo ADN, erit KO, ipſi
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              DN, parallela. </s>
              <s>Eadem ratione ſi iungerentur rectæ BH,
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              CF oſtenderemus & duos reliquos axes LP, MQ, eſ­
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              ſe axi DN parallelos: quatuor autem prædicti axes in­
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              ſiſtunt plano trianguli KLM, ita vt DN tranſeat per
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              centrum S: reliqui autem KO, LP, MQ, terminentur
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              ad angulorum vertices K, L, M, trianguli KLM; igi­
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              tur ſi tres æquales magnitudines habeant centra grauita­
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              tis in axibus KO, LP,
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                <expan abbr="Mq;">Mque</expan>
              compoſiti ex ijs
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              tribus magnitudinibus
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              in axe DN erit
                <expan abbr="centrũ">centrum</expan>
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              grauitatis. </s>
              <s>Rurſus
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              quoniam E ponitur
                <expan abbr="cẽ">cem</expan>
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                <expan abbr="trũ">trum</expan>
              pyramidis ABCD,
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              erit idem E centrum
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              octaedri FGHKLM,
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              idque in axe DN: eſt
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              autem idem
                <expan abbr="centrũ">centrum</expan>
              gra
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              uitatis octaedri, & figu
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              ræ: centrum igitur E
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              octaedri FCHKLM
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              erit in axe DN. </s>
              <s>Quod
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                <figure id="id.043.01.070.1.jpg" xlink:href="043/01/070/1.jpg" number="46"/>
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              ſi quatuor reliquæ pyramides dempto prædicto octaedro
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              ſimiliter diuidantur, ac pyramis ABCD diuiſa fuit, erunt
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              rurſus in ſingulis quatuor prædictarum pyramidum ſin­
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              gula octaedra centrum grauitatis habentia vnumquodque
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              in axe ſuæ pyramidis: quæ pyramides cum ſint inter ſe
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              æquales, earum dimidia octaedr a ipſis inſcripta inter ſe
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              erunt æqualia: ſunt autem eorum centra grauitatis in axi­
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              bus abſciſsarum pyramidum, DS, KO, LP, MQ
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              axis autem DS: eſt in axe DN; per ea igitur, quæ de-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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