Valerio, Luca, De centro gravitatis solidorvm libri tres

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              <s>
                <pb xlink:href="043/01/030.jpg" pagenum="22"/>
              lo KLM: ſed triangulum FGH, eſt ſimile triangulo
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              ABC, & triangulum KLM, ſimile eidem triangulo
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              ABC;
                <expan abbr="triangulũ">triangulum</expan>
              ergo FGH, ſimile erit triangulo KLM:
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              ſed & æquale propter æqualitatem laterum homologo­
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              rum. </s>
              <s>Similiter oſtenderemus reliquum ſolidum LKM
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              GFH continentia triangula bina oppoſita æqualia
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              inter ſe, & ſimilia, & parallela; octaedrum eſt igitur
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              LKMGFH. </s>
              <s>Dico iam punctum P, quod eſt cen­
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              trum pyramidis ABCD, eſse centrum octaedri L
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
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              MGFH. </s>
              <s>Quoniam enim DP, ponitur tripla ipſius PE,
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              & DO, eſt æqualis
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              OE (ſiquidem planum
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              trianguli KLM, plano
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                <expan abbr="triãguli">trianguli</expan>
              ABC, paralle
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              lum ſecat proportione
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                <expan abbr="oẽs">oens</expan>
              rectas lineas, quæ
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              ex puncto D, in ſubli­
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              mi pertinent ad ſubie­
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              ctum planum trianguli
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              ABC) erit OP, ipſi
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              PE, æqualis. </s>
              <s>Et quo­
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              niam BH eſt dupla
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              ipſius QH, quarum
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              BE eſt dupla ipſius
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                <figure id="id.043.01.030.1.jpg" xlink:href="043/01/030/1.jpg" number="16"/>
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              EH, ſiquidem E eſt centrum trianguli ABC; erit reli­
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              qua EH reliquæ EQ dupla: & quia eſt vt LD ad DB,
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              ita LN ad BH, propter ſimilitudinem triangulorum, &
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              eſt LD, dimidia ipſius BD, erit & LN, dimidia ipſius
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              BH: ſed QH eſt dimidia ipſius BH; æqualis igitur LN
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              ipſi QH. </s>
              <s>Iam igitur quia eſt vt BE ad EH, ita
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              LO ad ON: ſed BE, eſt dupla ipſius EH; dupla igi­
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              tur LO, erit ipſius ON: ſed & QH erat dupla ipſius
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              QE; vt igitur LN ad NO, ita erit HQ ad QE: & </s>
            </p>
          </chap>
        </body>
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    </archimedes>
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