Valerio, Luca, De centro gravitatis solidorvm libri tres

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    <archimedes>
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            <p type="main">
              <s>
                <pb xlink:href="043/01/220.jpg" pagenum="41"/>
              guli ABC quod ſit F, ſit ducta recta AFE. </s>
              <s>Dico AF
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              eſſe ipſius FE triplam: at BE ipſius EC ſeſquialteram.
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              </s>
              <s>Completo enim triangulo rectilineo ABC, ſectis que re­
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              ctis lineis bifariam AB in puncto H, & AC in puncto K
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              ducatur HDK, quæ parallela erit baſi BC: parabolæ igi­
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              tur ſegmenti BDA dia meter erit DH; in qua parabolæ
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              ADB, cuius vertex D ſit centrum grauitatis M: trian­
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              guli autem rectilinei ABC centrum grauitatis N, & iun
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              gatur MN: producta igitur MN occurret trianguli ABC
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              mixti centro grauitatis F. ſint igitur centra M, N, F, in
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              eadem recta linea:
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              & ducta recta AN
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              G ſecet baſim BC
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              bifariam in G pun
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              cto, neceſſe eſt e­
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              nim: & ex puncto
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              F ad rectam AG,
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              ducatur recta FO
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              ipſis BC, KH pa
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              rallela, & BD, DA
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              iungantur. </s>
              <s>
                <expan abbr="Quoniã">Quoniam</expan>
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              igitur AG ſecat
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              BC, KH paral­
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              lelas in rectolineo
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              triangulo ABC,
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                <figure id="id.043.01.220.1.jpg" xlink:href="043/01/220/1.jpg" number="162"/>
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              in eaſdem rationes; ſecta erit HK bifariam à linea AG:
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              cumque HD diameter parabolæ ADC, cuius vertex D,
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              ſit parallela diametro parabolæ, cuius vertex A, atque
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              ideo etiam BC incidenti parallela, erit DH pars ipſius
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              KH: quoniam igitur in triangulo mixto ABC recta KD
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              applicata parallela eſt ipſi BC, quæ itidem eſt parallela
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              diametro parabolæ, cuius vertex A; erit vt AC ad AK
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              potentia, ita BC ad DK longitudine, quod ſupra demon­
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              ſtrauimus: ſed AC quadrupla eſt potentia ipſius AK; </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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