Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/089.jpg" pagenum="2"/>
            <p type="main">
              <s>Sint quatuor magnitudines A prima, B ſecunda, C ter
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              tia, & D quarta: quantacumque autem magnitudine propo
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              ſita, ex infinitìs quæ proponi poſſunt eiuſdem generis cum
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              A, C, vel vna tantum, ſi AC ſint eiuſdem generis: vel
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              vna, & altera; ſi vna vnius, altera ſit alterius generis; ſemper
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              aliæ duæ magnitudines vnà maiores, quàm AC, minori
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              exceſsu magnitudine propoſita; eandem habeant proportio
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              nem, maior quàm A ad B, & maior quàm C ad D. </s>
              <s>Dico
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              eſse vt A ad B, ita C ad D. </s>
              <s>Poſita enim E ad D, vt
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              A ad B, & F maiori quàm C vtcumque, ſint aliæ duæ ma­
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              gnitudines, G maior quàm A minori exceſsu magnitudine
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              eiuſdem generis cum A, quam quis voluerit, & H maior
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              quàm C minori exceſsu quàm
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              quo F ſuperat C, ideſt, quæ ma­
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              ior ſit quàm C, & minor quàm
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              F: ſit autem vt G ad B, ita H
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              ad D. </s>
              <s>Quoniam igitur F maior
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              eſt, <34>H, maior erit proportio
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              ipſius F quàm H ad D, hoc eſt
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              quàm G ad B. </s>
              <s>Sed
                <expan abbr="cũ">cum</expan>
              G maior
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              ſit quàm A, maior eſt proportio
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                <figure id="id.043.01.089.1.jpg" xlink:href="043/01/089/1.jpg" number="60"/>
                <lb/>
              G ad B, quàm A ad B, multo igitur erit maior proportio F
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              ad D, quàm A ad B. </s>
              <s>Sed F ponitur maior quàm C, vtcum
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              que; nulla igitur magnitudo maior quàm C eſt ad D, vt
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              A ad B: ſed E ad D, eſt vt A ad B; non igitur eſt E ma­
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              ior quàm C; nec maior proportio E ad D, hoc eſt A ad
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              B, quàm C ad D. </s>
              <s>Eadem autem ratione nec maior erit
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              proportio C ad D quàm A ad B, hoc eſt non minor A
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              ad B, quàm C ad D; eadem igitur proportio A ad B,
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              quæ C ad D. </s>
            </p>
            <p type="main">
              <s>Sed aliæ duæ magnitudines vnà minores quàm A, C
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              minori defectu quantacumque magnitudine propoſita,
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              eandem habeant proportionem, minor quàm A ad B, &
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              minor quàm C, ad D. </s>
              <s>Dico eſse vt A ad B, ita C ad D. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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