Valerio, Luca, De centro gravitatis solidorvm libri tres

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/095.jpg" pagenum="8"/>
              gitaui, quo ſecunda
                <expan abbr="antecedẽs">antecedens</expan>
              hìc in illis tertia facilius ſer­
                <lb/>
              uiret ijs, in quibus certæ proportionis nomen,
                <expan abbr="tertiũ">tertium</expan>
              & quar
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              tum terminum ſubobſcurè indicat, vt in ſequenti XII iilud,
                <lb/>
              proportio dupla. </s>
              <s>Illo autem Lemmate, quod prima propofi­
                <lb/>
              tio inſcribebatur, nunc ita non egeo, vt primam, &
                <expan abbr="ſecundã">ſecundam</expan>
              ,
                <lb/>
              quæ ſecunda, & tertia erant, & facilius demonſtrem, & ea­
                <lb/>
              rum ſenſum paucioribus comprehendam. </s>
              <s>priora ergo ita
                <lb/>
              non improbo vt hæc ijs anteponam. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO IIII.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Si ſint tres magnitudines ſe ſe æqualiter exce­
                <lb/>
              dentes, minor erit proportio minimæ ad mediam
                <lb/>
              quàm mediæ ad maximam. </s>
            </p>
            <p type="main">
              <s>Sint tres magnitudines inæquales A, BC, DE, qua­
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              rum BC æquè excedat ipſam A, ac DE ipſam BC
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              Dico minorem eſse proportionem A, ad
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              BC, quàm BC, ad DE. </s>
              <s>Nam vt eſt
                <lb/>
              A ad BC, ita ſit BC ad LH, & au­
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              feratur BF æqualis A, & DG, & LK
                <lb/>
              æquales BC. </s>
              <s>Quoniam igitur eſt vt A,
                <lb/>
              hoc eſt FB ad BC, ita BC hoc eſt KL
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              ad LH; erit diuidendo vt BF ad FC,
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              ita LK ad KH: & componendo, ac per­
                <lb/>
              mutando vt BC ad LH, ita FC ad
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              KH. ſed BC eſt minor quàm LH; ergo
                <lb/>
              & FC hoc eſt EG erit minor quàm KH.
                <lb/>
              </s>
              <s>Sed DE, LH, ſuperant BC exceſsibus
                <lb/>
              EG, KH; minor igitur erit DE quàm
                <lb/>
              LH, & minor proportio BC ad LH,
                <lb/>
              quàm BC ad DE. </s>
              <s>Sed vt BC ad LH,
                <lb/>
                <figure id="id.043.01.095.1.jpg" xlink:href="043/01/095/1.jpg" number="69"/>
                <lb/>
              ita eſt A ad BC; minor igitur proportio erit A ad BC,
                <lb/>
              quàm BC ad DE. </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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