Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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          <pb o="191" file="0211" n="211" rhead="LIBER II."/>
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        <div xml:id="echoid-div482" type="section" level="1" n="290">
          <head xml:id="echoid-head306" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s4721" xml:space="preserve">_Q_Voniam poſterior pars Propoſ. </s>
            <s xml:id="echoid-s4722" xml:space="preserve">antec. </s>
            <s xml:id="echoid-s4723" xml:space="preserve">addita fuit poſt impreſionem
              <lb/>
            Lib. </s>
            <s xml:id="echoid-s4724" xml:space="preserve">3 4. </s>
            <s xml:id="echoid-s4725" xml:space="preserve">& </s>
            <s xml:id="echoid-s4726" xml:space="preserve">5. </s>
            <s xml:id="echoid-s4727" xml:space="preserve">ideò ne mireris, benigne Lector, ſi in eiſdem ali-
              <lb/>
            quando Propoſitiones offenderis nonnibil prolixiores, quam ſi per banc
              <lb/>
            poſteriorem partem fuiſſent demonſtrate, cum illaex priori parte tunc
              <lb/>
            deductæ fuerint, quod ſolerti Geometræ haud difficile erit in illis propo-
              <lb/>
            ſitionibus animaducrtere, in quibus banc viderit adhiberi.</s>
            <s xml:id="echoid-s4728" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div483" type="section" level="1" n="291">
          <head xml:id="echoid-head307" xml:space="preserve">THEOREMA XXXIX. PROPOS. XXXIX:</head>
          <p>
            <s xml:id="echoid-s4729" xml:space="preserve">SI recta linea bifariam, & </s>
            <s xml:id="echoid-s4730" xml:space="preserve">non bifariam ſecta fuerit, pa-
              <lb/>
            rallelepipedum ſub medietate propoſitæ lineæ, & </s>
            <s xml:id="echoid-s4731" xml:space="preserve">ſub
              <lb/>
            rectangulo inæqualibus partibus contento, cum parallele-
              <lb/>
            pipedo ſub eadem medietate, & </s>
            <s xml:id="echoid-s4732" xml:space="preserve">ſub quadrato ſectionibus
              <lb/>
            intermediæ, æquabitur cubo eiuſdem medietatis propoſi-
              <lb/>
            cæ lineæ.</s>
            <s xml:id="echoid-s4733" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4734" xml:space="preserve">Sit recta linea, AE, bifariam diuiſa in, B, non bifariam in C. </s>
            <s xml:id="echoid-s4735" xml:space="preserve">Di-
              <lb/>
            co parallelepipedum ſub, BE, & </s>
            <s xml:id="echoid-s4736" xml:space="preserve">rectangulo, ACE, vna cum pa-
              <lb/>
            rallelepipedo ſub, BE, & </s>
            <s xml:id="echoid-s4737" xml:space="preserve">ſub quadrato, BC, cubo eiuſdem, BE,
              <lb/>
            æquale eſſe; </s>
            <s xml:id="echoid-s4738" xml:space="preserve">Nam rectangulum, ACE, cum quadrato, BC, qua-
              <lb/>
              <note position="right" xlink:label="note-0211-01" xlink:href="note-0211-01a" xml:space="preserve">5. Secũdi
                <lb/>
              Elem.</note>
            drato, BE, eſt æquale, vt autem rectangulum, ACE, cum qua
              <lb/>
            drato, BC, ad quadratum, BE, ita (ſumpta communi altitudine,
              <lb/>
              <note position="right" xlink:label="note-0211-02" xlink:href="note-0211-02a" xml:space="preserve">5. huius,</note>
            BE,) parallelepipedum ſub, BE, & </s>
            <s xml:id="echoid-s4739" xml:space="preserve">rectangulo, ACE, & </s>
            <s xml:id="echoid-s4740" xml:space="preserve">ſub, B
              <lb/>
            E, & </s>
            <s xml:id="echoid-s4741" xml:space="preserve">quadrato, BC, ad parallelepipedum ſub, BE, & </s>
            <s xml:id="echoid-s4742" xml:space="preserve">quadrato,
              <lb/>
            BE, ideſt ad cubum, BE, ergo parallelepipedum ſub, EB, & </s>
            <s xml:id="echoid-s4743" xml:space="preserve">ſub
              <lb/>
            rectangulo, ACE, vna cum parallelepipedo ſub eadem, EB, & </s>
            <s xml:id="echoid-s4744" xml:space="preserve">ſub
              <lb/>
            quadrato, BC, erit æquale cubo, EB, quod oſtendendum erat.</s>
            <s xml:id="echoid-s4745" xml:space="preserve"/>
          </p>
          <figure number="127">
            <image file="0211-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0211-01"/>
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