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

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        <div xml:id="echoid-div473" type="section" level="1" n="286">
          <p>
            <s xml:id="echoid-s4631" xml:space="preserve">
              <pb o="189" file="0209" n="209" rhead="LIBER II."/>
            gulo totius in talem partem ductæ. </s>
            <s xml:id="echoid-s4632" xml:space="preserve">Idem autem parallelepi-
              <lb/>
            pedum ſub tota, & </s>
            <s xml:id="echoid-s4633" xml:space="preserve">talis partis quadrato, erit æquale paral-
              <lb/>
            lelepipedo ſub reliqua, & </s>
            <s xml:id="echoid-s4634" xml:space="preserve">quadrato talis partis, vna cum
              <lb/>
            cubo eiuſdem partis.</s>
            <s xml:id="echoid-s4635" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4636" xml:space="preserve">Sit ergo recta linea, AC, vtcumque ſectain, B, dico parallelepi-
              <lb/>
            pedum ſub, AC, & </s>
            <s xml:id="echoid-s4637" xml:space="preserve">quadrato, CB, & </s>
            <s xml:id="echoid-s4638" xml:space="preserve">quari parallelepipedo ſub, B
              <lb/>
              <figure xlink:label="fig-0209-01" xlink:href="fig-0209-01a" number="125">
                <image file="0209-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0209-01"/>
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            C, & </s>
            <s xml:id="echoid-s4639" xml:space="preserve">rectangulo, BCA, hoc autem patet
              <lb/>
            ex ſuperiori Scholio, nam parallelepipedum
              <lb/>
            ſub, AC, & </s>
            <s xml:id="echoid-s4640" xml:space="preserve">quadrato, CB, continetur ſub
              <lb/>
            tribus his rectis lineis, nempè, AC, & </s>
            <s xml:id="echoid-s4641" xml:space="preserve">dua-
              <lb/>
            bus, CB, & </s>
            <s xml:id="echoid-s4642" xml:space="preserve">ideòidem contìnetur ſub, CB, & </s>
            <s xml:id="echoid-s4643" xml:space="preserve">rectangulo, ACB,
              <lb/>
            ſiue eſt æquale contento ſub, BC, & </s>
            <s xml:id="echoid-s4644" xml:space="preserve">rectangulo, ACB.</s>
            <s xml:id="echoid-s4645" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4646" xml:space="preserve">Dico inſuper parallelepipedum ſub, AC, & </s>
            <s xml:id="echoid-s4647" xml:space="preserve">quadrato, CB, æ-
              <lb/>
            quari parallelepipedo ſub, AB, & </s>
            <s xml:id="echoid-s4648" xml:space="preserve">quadrato, CB, vna cum cubo, C
              <lb/>
            B, quod patet nam parallelepipedum ſub diuiſa altitudine, AC, & </s>
            <s xml:id="echoid-s4649" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0209-01" xlink:href="note-0209-01a" xml:space="preserve">Ex antec.</note>
            indiuiſa baſi, nempè quadrato, CB, æquatur parallelepipedis ſub
              <lb/>
            partibus ſingulis, & </s>
            <s xml:id="echoid-s4650" xml:space="preserve">baſi, ſcilicet ſub, AB, & </s>
            <s xml:id="echoid-s4651" xml:space="preserve">quadrato, BC, & </s>
            <s xml:id="echoid-s4652" xml:space="preserve">ſub,
              <lb/>
            BC, & </s>
            <s xml:id="echoid-s4653" xml:space="preserve">quadrato, BC, ideſt cubo, BC, quod erat oſtendendum.</s>
            <s xml:id="echoid-s4654" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div476" type="section" level="1" n="287">
          <head xml:id="echoid-head303" xml:space="preserve">THEOREMA XXXVII. PROPOS. XXXVII.</head>
          <p>
            <s xml:id="echoid-s4655" xml:space="preserve">SI recta linea in vno puncto ſecta ſit vtcumq; </s>
            <s xml:id="echoid-s4656" xml:space="preserve">cubus totius
              <lb/>
            æquabitur parall elepipedis ſub partibus, & </s>
            <s xml:id="echoid-s4657" xml:space="preserve">quadrato
              <lb/>
            eiuſdem. </s>
            <s xml:id="echoid-s4658" xml:space="preserve">Idem etiam erit æquale parallelepipedis ſub tota,
              <lb/>
            & </s>
            <s xml:id="echoid-s4659" xml:space="preserve">partibus quadrati totius per talem diuiſtonem factis, ideſt
              <lb/>
            parallelepipedis ſub tota, & </s>
            <s xml:id="echoid-s4660" xml:space="preserve">quadratis partium, & </s>
            <s xml:id="echoid-s4661" xml:space="preserve">rectan-
              <lb/>
            gulo ſub partibus bis contento.</s>
            <s xml:id="echoid-s4662" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4663" xml:space="preserve">Sit recta linea, AC, vtcumq; </s>
            <s xml:id="echoid-s4664" xml:space="preserve">ſecta in, B, dico cubum, AC, æquari
              <lb/>
            parallelepipedis ſub partibus, AB, BC, & </s>
            <s xml:id="echoid-s4665" xml:space="preserve">quadrato totius, quod
              <lb/>
            patet nam cubus, AC, ideſt parallelepipedum ſub diuiſa, AC, & </s>
            <s xml:id="echoid-s4666" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0209-02" xlink:href="note-0209-02a" xml:space="preserve">35. huius.</note>
            indiuiſa baſi quadrato, AC, eſt æquale parallelepipedis ſub partibus,
              <lb/>
            AB, BC, eiuſdem, AC, diuiſæ, & </s>
            <s xml:id="echoid-s4667" xml:space="preserve">ſub eadem baſi quadrato, AC.</s>
            <s xml:id="echoid-s4668" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4669" xml:space="preserve">Dico etiam cubum, AC, æquari parallelepipedis ſub, AC, & </s>
            <s xml:id="echoid-s4670" xml:space="preserve">
              <lb/>
            quadrato, AB, quadrato, BC, & </s>
            <s xml:id="echoid-s4671" xml:space="preserve">rectangulo bis ſub, ABC, nam
              <lb/>
            cubus, AC, ideſt parallelepipedum ſub indiuiſa altitudine, AC, & </s>
            <s xml:id="echoid-s4672" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0209-03" xlink:href="note-0209-03a" xml:space="preserve">35. huius.</note>
            diuiſa baſi in dicta quattuor ſpatia, æquatur parallelepipedis ſub ea-
              <lb/>
            dem indiuiſa altitudine, AC, & </s>
            <s xml:id="echoid-s4673" xml:space="preserve">ſub dictis baſis partibus, nempè ſub
              <lb/>
            quadrato, AB, quadrato, BC, & </s>
            <s xml:id="echoid-s4674" xml:space="preserve">rectangulo bis ſub, ABC, quod
              <lb/>
            erat oſtendendum.</s>
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