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

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        <div xml:id="echoid-div503" type="section" level="1" n="303">
          <p>
            <s xml:id="echoid-s4993" xml:space="preserve">
              <pb o="203" file="0223" n="223" rhead="LIBER III."/>
            ctangula triplicata, rectangulum autem ſub, DR, & </s>
            <s xml:id="echoid-s4994" xml:space="preserve">ſub compoſi-
              <lb/>
              <note position="right" xlink:label="note-0223-01" xlink:href="note-0223-01a" xml:space="preserve">1. 2. elem.</note>
            ta ex, {1/2}, RM, &</s>
            <s xml:id="echoid-s4995" xml:space="preserve">, MA, diuiditur in rectangula ſub, DR, &</s>
            <s xml:id="echoid-s4996" xml:space="preserve">, {1/2}, R
              <lb/>
            M, & </s>
            <s xml:id="echoid-s4997" xml:space="preserve">ſub, DR, &</s>
            <s xml:id="echoid-s4998" xml:space="preserve">, MA, triplicetur rectangulum ſub, DR, &</s>
            <s xml:id="echoid-s4999" xml:space="preserve">,
              <lb/>
              <note position="right" xlink:label="note-0223-02" xlink:href="note-0223-02a" xml:space="preserve">1. 2. elem.</note>
            {1/2}, RM, fit rectangulum ſub tripla, DR, & </s>
            <s xml:id="echoid-s5000" xml:space="preserve">ſub, {1/2}, RM, cui ſi ad-
              <lb/>
            datur rectangulum ſub, MR, &</s>
            <s xml:id="echoid-s5001" xml:space="preserve">, {1/2}, RM, fit rectangulum ſub com-
              <lb/>
            poſita ex tripla, RD, & </s>
            <s xml:id="echoid-s5002" xml:space="preserve">ex, RM, .</s>
            <s xml:id="echoid-s5003" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5004" xml:space="preserve">ſub compoſita ex, MD, & </s>
            <s xml:id="echoid-s5005" xml:space="preserve">
              <lb/>
            dupla, RD, & </s>
            <s xml:id="echoid-s5006" xml:space="preserve">ſub, {1/2}, RM, quod ſerua: </s>
            <s xml:id="echoid-s5007" xml:space="preserve">Remanent rectangula ad-
              <lb/>
              <note position="right" xlink:label="note-0223-03" xlink:href="note-0223-03a" xml:space="preserve">7. Lib. 2.</note>
            huc ſub, DR, MA, & </s>
            <s xml:id="echoid-s5008" xml:space="preserve">ſub, MR, &</s>
            <s xml:id="echoid-s5009" xml:space="preserve">, {1/2}, MA, triplicanda, quod
              <lb/>
            ſic fiet; </s>
            <s xml:id="echoid-s5010" xml:space="preserve">rectangulum ſub, DR, MA, æquatur rectangulo ſub dupla,
              <lb/>
              <note position="right" xlink:label="note-0223-04" xlink:href="note-0223-04a" xml:space="preserve">1. 2. ele@.</note>
            DR, &</s>
            <s xml:id="echoid-s5011" xml:space="preserve">, {1/2}, MA, cui ſi addatur rectangulum ſub, {1/2}, MA, & </s>
            <s xml:id="echoid-s5012" xml:space="preserve">ſub,
              <lb/>
            MR, fiet rectangulum ſub, {1/2}, MA, & </s>
            <s xml:id="echoid-s5013" xml:space="preserve">ſub compoſita ex, MR, & </s>
            <s xml:id="echoid-s5014" xml:space="preserve">
              <lb/>
            dupla, RD, .</s>
            <s xml:id="echoid-s5015" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5016" xml:space="preserve">ſub compoſita ex, MD, DR, quod triplicatum fit
              <lb/>
            rectangulum ſub compoſita ex, MD, DR, & </s>
            <s xml:id="echoid-s5017" xml:space="preserve">ſub ſexquialtera, M
              <lb/>
            A, quod ſimul cum rectangulo ſub compoſita ex, MD, & </s>
            <s xml:id="echoid-s5018" xml:space="preserve">dupla, D
              <lb/>
            R, & </s>
            <s xml:id="echoid-s5019" xml:space="preserve">ſub, {1/2}, MR, ad rectangulum, DRA, conuertendo, habe-
              <lb/>
            bit eandem rationem, quam omnia quadrata portionis, ICFS, ad
              <lb/>
            omnia quadrata trianguli, CMF; </s>
            <s xml:id="echoid-s5020" xml:space="preserve">quod etiam verificabitur, ſi di-
              <lb/>
              <note position="right" xlink:label="note-0223-05" xlink:href="note-0223-05a" xml:space="preserve">Ex 9. & @.
                <lb/>
              Coroll.
                <lb/>
              22. lib. 2@</note>
            ctum parallelogrammum, & </s>
            <s xml:id="echoid-s5021" xml:space="preserve">triangulum, ſint quidem in eadem baſi
              <lb/>
            cum portione, ſed non circa eundem axim, vel diametrum cum ea-
              <lb/>
            dem portione, vt ſupra patere poteſt in antecedentibus, quod erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s5022" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div506" type="section" level="1" n="304">
          <head xml:id="echoid-head321" xml:space="preserve">THEOREMA IV. PROPOS. IV.</head>
          <p>
            <s xml:id="echoid-s5023" xml:space="preserve">IN eadem antecedentis figura ſi parallelogrammum ſit
              <lb/>
            quidem in eadem altitudine cum portione, ſed in baſi æ-
              <lb/>
            quali ſecundæ diametro; </s>
            <s xml:id="echoid-s5024" xml:space="preserve">omnia quadrata dicti parallelo-
              <lb/>
            grammiad omnia quadrata dictę portionis erunt, vt quadra-
              <lb/>
            tum dimidijaxis, vel diametri eorumdem ad eadem conſe-
              <lb/>
            quentia rectangula, retenta eadem regula.</s>
            <s xml:id="echoid-s5025" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5026" xml:space="preserve">Exponatur denuò antece@entis figura,
              <lb/>
              <figure xlink:label="fig-0223-01" xlink:href="fig-0223-01a" number="136">
                <image file="0223-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0223-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s5027" xml:space="preserve">producatur, CF, ita vt, V @, ſit æqua-
              <lb/>
            lis ſecundæ diametro, quæ ſit, EH, &</s>
            <s xml:id="echoid-s5028" xml:space="preserve">,
              <lb/>
            VR, æqualis, RX, & </s>
            <s xml:id="echoid-s5029" xml:space="preserve">in, VX, baſi ſit
              <lb/>
            conſtructum parallelogrammum, GX,
              <lb/>
            in altitudine eadem cum portione, ICF
              <lb/>
            S, ſit etiam circa eandem axim, vel dia-
              <lb/>
            metrum, MR, cum portione, IECFH
              <lb/>
            S: </s>
            <s xml:id="echoid-s5030" xml:space="preserve">Omnia ergo quadrata parallelogram-
              <lb/>
            mi, GR, ad omnia quadrata parallelogrammi, BR, (regula, CF,)
              <lb/>
              <note position="right" xlink:label="note-0223-06" xlink:href="note-0223-06a" xml:space="preserve">9. Lib. 2.</note>
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