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

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            <s xml:id="echoid-s4278" xml:space="preserve">Inſuper rectangula ſub, AO, OB, ad omnia quadrata, OB, ſunt
              <lb/>
              <note position="left" xlink:label="note-0194-01" xlink:href="note-0194-01a" xml:space="preserve">14. huius.</note>
            vt rectangulum, HOM, ad quadratum, OM, & </s>
            <s xml:id="echoid-s4279" xml:space="preserve">omnia quadrata,
              <lb/>
            OB, ad omnia quadrata trapezij, BMNC, ſunt vt quadratum, O
              <lb/>
            M, ad rectangulum, OMN, cum, {1/3}, quadrati, NO, ergo, ex æ-
              <lb/>
              <note position="left" xlink:label="note-0194-02" xlink:href="note-0194-02a" xml:space="preserve">18. huius.</note>
            quali rectangula ſub, AO, OB, ad omnia quadrata trapezij, BM
              <lb/>
            NC, ſunt vt rectangulum, HOM, ad rectangulum, OMN, cum,
              <lb/>
            {1/3}, quadrati, NO, oſtenſa ſunt autem rectangula ſub, AO, OB, ad
              <lb/>
            rectangula ſub, AM, & </s>
            <s xml:id="echoid-s4280" xml:space="preserve">trapezio, BMNC, eſſe vt rectangulum,
              <lb/>
            HOM, ad rectangulum ſub, HM, & </s>
            <s xml:id="echoid-s4281" xml:space="preserve">compoſita ex, MN, &</s>
            <s xml:id="echoid-s4282" xml:space="preserve">, {1/2},
              <lb/>
              <figure xlink:label="fig-0194-01" xlink:href="fig-0194-01a" number="114">
                <image file="0194-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0194-01"/>
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            NO, ergo, colligendo, rectangula ſub,
              <lb/>
            AO, OB, ad rectangula ſub, AM, & </s>
            <s xml:id="echoid-s4283" xml:space="preserve">
              <lb/>
            trapezio, BMNC, cum omnibus
              <lb/>
              <note position="left" xlink:label="note-0194-03" xlink:href="note-0194-03a" xml:space="preserve">PerC. Co
                <lb/>
              rol. 23. hu
                <lb/>
              ius.</note>
            quadratis eiuſdem trapezij, ideſt ad re-
              <lb/>
            ctangula ſub trapezijs, AHNC, BM
              <lb/>
            NC, erunt vt rectangulum, HOM,
              <lb/>
            ad rectangulum ſub, HM, & </s>
            <s xml:id="echoid-s4284" xml:space="preserve">compo-
              <lb/>
            ſita ex, MN, &</s>
            <s xml:id="echoid-s4285" xml:space="preserve">, {1/2}, NO, vna cum re-
              <lb/>
            ctangulo ſub, OM, &</s>
            <s xml:id="echoid-s4286" xml:space="preserve">, MN, &</s>
            <s xml:id="echoid-s4287" xml:space="preserve">, {1/3},
              <lb/>
            quadrati, NO, rectangulum autem
              <lb/>
            ſub, HM, & </s>
            <s xml:id="echoid-s4288" xml:space="preserve">compoſita ex, MN, &</s>
            <s xml:id="echoid-s4289" xml:space="preserve">,
              <lb/>
            {1/2}, NO, diuiditur in rectangula ſub, H
              <lb/>
            M, &</s>
            <s xml:id="echoid-s4290" xml:space="preserve">, MN, & </s>
            <s xml:id="echoid-s4291" xml:space="preserve">ſub, HM, &</s>
            <s xml:id="echoid-s4292" xml:space="preserve">, {1/2}, NO, ſi ergo iunxeris rectangulum
              <lb/>
            ſub, HM, MN, cum rectangulo ſub, OM, MN, ſiet rectangulum
              <lb/>
              <note position="left" xlink:label="note-0194-04" xlink:href="note-0194-04a" xml:space="preserve">i. Secundi
                <lb/>
              Elem.</note>
            ſub tota, HO, & </s>
            <s xml:id="echoid-s4293" xml:space="preserve">ſub, MN, & </s>
            <s xml:id="echoid-s4294" xml:space="preserve">remanebit rectangulum ſub, HM,
              <lb/>
            & </s>
            <s xml:id="echoid-s4295" xml:space="preserve">ſub, {1/2}, NO, cum, {1/3}, quadrati, NO, ideſt cum rectangulo ſub,
              <lb/>
            NO, &</s>
            <s xml:id="echoid-s4296" xml:space="preserve">, {1/3}, NO, eſt autem rectangulum ſub, HM, &</s>
            <s xml:id="echoid-s4297" xml:space="preserve">, {1/2}, NO,
              <lb/>
              <note position="left" xlink:label="note-0194-05" xlink:href="note-0194-05a" xml:space="preserve">7. huius.</note>
            æquale rectangulo ſub, {1/2}, HM, & </s>
            <s xml:id="echoid-s4298" xml:space="preserve">ſub, NO, hoc ergo ſi iunxeris
              <lb/>
            rectangulo ſub, NO, &</s>
            <s xml:id="echoid-s4299" xml:space="preserve">, {1/3}, NO, conficiemus rectangulum ſub com-
              <lb/>
            poſita ex, {1/2}, HM, &</s>
            <s xml:id="echoid-s4300" xml:space="preserve">, {1/3}, NO, & </s>
            <s xml:id="echoid-s4301" xml:space="preserve">ſub, NO, totum igitur conſe-
              <lb/>
            quens iam dictum diuiſum eſt in hæc duo rectangula, nempè vnum
              <lb/>
            ſub, HO, MN, aliud ſub compoſita ex, {1/2}, HM, &</s>
            <s xml:id="echoid-s4302" xml:space="preserve">, {1/3}, NO, & </s>
            <s xml:id="echoid-s4303" xml:space="preserve">
              <lb/>
            ſub, NO; </s>
            <s xml:id="echoid-s4304" xml:space="preserve">ad hæc ergo ſimul ſumpta rectangulum, HOM, erit vt
              <lb/>
            rectangula ſub, AO, OB, ad rectangula ſub trapezijs, AHNC, B
              <lb/>
            MNC, quod oſtendendum erat.</s>
            <s xml:id="echoid-s4305" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div433" type="section" level="1" n="261">
          <head xml:id="echoid-head276" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s4306" xml:space="preserve">_H_Inc etiam patet, ſi ſupponamus, FE, eſſe æqualem ipſi, EB, & </s>
            <s xml:id="echoid-s4307" xml:space="preserve">ipſi,
              <lb/>
            EB, in directum adiunctam ipſam, EZ, ſumamus tamen cum,
              <lb/>
            EZ, ipſam, EM, ex quibus conſiciamus, MZ, adiunctam maximis ab-
              <lb/>
            ſciſſarum, vel abſciſſis ipſius, BM, propoſitæ vtcunque lineæ, quod fa-
              <lb/>
              <note position="left" xlink:label="note-0194-06" xlink:href="note-0194-06a" xml:space="preserve">_Vt in Cor._
                <lb/>
              _21. huius._</note>
            cilè oſtendemus omnes lineas parallelogrammi, AO, æquari </s>
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