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

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          <pb o="176" file="0196" n="196" rhead="GEOMETRIÆ"/>
          <p>
            <s xml:id="echoid-s4339" xml:space="preserve">Inſuper rectangula ſub, AE, ER, ad rectangula ſub, BF, FR,
              <lb/>
              <note position="left" xlink:label="note-0196-01" xlink:href="note-0196-01a" xml:space="preserve">@4. huius.</note>
            ſunt vt rectangulum, DES, ad rectangulum, EFS; </s>
            <s xml:id="echoid-s4340" xml:space="preserve">item rectan-
              <lb/>
            gula ſub, BF, FR, ad rectangula ſub triangulo, BEC, & </s>
            <s xml:id="echoid-s4341" xml:space="preserve">trapezio,
              <lb/>
            CESR, ſunt vt, FS, ad compoſitam ex, {1/2}, SF, &</s>
            <s xml:id="echoid-s4342" xml:space="preserve">, {1/6}, FE, ideſt
              <lb/>
              <note position="left" xlink:label="note-0196-02" xlink:href="note-0196-02a" xml:space="preserve">@@. huius.</note>
            ſumpta, EF, communi altitudine, vt rectangulum, EFS, ad rectan-
              <lb/>
              <figure xlink:label="fig-0196-01" xlink:href="fig-0196-01a" number="115">
                <image file="0196-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0196-01"/>
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            gulum ſub, EF, & </s>
            <s xml:id="echoid-s4343" xml:space="preserve">compoſita ex,
              <lb/>
            {1/6}, EF, &</s>
            <s xml:id="echoid-s4344" xml:space="preserve">, {1/2}, FS, ergo ex æquali
              <lb/>
              <note position="left" xlink:label="note-0196-03" xlink:href="note-0196-03a" xml:space="preserve">6. huius.</note>
            rectangula ſub, AE, ER, ad re-
              <lb/>
            ctangula ſub triangulo, BEC, & </s>
            <s xml:id="echoid-s4345" xml:space="preserve">
              <lb/>
            trapezio, CESR, erunt vt rectan-
              <lb/>
            gulum, DES, ad rectangulum ſub,
              <lb/>
            EF, & </s>
            <s xml:id="echoid-s4346" xml:space="preserve">compoſita ex, {1/6}, EF, &</s>
            <s xml:id="echoid-s4347" xml:space="preserve">,
              <lb/>
            {1/2}, FS; </s>
            <s xml:id="echoid-s4348" xml:space="preserve">erant autem eadem rectan-
              <lb/>
            gula ſub, AE, ER, ad rectangula
              <lb/>
            ſub, AE, & </s>
            <s xml:id="echoid-s4349" xml:space="preserve">trapezio, CESR, vt
              <lb/>
            idem rectangulum, DES, ad re-
              <lb/>
            ctangulum ſub, DE, & </s>
            <s xml:id="echoid-s4350" xml:space="preserve">compoſita
              <lb/>
            ex, SF, &</s>
            <s xml:id="echoid-s4351" xml:space="preserve">, {1/2}, FE, ergo, colligen-
              <lb/>
            do, rectangula ſub, AE, ER, ad rectangula ſub, AF, & </s>
            <s xml:id="echoid-s4352" xml:space="preserve">trapezio,
              <lb/>
            CESR, & </s>
            <s xml:id="echoid-s4353" xml:space="preserve">ſub triangulo, BEC, & </s>
            <s xml:id="echoid-s4354" xml:space="preserve">eodem trapezio, CESR, .</s>
            <s xml:id="echoid-s4355" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s4356" xml:space="preserve">ad rectangula ſub trapezio, ADEC, & </s>
            <s xml:id="echoid-s4357" xml:space="preserve">trapezio, CESR, erunt
              <lb/>
              <note position="left" xlink:label="note-0196-04" xlink:href="note-0196-04a" xml:space="preserve">Per A.
                <lb/>
              Corol.
                <lb/>
              23. huius.</note>
            vt rectangulum, DES, ad rectangulum ſub, DE, & </s>
            <s xml:id="echoid-s4358" xml:space="preserve">compoſita ex,
              <lb/>
            SF, &</s>
            <s xml:id="echoid-s4359" xml:space="preserve">, {1/2}, FE, vna cum rectangulo ſub, EF, & </s>
            <s xml:id="echoid-s4360" xml:space="preserve">compoſita ex, {1/6},
              <lb/>
            EF, &</s>
            <s xml:id="echoid-s4361" xml:space="preserve">, {1/2}, FS, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s4362" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div438" type="section" level="1" n="263">
          <head xml:id="echoid-head278" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s4363" xml:space="preserve">_Q_Voniam verò ſi ſupponamus, FE, eſſe æqualem ipſi, EB, faci’e,
              <lb/>
              <note position="left" xlink:label="note-0196-05" xlink:href="note-0196-05a" xml:space="preserve">_Corol._
                <lb/>
              _20. huius._</note>
            modo vſitato oſtendemus omnes lineas trapezij. </s>
            <s xml:id="echoid-s4364" xml:space="preserve">ADEC, æquari
              <lb/>
            reſiduis amnium abſciſſarum, BE, ſumptis verſus, E, adiuncti,
              <lb/>
            EZ, & </s>
            <s xml:id="echoid-s4365" xml:space="preserve">omnes lineas trapezij, CESR, æquari omnibus abſciſſis, EB,
              <lb/>
            adiuncta recta linea æquali ipſi, FS, ad punctum, B, quæ ſit, BV, & </s>
            <s xml:id="echoid-s4366" xml:space="preserve">
              <lb/>
            omnes lineas, AE, æquari tot æqualibus adiunctæ, ZE, quot ſunt
              <lb/>
            omnes abſciſſæ, BE, & </s>
            <s xml:id="echoid-s4367" xml:space="preserve">omnes lineas, ER, æquari maximis abſciſſa-
              <lb/>
            rum, EB, adiuncta, BV, ideò rectangula ſub iſtis erunt etiam æqualia
              <lb/>
            rectangulis ſub dictis trapezijs, & </s>
            <s xml:id="echoid-s4368" xml:space="preserve">parallelogrammis, vnde propoſita
              <lb/>
            vtcunq; </s>
            <s xml:id="echoid-s4369" xml:space="preserve">linea, VZ, eaq; </s>
            <s xml:id="echoid-s4370" xml:space="preserve">vtcunq; </s>
            <s xml:id="echoid-s4371" xml:space="preserve">ſecta in duobus punctis, BE, pate-
              <lb/>
            bit rectangula ſub tot æqualibus, ZE, quot ſunt omnes abſciſſæ, ſiue,
              <lb/>
            maximæ abſciſſarum, EB, & </s>
            <s xml:id="echoid-s4372" xml:space="preserve">ſub maximis abſciſſirum, EB, adiuncta,
              <lb/>
            BV, ad rectangula ſub reſiduis omnium abſciſſarum, BE, adiuncta,
              <lb/>
            EZ, & </s>
            <s xml:id="echoid-s4373" xml:space="preserve">ſub omnibus abſciſſis, EB, adiuncta, BV, eſſe vt </s>
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