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

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          <p>
            <s xml:id="echoid-s6218" xml:space="preserve">
              <pb o="250" file="0270" n="270" rhead="GEOMETRIÆ"/>
            libet portiones extra figuram ad oppoſita latera terminan-
              <lb/>
            tes, & </s>
            <s xml:id="echoid-s6219" xml:space="preserve">in eadem recta linea conſtitutæ integræ, & </s>
            <s xml:id="echoid-s6220" xml:space="preserve">inter ſe
              <lb/>
            æquales: </s>
            <s xml:id="echoid-s6221" xml:space="preserve">Omnia quadrata dicti parallelogrammi ad omnia
              <lb/>
            quadrata inſcriptæ figuræ, cum rectangulis bis ſub eadem
              <lb/>
            figura, & </s>
            <s xml:id="echoid-s6222" xml:space="preserve">ſub dictarum portionum ijs omnibus, quę extra fi-
              <lb/>
            guram ad vnum dictorum laterum oppoſitorum eiuſdem pa-
              <lb/>
            rallelogrammi terminantur, erunt vt prædictum parallelo-
              <lb/>
            grammum ad inſcriptam figuram.</s>
            <s xml:id="echoid-s6223" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6224" xml:space="preserve">Sitigitur parallelogrammum, AN, & </s>
            <s xml:id="echoid-s6225" xml:space="preserve">illi inſcripta vtcunq; </s>
            <s xml:id="echoid-s6226" xml:space="preserve">figu-
              <lb/>
            ra, BDMO, & </s>
            <s xml:id="echoid-s6227" xml:space="preserve">ſumpta pro regula, EN, ſit ducta vtcunque intra
              <lb/>
            parallelogrammum, AN, ipſa, DO, quę cadat etiam tota intra fi-
              <lb/>
            guram, BDMO, ſit etiam ducta alia vtcunque parallela ipſi, EN,
              <lb/>
            nempè, VR, portiones autem eiuſdem, VR, ſint extra figuram,
              <lb/>
            ad latera oppoſita, AE, CN, terminantes .</s>
            <s xml:id="echoid-s6228" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6229" xml:space="preserve">VI, SR, quæ ſint in-
              <lb/>
            tegræ, & </s>
            <s xml:id="echoid-s6230" xml:space="preserve">inter ſe æquales. </s>
            <s xml:id="echoid-s6231" xml:space="preserve">Dico omnia quadrata, AN, ad omnia
              <lb/>
            quadrata figuræ, BDMO, cum rectangulis bis ſub figuræ, BDM
              <lb/>
            O, & </s>
            <s xml:id="echoid-s6232" xml:space="preserve">ſub trilineis, BCO, ONM, .</s>
            <s xml:id="echoid-s6233" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6234" xml:space="preserve">ſub omnibus portionibus, quę
              <lb/>
            terminant ad latus, CN, extra figuram, BDMO, conſtitutis, elie
              <lb/>
              <figure xlink:label="fig-0270-01" xlink:href="fig-0270-01a" number="166">
                <image file="0270-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0270-01"/>
              </figure>
            vt, AN, ad figuram, BDMO: </s>
            <s xml:id="echoid-s6235" xml:space="preserve">Omnia
              <lb/>
            enim quadrata, AN, ad rectangula ſub,
              <lb/>
            A N, & </s>
            <s xml:id="echoid-s6236" xml:space="preserve">ſub figura, BDMO, ſunt vt, A
              <lb/>
            N, ad figuram, BDMO, ſed rectangula
              <lb/>
            ſub, AN, & </s>
            <s xml:id="echoid-s6237" xml:space="preserve">ſub figura, BDMO, diui-
              <lb/>
              <note position="left" xlink:label="note-0270-01" xlink:href="note-0270-01a" xml:space="preserve">Coroll. 1.
                <lb/>
              26. lib. 2.</note>
            duntur in rectangula ſub eadem figura, B
              <lb/>
            D MO, & </s>
            <s xml:id="echoid-s6238" xml:space="preserve">ſub trilineis, BAD, DEM,
              <lb/>
            ſub eadem, & </s>
            <s xml:id="echoid-s6239" xml:space="preserve">ſub trilineis, BCO, ON
              <lb/>
            M, & </s>
            <s xml:id="echoid-s6240" xml:space="preserve">in rectangula ſub eadem in eandem
              <lb/>
              <note position="left" xlink:label="note-0270-02" xlink:href="note-0270-02a" xml:space="preserve">A. 23. l. 2.</note>
            figuram .</s>
            <s xml:id="echoid-s6241" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6242" xml:space="preserve">in omnia quadrata eiuſdem fi-
              <lb/>
            guræ, BDMO, quia verò linearum æqui-
              <lb/>
            diſtantium, regulæ, EN, portiones, quæ
              <lb/>
            ſunt in eadem recta linea extra figuram adiacentes lateribus oppoſi-
              <lb/>
            tis, AE, CN, ſunt & </s>
            <s xml:id="echoid-s6243" xml:space="preserve">integræ, & </s>
            <s xml:id="echoid-s6244" xml:space="preserve">æquales, ideò ſicuti rectangu-
              <lb/>
            lum, VIS, eſt æquale rectangulo, ISR, ita rectangula ſub figura,
              <lb/>
            B DMO, & </s>
            <s xml:id="echoid-s6245" xml:space="preserve">trilineis, BAD, DEM, erunt æqualia rectangulis
              <lb/>
            ſub eadem figura, BDMO, & </s>
            <s xml:id="echoid-s6246" xml:space="preserve">ſub trilineis, BCO, ONM, ſunt
              <lb/>
            ergo rectangula ſub, AN, & </s>
            <s xml:id="echoid-s6247" xml:space="preserve">ſub figura, BDMO, æqualia om-
              <lb/>
            nibus quadratis figuræ, BDMO, cum rectangulis bis ſub eadem,
              <lb/>
            & </s>
            <s xml:id="echoid-s6248" xml:space="preserve">ſub trilineis, BCO, ONM; </s>
            <s xml:id="echoid-s6249" xml:space="preserve">omnia autem quadrata, AN, ad
              <lb/>
            rectangula ſub, AN, & </s>
            <s xml:id="echoid-s6250" xml:space="preserve">ſub figura, BDMO, ſunt vt, AN, ad fi-
              <lb/>
            guram, BDMO; </s>
            <s xml:id="echoid-s6251" xml:space="preserve">ergo omnia quadrata, AN, ad omnia </s>
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