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

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          <p>
            <s xml:id="echoid-s3687" xml:space="preserve">
              <pb o="156" file="0176" n="176" rhead="GEOMETRIÆ"/>
            quoties, BD, ſecta eſſe ſupponitur, exceptis tamen extremis, vt ex.
              <lb/>
            </s>
            <s xml:id="echoid-s3688" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3689" xml:space="preserve">ipſa, CI, in qua parte, CI, quæin recta, CI, feparari debuiſ-
              <lb/>
            ſent per lineas, AEC, AFI, in puncta, C, I, partibus, BE, FD,
              <lb/>
            reſpondentia degenerauerunt. </s>
            <s xml:id="echoid-s3690" xml:space="preserve">Dico quæcunque demonſtrantur in
              <lb/>
            linea, BD, circa quadrata, vel rectangula, illi, vel illius partibus ap-
              <lb/>
            plicata, verificari de omnibus quadratis totius figurę, BADC, ſiue
              <lb/>
            partium eiuſdem figuræ per dictas lineas conſtitutarum, ſiue de re-
              <lb/>
            ctangulis ſub eiuſdem partibus. </s>
            <s xml:id="echoid-s3691" xml:space="preserve">Vtex gr. </s>
            <s xml:id="echoid-s3692" xml:space="preserve">quia in 3. </s>
            <s xml:id="echoid-s3693" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s3694" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3695" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3696" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0176-01" xlink:href="note-0176-01a" xml:space="preserve">Vide D.
                <lb/>
              Defin. 8.
                <lb/>
              huius.</note>
            Elem. </s>
            <s xml:id="echoid-s3697" xml:space="preserve">oſtenditur rectangulum ſub, BD, DF, æquari rectangulo
              <lb/>
            ſub, BFD, cum quadrato, FD, ſic dico verum eſſe rectangula ſub
              <lb/>
              <figure xlink:label="fig-0176-01" xlink:href="fig-0176-01a" number="101">
                <image file="0176-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0176-01"/>
              </figure>
            figura, ABCD, & </s>
            <s xml:id="echoid-s3698" xml:space="preserve">figura, ADI, æquari re-
              <lb/>
            ctangulis ſub figuris, ABIF, ADIF, cum om-
              <lb/>
            nibus quadratis figuræ, ADIF, ſi enim aliam
              <lb/>
            vtcunque duxerimus regulæ, BD, parallelam,
              <lb/>
            vt, HO, ſecantem lineas, AC, in, M, &</s>
            <s xml:id="echoid-s3699" xml:space="preserve">, A
              <lb/>
            I, in, N, verum eſſe comperiemus rectangulum,
              <lb/>
            HON, æquari rectangulo, HNO, cum qua-
              <lb/>
            drato, NO, & </s>
            <s xml:id="echoid-s3700" xml:space="preserve">idem in cęteris regulę, BD, pa-
              <lb/>
            rallelis in figura, ABCD, ductis reperiemus,
              <lb/>
            ergo verum erit rectangula illa ſimul collecta, ideſt rectangula ſub fi-
              <lb/>
              <note position="left" xlink:label="note-0176-02" xlink:href="note-0176-02a" xml:space="preserve">Coroll. 4.
                <lb/>
              huius.</note>
            gura, ABID, & </s>
            <s xml:id="echoid-s3701" xml:space="preserve">figura, ADI, æquari rectangulis ſub figuris, AB
              <lb/>
            I, ADI, cum omnibus quadratis, ADI, quod 3. </s>
            <s xml:id="echoid-s3702" xml:space="preserve">Propoſit. </s>
            <s xml:id="echoid-s3703" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3704" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s3705" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s3706" xml:space="preserve">reſpondet.</s>
            <s xml:id="echoid-s3707" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3708" xml:space="preserve">Similiter ſi ſupponamus, BF, bifariam ſecari in, E, cui adiunga-
              <lb/>
            tur, FD, ſuppoſuerimus etiam lineam, AC, bifariam ſecare quam-
              <lb/>
            libet omnium linearum figuræ, ABI, regula, BD, ſupradictarum,
              <lb/>
            quarum ſingulis aditur, quę in directum manetin figura, ADI, ve-
              <lb/>
            luti Propoſ. </s>
            <s xml:id="echoid-s3709" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3710" xml:space="preserve">oſtenditur rectangulum, BDF, cum quadrato, FE,
              <lb/>
            æquari quadrato, ED, ita hic ad modum ſuperioris oſtendemus re-
              <lb/>
            ctangula ſub figura, ABID, &</s>
            <s xml:id="echoid-s3711" xml:space="preserve">, ADI, cum omnibus quadratis fi-
              <lb/>
            guræ, ACI, æquari omnibus quadratis figuræ, ACD, quod re-
              <lb/>
            ſpondet Prop. </s>
            <s xml:id="echoid-s3712" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3713" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s3714" xml:space="preserve">Conſimiliter reliqua demonſtrabimus,
              <lb/>
            vnde iuxta I. </s>
            <s xml:id="echoid-s3715" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s3716" xml:space="preserve">Secundi Elem. </s>
            <s xml:id="echoid-s3717" xml:space="preserve">colligemus.</s>
            <s xml:id="echoid-s3718" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div391" type="section" level="1" n="235">
          <head xml:id="echoid-head250" xml:space="preserve">A. COROLLARII SECTIO I.</head>
          <p style="it">
            <s xml:id="echoid-s3719" xml:space="preserve">_R_Ectangula ſub figura indiuiſa, ABID, & </s>
            <s xml:id="echoid-s3720" xml:space="preserve">ſub diuiſa, ACD, per
              <lb/>
            lineam, AI, æquari rectangulis ſub indiuiſa, ABID, & </s>
            <s xml:id="echoid-s3721" xml:space="preserve">ſub
              <lb/>
            partibus diuiſæ, quæ ſunt, ACI, AID.</s>
            <s xml:id="echoid-s3722" xml:space="preserve"/>
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