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

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          <p>
            <s xml:id="echoid-s2786" xml:space="preserve">
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            P, in eadem altitudine ſumpta iuxta baſes, TP, OP, & </s>
            <s xml:id="echoid-s2787" xml:space="preserve">ideò eſſent,
              <lb/>
              <note position="left" xlink:label="note-0138-01" xlink:href="note-0138-01a" xml:space="preserve">Ex prima
                <lb/>
              par. huius
                <lb/>
              Propoſ.</note>
            vt ipſæ baſes, TP, OP, ideſt vt latera, TP, OP, æqualiter baſi,
              <lb/>
            NP, inclinata, hæc autem pariter verificabuntur etiamſi baſis, NP,
              <lb/>
            non ſit communis, ſint tamen duæ baſes æquales, quæ oſtendere o-
              <lb/>
            pus erat.</s>
            <s xml:id="echoid-s2788" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div289" type="section" level="1" n="182">
          <head xml:id="echoid-head197" xml:space="preserve">THEOREMA VI. PROPOS. VI.</head>
          <p>
            <s xml:id="echoid-s2789" xml:space="preserve">PArallelogramma habent rationem compoſitam ex ra-
              <lb/>
            tione baſium, & </s>
            <s xml:id="echoid-s2790" xml:space="preserve">altitudinum iuxta eaſdem baſes ſum-
              <lb/>
            ptarum, ſiue laterum æqualiter baſibus inclinatorum, cum
              <lb/>
            ſcilicetilla ſunt æquiangula.</s>
            <s xml:id="echoid-s2791" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2792" xml:space="preserve">Sint parallelogramma vtcunque, AD, FM. </s>
            <s xml:id="echoid-s2793" xml:space="preserve">Dico eadem habe.
              <lb/>
            </s>
            <s xml:id="echoid-s2794" xml:space="preserve">re inter ſe rationem compoſitam ex rationibus baſium, quæ ſint, C
              <lb/>
              <note position="left" xlink:label="note-0138-02" xlink:href="note-0138-02a" xml:space="preserve">Defin. 12.
                <lb/>
              lib. 1.</note>
            D, GM, & </s>
            <s xml:id="echoid-s2795" xml:space="preserve">altitudinum, quę ſint, BV, ON, ſumptæ iuxta baſes,
              <lb/>
            CD, GM, illiſque productis, ſi opus ſit, in punctis, V, N, occur-
              <lb/>
            rentes, ſiue ex ratione laterum, BD, OM, ſi ſint æquiangula: </s>
            <s xml:id="echoid-s2796" xml:space="preserve">Ab-
              <lb/>
              <figure xlink:label="fig-0138-01" xlink:href="fig-0138-01a" number="78">
                <image file="0138-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0138-01"/>
              </figure>
            ſcindatur à, BV, verſus, V, ipſa,
              <lb/>
            XV, æqualis ipſi, ON, & </s>
            <s xml:id="echoid-s2797" xml:space="preserve">per, X,
              <lb/>
            ducatur, XP, parallela, CD, ſe-
              <lb/>
            cans, BD, in, R, vt fiat paralle-
              <lb/>
            logrammum, PD, in eadem altitu-
              <lb/>
            dine cum parallelogrammo, FM,
              <lb/>
            & </s>
            <s xml:id="echoid-s2798" xml:space="preserve">in eadẽ baſi cum parallelogram-
              <lb/>
            mo, AD. </s>
            <s xml:id="echoid-s2799" xml:space="preserve">Parallelogrammum er-
              <lb/>
            go, AD, ad parallelogrammum,
              <lb/>
            FM, ſumpto medio de foris parallelogrammo, PD, habet ratio-
              <lb/>
              <note position="left" xlink:label="note-0138-03" xlink:href="note-0138-03a" xml:space="preserve">Defin. 12.
                <lb/>
              lib. 1.</note>
            nem compoſitam ex ratione parallelogrammi, AD, ad parallelo-
              <lb/>
            grammum, PD, ideſt ex ratione, quam habet, BV, ad, VX, vel,
              <lb/>
            ON, ſiue, BD, ad, DR, quoniam, AD, PD, ſunt æquiangu-
              <lb/>
            la, ideſt ex ratione, BD, ad, OM, & </s>
            <s xml:id="echoid-s2800" xml:space="preserve">hoc quotieſcunque, PD, F
              <lb/>
              <note position="left" xlink:label="note-0138-04" xlink:href="note-0138-04a" xml:space="preserve">Exſecun.
                <lb/>
              par. ant.</note>
            M, ſint pariter æquiangula, & </s>
            <s xml:id="echoid-s2801" xml:space="preserve">inſuper eſt compoſita ex ea, quam
              <lb/>
            habet parallelogrammum, PD, ad parallelogrammum, FM, ideſt
              <lb/>
            ex ea, quam habet, CD, ad, GM, ergo parallelogrammum, AD,
              <lb/>
              <note position="left" xlink:label="note-0138-05" xlink:href="note-0138-05a" xml:space="preserve">Ex prima
                <lb/>
              parte an-
                <lb/>
              teced.</note>
            ad parallelogrammum, FM, habet rationem compoſitam ex ea,
              <lb/>
            quam habet, BV, ad, ON, quæ ſunt altitudines, vel etiam ex ea,
              <lb/>
            quam habet, BD, ad, OM, ſi, AD, FM, ſint æquiangula; </s>
            <s xml:id="echoid-s2802" xml:space="preserve">& </s>
            <s xml:id="echoid-s2803" xml:space="preserve">ex
              <lb/>
            ea, quam habet, CD, ad, GM, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s2804" xml:space="preserve"/>
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