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

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          <p>
            <s xml:id="echoid-s3452" xml:space="preserve">
              <pb o="146" file="0166" n="166" rhead="GEOMETRIÆ"/>
            FG, HM, homologæ figurarum, FGP, HMQ, quę figurę vo-
              <lb/>
            cantur in ipſis ſolidis homologæ. </s>
            <s xml:id="echoid-s3453" xml:space="preserve">Dico hæc ſolida eſſe proportiona-
              <lb/>
            lia; </s>
            <s xml:id="echoid-s3454" xml:space="preserve">ſit duarum, AB, CD, tertia proportionalis, R, quarta, S, & </s>
            <s xml:id="echoid-s3455" xml:space="preserve">
              <lb/>
            duarum, FG, HM, tertia, I, quarta, T, eſt igitur ſolidum, AXB,
              <lb/>
            ad, CVD, vt, AB, ad, S, .</s>
            <s xml:id="echoid-s3456" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3457" xml:space="preserve">vt, FG, ad, T, (quia vt, AB, ad,
              <lb/>
              <note position="left" xlink:label="note-0166-01" xlink:href="note-0166-01a" xml:space="preserve">Ex Corol.
                <lb/>
              2. antec.</note>
            CD, ita eſt, FG, ad, HM,) .</s>
            <s xml:id="echoid-s3458" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3459" xml:space="preserve">vt ſolidum, FOGP, ad, HNM
              <lb/>
            Q, quod eſt propoſitum.</s>
            <s xml:id="echoid-s3460" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3461" xml:space="preserve">Sit nunc ſolidum, AXB, ad ſibi ſimile, CVD, vt, FOGP, ad
              <lb/>
              <figure xlink:label="fig-0166-01" xlink:href="fig-0166-01a" number="95">
                <image file="0166-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0166-01"/>
              </figure>
            ſibi ſimile, HNMQ, & </s>
            <s xml:id="echoid-s3462" xml:space="preserve">ſint ea-
              <lb/>
            dem deſcribentes, AB, CD, li-
              <lb/>
            neæ, vel latera homologa figura-
              <lb/>
            rum homologarum, AEBY, C
              <lb/>
            KD ℟, &</s>
            <s xml:id="echoid-s3463" xml:space="preserve">, FG, HM, duo po
              <lb/>
            ſtrema deſcribentes ſint lineæ, vel
              <lb/>
            latera homologa figurarum ho-
              <lb/>
            mologarum, FGP, HMQ. </s>
            <s xml:id="echoid-s3464" xml:space="preserve">Di-
              <lb/>
            co has eſſe proportionales; </s>
            <s xml:id="echoid-s3465" xml:space="preserve">ſint
              <lb/>
            adhuc duarum, AB, CD, tertia
              <lb/>
            proportionalis, R, quarta, S, & </s>
            <s xml:id="echoid-s3466" xml:space="preserve">
              <lb/>
            duarum, FG, HM, tertia, I,
              <lb/>
            quarta, T, quia ergo ſolida, AX
              <lb/>
            B, CVD, ſunt ſimilia erit, AXB, ad, CVD, vt, AB, ad, S, &</s>
            <s xml:id="echoid-s3467" xml:space="preserve">,
              <lb/>
              <note position="left" xlink:label="note-0166-02" xlink:href="note-0166-02a" xml:space="preserve">Ex Corol.
                <lb/>
              2. antec.</note>
            FOGP, ad, HNMP, vt, FG, ad, T, ſunt autem hæc quatuor
              <lb/>
            ſolida proportionalia, ergo &</s>
            <s xml:id="echoid-s3468" xml:space="preserve">, AB, ad, S, erit vt, FG, ad, T, er-
              <lb/>
            go, AB, ad, CD, erit vt, FG, ad, HM, quod oſtendendum erat.</s>
            <s xml:id="echoid-s3469" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div359" type="section" level="1" n="219">
          <head xml:id="echoid-head234" xml:space="preserve">THE OREMA XIX. PROPOS. XIX.</head>
          <p>
            <s xml:id="echoid-s3470" xml:space="preserve">SI in parallelogrammo diameter ducta fuerit, parallelo-
              <lb/>
            grammum duplum eſt cuiuſuis triangulorum per ipſam
              <lb/>
            diametrum conſtitutorum.</s>
            <s xml:id="echoid-s3471" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3472" xml:space="preserve">Sit parallelogrammum vtcunque, AD, in
              <lb/>
              <figure xlink:label="fig-0166-02" xlink:href="fig-0166-02a" number="96">
                <image file="0166-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0166-02"/>
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            quo ducta diameter, FC, ipſum diuidat in tri-
              <lb/>
            angula, FAC, CDF. </s>
            <s xml:id="echoid-s3473" xml:space="preserve">Dico parallelogram-
              <lb/>
            mum, AD, duplum eſſe cuiuſuis triangulo-
              <lb/>
            rum, FAC, CDF; </s>
            <s xml:id="echoid-s3474" xml:space="preserve">abſcindanturab, FD, C
              <lb/>
            A, verſus puncta, F, C, partes æquales, FE,
              <lb/>
            CB, & </s>
            <s xml:id="echoid-s3475" xml:space="preserve">per puncta, B, E, parallelæ ipſi baſi,
              <lb/>
            CD, ducantur, EH, BM, incidentes diame-
              <lb/>
            tro, FC, in punctis, H, M; </s>
            <s xml:id="echoid-s3476" xml:space="preserve">quoniam ergo in triangulis, FHE, </s>
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