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

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            <s xml:id="echoid-s966" xml:space="preserve">
              <pb o="36" file="0056" n="56" rhead="GEOMETRIÆ"/>
            planumper, VK, XN, ductum in recta, KN, rurſus diuidatur, H
              <lb/>
            P, vtcumq; </s>
            <s xml:id="echoid-s967" xml:space="preserve">in puncto, G, à quo ducatur ipſi, SP, parallela, GD,
              <lb/>
            ſecans baſis ambitum in punctis, F, E, C, D, deinde extendatur
              <lb/>
            planum per, A, verticem, & </s>
            <s xml:id="echoid-s968" xml:space="preserve">rectam, DG, quod per conici latera
              <lb/>
              <note position="left" xlink:label="note-0056-01" xlink:href="note-0056-01a" xml:space="preserve">16. Huius.</note>
            tranſibit, & </s>
            <s xml:id="echoid-s969" xml:space="preserve">producet triangula ſiueintus, ſiue extra conicum, quæ
              <lb/>
            ſint, ADC, ACE, AEF, AFG, ſecabitque figuram, VBO, ſe-
              <lb/>
            cet eius productum planum in recta, BM, quæ ambitum eiuſdem,
              <lb/>
            VBO, diuidat in punctis, B, R, I, O, habebimus etiam triangula,
              <lb/>
            ABR, ARI, AIO, AOM, quorum latera erunt portiones late-
              <lb/>
            rum inferiorum triangulorum, per planum autem, ADG, ſiue per
              <lb/>
            rectam, AG, ſit ſecta, KN, in puncto, M. </s>
            <s xml:id="echoid-s970" xml:space="preserve">Quia ergo plana, quę
              <lb/>
              <figure xlink:label="fig-0056-01" xlink:href="fig-0056-01a" number="28">
                <image file="0056-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0056-01"/>
              </figure>
            per rectas, VK, XN, & </s>
            <s xml:id="echoid-s971" xml:space="preserve">
              <lb/>
            per, TH, SP, tranſeunt
              <lb/>
            ſunt parallela, & </s>
            <s xml:id="echoid-s972" xml:space="preserve">ſecan-
              <lb/>
            tur à plano, APH, com-
              <lb/>
              <note position="left" xlink:label="note-0056-02" xlink:href="note-0056-02a" xml:space="preserve">10. Vnde-
                <lb/>
              cimi El.</note>
            munes eorum ſectionese-
              <lb/>
            runt parallelę.</s>
            <s xml:id="echoid-s973" xml:space="preserve">ſ.</s>
            <s xml:id="echoid-s974" xml:space="preserve">KN, ipſi,
              <lb/>
            HP, igitur triangulus, A
              <lb/>
            MN, æquiangulus erit
              <lb/>
            triangulo, AGP, & </s>
            <s xml:id="echoid-s975" xml:space="preserve">ideo
              <lb/>
            circa æquales angulos e-
              <lb/>
              <note position="left" xlink:label="note-0056-03" xlink:href="note-0056-03a" xml:space="preserve">4. Sexti
                <lb/>
              Elem.</note>
            runt latera proportiona-
              <lb/>
            lia, ergo vt, PG, ad, G
              <lb/>
            A, ſic erit, NM, ad, M
              <lb/>
            A, eodem modo oſtende-
              <lb/>
            mus, vt, AG, ad, GH, ita eſſe, AM, ad, MK, ergo ex æquali
              <lb/>
            PG, ad, GH, erit vt, NM, ad, MK, ſunt igitur, PH, NK, ſi-
              <lb/>
            militer ad eandem partem diuiſæ in punctis, M, G: </s>
            <s xml:id="echoid-s976" xml:space="preserve">Eodem modo
              <lb/>
            oſtendemus triangulum, AMO, eſſe ęquiangulum ipſi, AGF, &</s>
            <s xml:id="echoid-s977" xml:space="preserve">,
              <lb/>
            AMI, ipſi, AGE, &</s>
            <s xml:id="echoid-s978" xml:space="preserve">, AMR, ipſi, AGC, & </s>
            <s xml:id="echoid-s979" xml:space="preserve">tandem, AMB,
              <lb/>
            ipſi, AGD, igitur, vt, GA, ad, AM, ſic erit, permutando, FG,
              <lb/>
            ad, OM, vt verò, GA, ad, AM, ſic permutando eſt, PG, ad,
              <lb/>
            NM, ideſt, PH, ad, NK, ergo, FG, ad, OM, eſt vt, PH, ad,
              <lb/>
            NK, ſimiliter oſtendemus, EG, ad, IM, &</s>
            <s xml:id="echoid-s980" xml:space="preserve">, CG, ad, RM, & </s>
            <s xml:id="echoid-s981" xml:space="preserve">
              <lb/>
            tandem, DG, ad, BM, eſſe vt, PH, ad, NK, & </s>
            <s xml:id="echoid-s982" xml:space="preserve">quia, KN, eſt
              <lb/>
            parallela ipſi, HP, &</s>
            <s xml:id="echoid-s983" xml:space="preserve">, NX, ipſi, PS, ideò angulus, KNX, eſt
              <lb/>
              <note position="left" xlink:label="note-0056-04" xlink:href="note-0056-04a" xml:space="preserve">10. Vnde-
                <lb/>
              Fimi El.</note>
            æqualis angulo, HPS; </s>
            <s xml:id="echoid-s984" xml:space="preserve">habemus igitur duas figuras planas, VBO,
              <lb/>
            TDF, quarum ductæ ſunt oppoſitæ tangentes, VK, XN, vnius,
              <lb/>
            &</s>
            <s xml:id="echoid-s985" xml:space="preserve">, TH, SP, alterius, inuenimus autem rectas, KN, HP, inter
              <lb/>
            eaſdem poſitas, cum eis ad eandem partem angulos æquales conti-
              <lb/>
            nentes, ita ſe habere, vt ductis duabus vtcumque ipſis tangentibus
              <lb/>
            parallelis, quæ diuidant ipſas ſimiliter ad eandem partem, </s>
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