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

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          <p>
            <s xml:id="echoid-s6320" xml:space="preserve">
              <pb o="253" file="0273" n="273" rhead="LIBER III."/>
            homologa ſunt æqualia, ergo etiam, BC, æquabitur ipſi, FM, &</s>
            <s xml:id="echoid-s6321" xml:space="preserve">,
              <lb/>
            CG, ipſi, DF, eſt autem, AC, æqualis ipſi, FR, &</s>
            <s xml:id="echoid-s6322" xml:space="preserve">, AF, ipſi, C
              <lb/>
            R, ergo reliqua, AB, æquabitur reliquæ, MR, & </s>
            <s xml:id="echoid-s6323" xml:space="preserve">reliqua, AD, re-
              <lb/>
            liquæ, GR; </s>
            <s xml:id="echoid-s6324" xml:space="preserve">ſuntigitur portiones laterum parallelogrammi, AR,
              <lb/>
            coalterne tangentes inter ſe æquales.</s>
            <s xml:id="echoid-s6325" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6326" xml:space="preserve">Sumantur nunc vtcunque duæ coalternè tangentes, AD, RG,
              <lb/>
            & </s>
            <s xml:id="echoid-s6327" xml:space="preserve">ab ipſis verſus puncta contactuum, DG, abſcindantur vtcunque
              <lb/>
            duæ rectæ æquales, PD, VG, & </s>
            <s xml:id="echoid-s6328" xml:space="preserve">per puncta, PV, ducantur baſi,
              <lb/>
            FR, parallelæ, PQ, EV, ſecantes curuam ellipſis in punctis, HI,
              <lb/>
            ipſa, PQ, & </s>
            <s xml:id="echoid-s6329" xml:space="preserve">in punctis, NO, ipſa, EV. </s>
            <s xml:id="echoid-s6330" xml:space="preserve">Quoniam ergo, AB, A
              <lb/>
            D, tangunt ellipſim, BDMG, coincidentes in puncto, A, eſt au-
              <lb/>
            tem, QP, parallela vni tangentium. </s>
            <s xml:id="echoid-s6331" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6332" xml:space="preserve">ipſi, AB, ſecans curuam el-
              <lb/>
            lipſis in, H, & </s>
            <s xml:id="echoid-s6333" xml:space="preserve">aliam tangentem in, P, rectangulum ergo, IPH, ad
              <lb/>
              <note position="right" xlink:label="note-0273-01" xlink:href="note-0273-01a" xml:space="preserve">16. 3. Con.</note>
            quadratum, PD, erit vt quadratum, BA, ad quadratum, AD,. </s>
            <s xml:id="echoid-s6334" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s6335" xml:space="preserve">vt quadratum, MR, ad quadratum, RG: </s>
            <s xml:id="echoid-s6336" xml:space="preserve">conſimili modo oſtende-
              <lb/>
            mus rectangulum, NVO, ad quadratum, VG, eſſe vt quadratum,
              <lb/>
            MR, ad quadratum, RG, . </s>
            <s xml:id="echoid-s6337" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6338" xml:space="preserve">vt rectangulum, IPH, ad quadratum,
              <lb/>
            PD, vel ad quadratum, VG, ergo rectangulum, IPH, eſt æquale
              <lb/>
            rectangulo, NVO. </s>
            <s xml:id="echoid-s6339" xml:space="preserve">Nunc oſtendemus, PH, eſſe æqualem ipſi, O
              <lb/>
            V, conſideremus duo quadrilatera, APXB, MTVR, quæ ſunt ſi-
              <lb/>
            milia polygona, nam angulus, PAB, eſt æqualis angulo, MRV,
              <lb/>
            &</s>
            <s xml:id="echoid-s6340" xml:space="preserve">, ABX, ipſi, RMT, tum, BXP, ipſi, MTV, & </s>
            <s xml:id="echoid-s6341" xml:space="preserve">tandem, XP
              <lb/>
            A, ipſi, TVR, quę facilè apparent, & </s>
            <s xml:id="echoid-s6342" xml:space="preserve">duo latera, AB, MR, ſunt
              <lb/>
            æqualia, vt etiam, AP, RV, ergo reliqua latera erunt æqualia, quę
              <lb/>
            æqualibus adiacent angulis, vnde, TV, erit æqualis ipſi, PX, &</s>
            <s xml:id="echoid-s6343" xml:space="preserve">,
              <lb/>
            MT, ipſi, BX, vnde rectangulum, MTB, æquabitur rectangulo,
              <lb/>
            MXB, & </s>
            <s xml:id="echoid-s6344" xml:space="preserve">quoniam, vt rectangulum, MTB, ad rectangulum, M
              <lb/>
              <note position="right" xlink:label="note-0273-02" xlink:href="note-0273-02a" xml:space="preserve">Ex 40, 1.
                <lb/>
              lib. & eiu.
                <lb/>
              ldẽ Scho-
                <lb/>
              lio.</note>
            XB, ita quadratum, TO, ad quadratum, XI, quoniam, NO, H
              <lb/>
            I, ſunt parallelæ tangenti, AC, & </s>
            <s xml:id="echoid-s6345" xml:space="preserve">ideò ordinatim applicatę ad dia
              <lb/>
            metrum, BM, erit ergo quadratum, TO, æquale quadrato, XI,
              <lb/>
            &</s>
            <s xml:id="echoid-s6346" xml:space="preserve">, TO, ipſi, XI, vel, HX, ergo reliqua, OV, erit æqualis reli-
              <lb/>
            quæ, PH, & </s>
            <s xml:id="echoid-s6347" xml:space="preserve">quia rectangulum, IPH, eſt æquale rectangulo, N
              <lb/>
            VO, erit, IP, æqualis ipſi, NV, & </s>
            <s xml:id="echoid-s6348" xml:space="preserve">quia, PH, eſt æ qualis, OV,
              <lb/>
            erit, HI, æqualis, NO, & </s>
            <s xml:id="echoid-s6349" xml:space="preserve">ideò rectangulum, IHP, erit æquale re-
              <lb/>
            ctangulo, NOV.</s>
            <s xml:id="echoid-s6350" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6351" xml:space="preserve">Vel breuius ſic proceſſiſſet demonſtratio, dimiſſo Apollonij theo-
              <lb/>
            remate, oſtenſo. </s>
            <s xml:id="echoid-s6352" xml:space="preserve">n. </s>
            <s xml:id="echoid-s6353" xml:space="preserve">OV, eſſe æqualem ipſi, PH, &</s>
            <s xml:id="echoid-s6354" xml:space="preserve">, TO, ipſi, XI,
              <lb/>
            manet oſtenſum, NO, æquari ipſi, HI, quoniam, NO, HI, bi-
              <lb/>
            faria diuiduntur a diametro, BM, & </s>
            <s xml:id="echoid-s6355" xml:space="preserve">ideo illicò manifeſtum euadit
              <lb/>
            rectangulum, NOV, æquari rectangulo, IHP, quod oſtendere
              <lb/>
            oportebat.</s>
            <s xml:id="echoid-s6356" xml:space="preserve"/>
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