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

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              <pb o="66" file="0086" n="86" rhead="GEOMETRIÆ"/>
            ad, PI, vt, dY, ad, dX, ergo ex æquali, KP, ad, PI, erit vt, u
              <lb/>
            d, ad, dX, eſt autem, PI, ad, IK, vt, dX, ad, Xu, ergo trian-
              <lb/>
            gula quoque, PKI, duX, pariter ſimilia erunt, vnde anguli, LP
              <lb/>
            I, YdX; </s>
            <s xml:id="echoid-s1706" xml:space="preserve">PIK, dXu, &</s>
            <s xml:id="echoid-s1707" xml:space="preserve">, IKL, XuY, æquales erunt. </s>
            <s xml:id="echoid-s1708" xml:space="preserve">Ducantur
              <lb/>
            nunc in planis figurarum, LHMP, YVZd, à punctis, L, Y, pa-
              <lb/>
              <figure xlink:label="fig-0086-01" xlink:href="fig-0086-01a" number="45">
                <image file="0086-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0086-01"/>
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            rallelæ, KN, ug, ipſæ, L3,
              <lb/>
            Y4. </s>
            <s xml:id="echoid-s1709" xml:space="preserve">Cum igitur anguli, LK
              <lb/>
            I, YuX, ſint ęquales, etiam,
              <lb/>
            KL3, uY4, æquales erunt,
              <lb/>
              <note position="left" xlink:label="note-0086-01" xlink:href="note-0086-01a" xml:space="preserve">Corol. 27
                <lb/>
              huius.</note>
            ſed &</s>
            <s xml:id="echoid-s1710" xml:space="preserve">, KLP, uYd, ſuntæ-
              <lb/>
            quales, ergo reſidui quoque, 3
              <lb/>
            LP, 4Yd, erunt ęquales, vn-
              <lb/>
            de cum ipſæ, L3, Y4, con-
              <lb/>
            tineant cum lateribus homo-
              <lb/>
            logis, LP, Yd, ad eandem
              <lb/>
            partem angulos æquales, e-
              <lb/>
            runt regulę homologarum ſi-
              <lb/>
            milium figurarum, LHMP,
              <lb/>
            YVZd, vnde etiam ipſæ, K
              <lb/>
            N, ug, velipſæ OS, fp, e-
              <lb/>
            runt regulæ homologarum
              <lb/>
            earundem, ſunt. </s>
            <s xml:id="echoid-s1711" xml:space="preserve">n. </s>
            <s xml:id="echoid-s1712" xml:space="preserve">OS, KN,
              <lb/>
            parallelæ, vt etiam, ug, fp,
              <lb/>
            vnde omnes homologæ ſimi-
              <lb/>
            lium figurarum, LHMP, Y
              <lb/>
            VZd, ipſis regulis, OS, fp,
              <lb/>
            æquidiſtabunt, quod & </s>
            <s xml:id="echoid-s1713" xml:space="preserve">de cę-
              <lb/>
            teris eodem modo oſtende-
              <lb/>
            tur, dumſectio fiet in figuris,
              <lb/>
            AESo, Tlps. </s>
            <s xml:id="echoid-s1714" xml:space="preserve">Quod ſi fi-
              <lb/>
            guris, AESO, Tlps, aliæ
              <lb/>
            figuræ planæ continuarentur
              <lb/>
            citra cõtactum planorum ba-
              <lb/>
            ſibus oppoſitorum, cum his
              <lb/>
            in lateribus homologis, AE,
              <lb/>
            Tl, conuenientes, quibus eſ-
              <lb/>
            ſent inclinatę, parum diſſimili
              <lb/>
            methodo, producentes, OB,
              <lb/>
            fQ, vſq; </s>
            <s xml:id="echoid-s1715" xml:space="preserve">ad tangentia plana, & </s>
            <s xml:id="echoid-s1716" xml:space="preserve">occurſuum puncta cum ipſis, S, p,
              <lb/>
            iungentes, necnon extrema laterum homologorum, qualia fuerunt,
              <lb/>
            LP, Yd, cum extremis rectarum in triangulis (qualia fuerunt, BO
              <lb/>
            S, Qfp,) productarum, panter iungentes, vt fecimus cum ipſis, </s>
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