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

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            <s xml:id="echoid-s1093" xml:space="preserve">
              <pb o="41" file="0061" n="61" rhead="LIBERI."/>
            vt incidentes) ynde etiam figuræ eſſent æquales, & </s>
            <s xml:id="echoid-s1094" xml:space="preserve">ſi minores, etiam
              <lb/>
            ipſa figura, TDF, eſſet minor figura, BVO, contra ſuppoſitum,
              <lb/>
            eſtigitur, DC, maior ipſa, BR, eſt autem, vt, DC, ad, BR, ita,
              <lb/>
            PH, ad, NK, nam vt, DG, ad, BM, itaeſt, PH, ad, NK, & </s>
            <s xml:id="echoid-s1095" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0061-01" xlink:href="note-0061-01a" xml:space="preserve">A. Defin.
                <lb/>
              10.</note>
            etiamita, CG, ad, RM, ergo reliqua, DC, ad reliquam, BR,
              <lb/>
            erit vt, PH, ad, NK, ſic etiam eſſe oſtendemus, EF, ad, IO, vt,
              <lb/>
            PH, ad, NK, & </s>
            <s xml:id="echoid-s1096" xml:space="preserve">quia, DC, eſt maior ipſa, BR, vel, EF, ipſa,
              <lb/>
            IO, ideò, HP, erit maior, KN, ſi igitur iunxerimus puncta, PN,
              <lb/>
            HK, ipſæ, PN, HK, ſi producantur ad partes ipſius, NK, con-
              <lb/>
            current, vt in, A. </s>
            <s xml:id="echoid-s1097" xml:space="preserve">Dico, A, eſſe verticem conici, cuius eſt baſis ipſa,
              <lb/>
              <figure xlink:label="fig-0061-01" xlink:href="fig-0061-01a" number="30">
                <image file="0061-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0061-01"/>
              </figure>
            TDF, & </s>
            <s xml:id="echoid-s1098" xml:space="preserve">explano ipſi,
              <lb/>
            TDF, ęquidiſtanter du-
              <lb/>
            cto eſt in ipſo concepta
              <lb/>
            figura, VBO. </s>
            <s xml:id="echoid-s1099" xml:space="preserve">Quia er-
              <lb/>
              <note position="right" xlink:label="note-0061-02" xlink:href="note-0061-02a" xml:space="preserve">4. Sexti
                <lb/>
              Elem.</note>
            go, NK, eſt parallela
              <lb/>
            ipſi, PH, erunt triangu-
              <lb/>
            la, ANK, APH, ęqui-
              <lb/>
            angula, & </s>
            <s xml:id="echoid-s1100" xml:space="preserve">circa æquales
              <lb/>
            angulos latera propor-
              <lb/>
            tionalia, igitur, HP, ad,
              <lb/>
            PA, erit vt, KN, ad, N
              <lb/>
            A, &</s>
            <s xml:id="echoid-s1101" xml:space="preserve">, permutando, H
              <lb/>
            P, ad, NK, erit vt, PA,
              <lb/>
            ad, AN, vt autem, PH,
              <lb/>
            ad, NK, ita eſt, PG, ad, NM, nam ipſa, HP, KN, ſimiliter
              <lb/>
            ſunt diuiſæ in punctis, G, M, ergo, PA, ad, AN, erit vt, PG,
              <lb/>
            ad, NM, & </s>
            <s xml:id="echoid-s1102" xml:space="preserve">ſunt parallelæ ipſæ, PG, NM, ergo puncta, G, M,
              <lb/>
            A, erunt in vna recta linea, ſit illa, AG, igitur, vt, PG, ad, NM,
              <lb/>
              <note position="right" xlink:label="note-0061-03" xlink:href="note-0061-03a" xml:space="preserve">Ex Lem-
                <lb/>
              mate leq.</note>
            vel, PH, ad, NK, ita erit, GA, ad, AM, eſt autem, PH, ad,
              <lb/>
            NK, vt, FG, ad, OM, & </s>
            <s xml:id="echoid-s1103" xml:space="preserve">vt, EG, ad, IM, & </s>
            <s xml:id="echoid-s1104" xml:space="preserve">tandem, vt, D
              <lb/>
            G, ad, BM, ergo, vt, GA, ad, AM, ita erit, FG, ad, OM; </s>
            <s xml:id="echoid-s1105" xml:space="preserve">E
              <lb/>
            G, ad, IM; </s>
            <s xml:id="echoid-s1106" xml:space="preserve">CG, ad, RM; </s>
            <s xml:id="echoid-s1107" xml:space="preserve">&</s>
            <s xml:id="echoid-s1108" xml:space="preserve">, DG, ad, BM, ergo, cum ſint
              <lb/>
            parallelæ, erunt tum puncta, AOF, tum, AIE, ARC, tum etiam,
              <lb/>
            ABD, in vna recta linea, extendantur ergo dictæ rectæ lineæ, quę
              <lb/>
              <note position="right" xlink:label="note-0061-04" xlink:href="note-0061-04a" xml:space="preserve">Ex Lem-
                <lb/>
              mate leq.</note>
            erunt, AF, AE, AD, AC. </s>
            <s xml:id="echoid-s1109" xml:space="preserve">Eodem modo, ſi per duas quaslibet
              <lb/>
            homologas figurarum, VBO, TDF, planum extendamus, fiet in
              <lb/>
            cæteris demonſtratio; </s>
            <s xml:id="echoid-s1110" xml:space="preserve">igitur ſi ſumantur in ambitu figurę, TDF,
              <lb/>
            quęcumq; </s>
            <s xml:id="echoid-s1111" xml:space="preserve">puncta, quę iungantur cum puncto, A, ſemper iungen-
              <lb/>
            tes tranſibunt per circuitum figuræ, VBO, ergo figurę, TDF, &</s>
            <s xml:id="echoid-s1112" xml:space="preserve">,
              <lb/>
            VBO, erunt fruſti conici oppoſitę baſes, quod à conico, ATDF,
              <lb/>
              <note position="right" xlink:label="note-0061-05" xlink:href="note-0061-05a" xml:space="preserve">Defin. 4.</note>
            abſcinditur per figuram, VBO, quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1113" xml:space="preserve"/>
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