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

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          <p>
            <s xml:id="echoid-s1150" xml:space="preserve">
              <pb o="44" file="0064" n="64" rhead="GEOMETRIÆ"/>
            cuitum figurarum eodem ordine ſumptas, ita ſe habere, ve-
              <lb/>
            lut illæ, quæ dictis tangentibus inciderunt, iſtæ, quæ illis
              <lb/>
            inciderunt, erunt tum ſimilium propoſitarum figurarum, tum
              <lb/>
            ductarum tangentium, incidentes.</s>
            <s xml:id="echoid-s1151" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1152" xml:space="preserve">Sint duę quęcumq; </s>
            <s xml:id="echoid-s1153" xml:space="preserve">ſimiles planę figurę, ACEI, MTVS, qua-
              <lb/>
            rum ſint ductæ oppoſitæ tangentes homologarum earundem regu-
              <lb/>
            læ, AB, EF, figuræ, AE, &</s>
            <s xml:id="echoid-s1154" xml:space="preserve">, MN, VR, figurę, MV, incidant
              <lb/>
            autem eiſdem ad eundem angulum ex eadem parte duæ, BF, NR,
              <lb/>
            & </s>
            <s xml:id="echoid-s1155" xml:space="preserve">ductæ ſint quædam duæ ipſis tangentibus parallelæ, CD, TO,
              <lb/>
            ſecantes ipſas, BF, NR, (& </s>
            <s xml:id="echoid-s1156" xml:space="preserve">coniequenter incidentes, vt facilè
              <lb/>
            patet) ſimiliter ad eandem partem, reperiamus, CD, ad, TO, & </s>
            <s xml:id="echoid-s1157" xml:space="preserve">
              <lb/>
            pariter, ID, ad, SO, eſſe vt, BF, ad, NR. </s>
            <s xml:id="echoid-s1158" xml:space="preserve">Dico ipſas, BF, N
              <lb/>
            R, eſſe incidentes ſimilium figurarum, AE, MV, & </s>
            <s xml:id="echoid-s1159" xml:space="preserve">ductarum op-
              <lb/>
              <figure xlink:label="fig-0064-01" xlink:href="fig-0064-01a" number="32">
                <image file="0064-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0064-01"/>
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            poſitarum tangentium, VR, MN;
              <lb/>
            </s>
            <s xml:id="echoid-s1160" xml:space="preserve">EF, AB. </s>
            <s xml:id="echoid-s1161" xml:space="preserve">Ex dictis igitur ipſę, CI, T
              <lb/>
              <note position="left" xlink:label="note-0064-01" xlink:href="note-0064-01a" xml:space="preserve">C. 10. defi.
                <lb/>
              mitionis.</note>
            S, erunt homologę earundem ſimilium
              <lb/>
            figurarum, AE, MV, & </s>
            <s xml:id="echoid-s1162" xml:space="preserve">quia, CD,
              <lb/>
              <note position="left" xlink:label="note-0064-02" xlink:href="note-0064-02a" xml:space="preserve">Ex cor. 2.
                <lb/>
              19. & 22.
                <lb/>
              huius.</note>
            ad, TO, eſt vt, BF, ad, NR, &</s>
            <s xml:id="echoid-s1163" xml:space="preserve">, B
              <lb/>
            F, ad, NR, vt, ID, ad, SO, erit, C
              <lb/>
            D, ad, TO, vt, ID, ad, SO, igitur
              <lb/>
            puncta, D, O, reperientur in duabus
              <lb/>
            dictarum fimilium figurarum, & </s>
            <s xml:id="echoid-s1164" xml:space="preserve">op-
              <lb/>
            poſitarum tangentium, incidentibus,
              <lb/>
            ſint illæ ipſæ, HG, PL, quę cum ip-
              <lb/>
            ſis, TO, CD, æquales angulos ad
              <lb/>
            eandem partem continebunt. </s>
            <s xml:id="echoid-s1165" xml:space="preserve">Dico ta-
              <lb/>
            men etiam ipſas, NR, BF, eſſe ea-
              <lb/>
            rundem figurarum, & </s>
            <s xml:id="echoid-s1166" xml:space="preserve">tangentium, in-
              <lb/>
            cidentes: </s>
            <s xml:id="echoid-s1167" xml:space="preserve">Sint puncta contactus tangentium, FE, RV, proxima ip-
              <lb/>
            ſis, NR, BF, ipſa, V, E. </s>
            <s xml:id="echoid-s1168" xml:space="preserve">Dico, EF, ad, VR, eſſe vt, FB, ad,
              <lb/>
              <note position="left" xlink:label="note-0064-03" xlink:href="note-0064-03a" xml:space="preserve">3. Defin.
                <lb/>
              10.</note>
            RN, nam, EL, ad, VG, eſt vt, LP, ad, GH, quia verò angu-
              <lb/>
            lus, CDP, æquatur angulo, TOH, &</s>
            <s xml:id="echoid-s1169" xml:space="preserve">, CDB, ipſi, TON, re-
              <lb/>
            liquus, PDB, ęquabitur reliquo, HON, & </s>
            <s xml:id="echoid-s1170" xml:space="preserve">ſic etiam, FDL, ipſi,
              <lb/>
            ROG, eſt etiam angulus, PLE, ęqualis angulo, HGV, ideò re-
              <lb/>
              <note position="left" xlink:label="note-0064-04" xlink:href="note-0064-04a" xml:space="preserve">4. Sexti
                <lb/>
              Elem.</note>
            liquus in triangulo, DFL, ideſt angulus, DFL, erit ęqualis angu-
              <lb/>
            lo, ORG, & </s>
            <s xml:id="echoid-s1171" xml:space="preserve">ſic triangula, FDL, ORG, erunt æquiangula, vt
              <lb/>
            etiam probabimus triangula, DPB, OHN, eſſe ęquiangula, ſicut
              <lb/>
            ſunt ęquiangula inter ſetriangula, FDL, PDB, &</s>
            <s xml:id="echoid-s1172" xml:space="preserve">, ROG, HO
              <lb/>
            N, vnde vt, LD, ad, DF, ſic erit, PD, ad, DB, permutando,
              <lb/>
            LD, ad, DP, erit vt, FD, ad, DB, componendo, LP, ad, PD,
              <lb/>
            erit vt, FB, ad, BD, permutando, LP, ad, FB, erit vt, PD, </s>
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