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

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        <div xml:id="echoid-div218" type="section" level="1" n="141">
          <p style="it">
            <s xml:id="echoid-s2219" xml:space="preserve">
              <pb o="90" file="0110" n="110" rhead="GEOMETRI Æ"/>
            byperbolam hic babentur, circa ſectiones oppoſitas, quirum communes
              <lb/>
            ſunt dictæ paſſiones, quoq; </s>
            <s xml:id="echoid-s2220" xml:space="preserve">intelligi poſſe. </s>
            <s xml:id="echoid-s2221" xml:space="preserve">Eadem verò nedum in dictis
              <lb/>
            integris ſolidis, ſed etiam in eorum portionibus, ſiue in portionibus ſe-
              <lb/>
            ctionum coni abſciſſis per line as ad earum axim, vel diametrum ordina-
              <lb/>
            tim ductas, pariter verificari manifeſtum eſt.</s>
            <s xml:id="echoid-s2222" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div219" type="section" level="1" n="142">
          <head xml:id="echoid-head153" xml:space="preserve">LEMMA.</head>
          <p>
            <s xml:id="echoid-s2223" xml:space="preserve">PRopoſitis duabus quibuſcumq; </s>
            <s xml:id="echoid-s2224" xml:space="preserve">ſimilibus figuris, duæ quæuis re-
              <lb/>
            ctæ lineæ earum homologę poterunt eſſe incidentes, vel in ipſis
              <lb/>
            productis reperientur ſaltem earum incidentes, & </s>
            <s xml:id="echoid-s2225" xml:space="preserve">oppoſitarum tan-
              <lb/>
            gentium, quibus ipſæ incidunt ad eundem angulum ex eadem parte,
              <lb/>
            erunt autem dictæ homologæ ſemper inuentarum incidentium par-
              <lb/>
            tes proportionales.</s>
            <s xml:id="echoid-s2226" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2227" xml:space="preserve">Sint duæ quæcunq; </s>
            <s xml:id="echoid-s2228" xml:space="preserve">ſimiles figuræ planæ, IQsP, 487R, in eiſ-
              <lb/>
            que duæ quælibet homologę, Is, 47. </s>
            <s xml:id="echoid-s2229" xml:space="preserve">Dico has eſſe vel incidentes,
              <lb/>
            vel in eiſdem productis reperiri poſſe incidentes prædictarum figura-
              <lb/>
            rum, & </s>
            <s xml:id="echoid-s2230" xml:space="preserve">oppoſitarum tangentium, quibus occurrant ipſæ homolo-
              <lb/>
            gæ, productæ, ad eundem angulum ex eadem parte, quales ſint, D
              <lb/>
            L, dO; </s>
            <s xml:id="echoid-s2231" xml:space="preserve">pu, g Y. </s>
            <s xml:id="echoid-s2232" xml:space="preserve">Ducantur autem vlterius oppoſitę tangentes, quę
              <lb/>
              <figure xlink:label="fig-0110-01" xlink:href="fig-0110-01a" number="62">
                <image file="0110-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0110-01"/>
              </figure>
            ſunt regulæ homologarum,
              <lb/>
            ls, 47, ipſæ, Ad, Co; </s>
            <s xml:id="echoid-s2233" xml:space="preserve">F
              <lb/>
            g, KZ, quarum, & </s>
            <s xml:id="echoid-s2234" xml:space="preserve">dicta-
              <lb/>
              <note position="left" xlink:label="note-0110-01" xlink:href="note-0110-01a" xml:space="preserve">Corol. 19.
                <lb/>
              & p. 24.</note>
            rum figurarum incidentes
              <lb/>
            ſint, AC, FK, parallelæ
              <lb/>
              <note position="left" xlink:label="note-0110-02" xlink:href="note-0110-02a" xml:space="preserve">23. huius.</note>
            ipſis, DL, pu, hoc .</s>
            <s xml:id="echoid-s2235" xml:space="preserve">n. </s>
            <s xml:id="echoid-s2236" xml:space="preserve">fieri
              <lb/>
              <note position="left" xlink:label="note-0110-03" xlink:href="note-0110-03a" xml:space="preserve">Coroll.
                <lb/>
              2. 19. & p.
                <lb/>
              24.</note>
            poteſt; </s>
            <s xml:id="echoid-s2237" xml:space="preserve">erunt autem etiam
              <lb/>
            ipſæ, d O, g Y, regulæ ho-
              <lb/>
            mologarum, cum faciant
              <lb/>
            angulos æquales cum regu-
              <lb/>
            lis, dA, gF, vt ſuppono,
              <lb/>
            & </s>
            <s xml:id="echoid-s2238" xml:space="preserve">inueniri poterunt earum,
              <lb/>
            & </s>
            <s xml:id="echoid-s2239" xml:space="preserve">dictarum figurarum inci-
              <lb/>
            dentes parallelæ eiſdem, A
              <lb/>
            d, Fg, ſint ipſę, LO, uY,
              <lb/>
            tales incidentes: </s>
            <s xml:id="echoid-s2240" xml:space="preserve">Vel ergo
              <lb/>
            homologæ datæ, ls, 47,
              <lb/>
            terminantur ad oppofitas
              <lb/>
            tangentes, DL, dO; </s>
            <s xml:id="echoid-s2241" xml:space="preserve">pu,
              <lb/>
            gY, velnon, & </s>
            <s xml:id="echoid-s2242" xml:space="preserve">tunc producantur, & </s>
            <s xml:id="echoid-s2243" xml:space="preserve">ipſis incidant in punctis, E,
              <lb/>
            f; </s>
            <s xml:id="echoid-s2244" xml:space="preserve">℟, &</s>
            <s xml:id="echoid-s2245" xml:space="preserve">, & </s>
            <s xml:id="echoid-s2246" xml:space="preserve">vlterius productæ vſque ad, AC, FK, ſecent ipſas in
              <lb/>
            punctis, B, G. </s>
            <s xml:id="echoid-s2247" xml:space="preserve">Vlterius vel, Ho, XZ, tangunt ſetotis, vel </s>
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