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

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            <s xml:id="echoid-s1762" xml:space="preserve">
              <pb o="69" file="0089" n="89" rhead="LIBER I."/>
            incidentes, ac oppoſitarum tangentium, HK, MN, Vu, Zg, ip-
              <lb/>
            ſas, KN, ug, ſi. </s>
            <s xml:id="echoid-s1763" xml:space="preserve">n. </s>
            <s xml:id="echoid-s1764" xml:space="preserve">iungeremus, MK, Zu, probaretur, MH, ad,
              <lb/>
            HK, eſſe vt, ZV, ad, Vu, (ſunt. </s>
            <s xml:id="echoid-s1765" xml:space="preserve">n. </s>
            <s xml:id="echoid-s1766" xml:space="preserve">ſimiles figuræ, HMPL, V
              <lb/>
            ZdY, necnon, LPK, Ydu, circumſtant autem latera proportio-
              <lb/>
            nalia angulos æquales, MHK, ZVu, & </s>
            <s xml:id="echoid-s1767" xml:space="preserve">ideò oſtenderemus trian-
              <lb/>
            gula, MHK, ZVu, eſſe ſimilia, vnde pateret angulos, HKM,
              <lb/>
            VuZ, eſſe æquales, ſed etiam, HKN, Vug, ſunt ęquales, ergo
              <lb/>
              <note position="right" xlink:label="note-0089-01" xlink:href="note-0089-01a" xml:space="preserve">6. Sex. El.</note>
            pateret angulos, MKN, Zug, eſſe æquales, ſunt autem etiam æ-
              <lb/>
            quales, MNK, Zgu, ergo triangula, MKN, Zug, eſſent æ-
              <lb/>
            quiangula, vnde, MN, ad, Zg, eſſet vt, KN, ad, ug, incidunt
              <lb/>
            autem, KN, ug, oppoſitis tangentibus, HK, MN, Vu, Zg, ad
              <lb/>
            eundem angulum ex eadem parte, ergo ipſarum tangentium, ac fi-
              <lb/>
              <note position="right" xlink:label="note-0089-02" xlink:href="note-0089-02a" xml:space="preserve">24. huius.</note>
            gurarum ſunt incidentes, KN, ug, cum verò, KN, ad, ug, ſit vt,
              <lb/>
            MK, ad, Zu, ideſt vt, MH, ad, ZV, vel vt quoduis ſolidorum
              <lb/>
            latus homologum ad quoduis latus homologum, ideſt vt, GO, ad,
              <lb/>
            8f, ideſt vt, OD, ad, f℟; </s>
            <s xml:id="echoid-s1768" xml:space="preserve">OD, autem ad, f℟, ſit vt, Bo, ad, Qf,
              <lb/>
            ideò, KN, ad, ug, erit vt, BO, ad, Qf, & </s>
            <s xml:id="echoid-s1769" xml:space="preserve">diuidunt ſimiliter ad
              <lb/>
            eandem partem ipſas, BO, Qf, in punctis, Ku, quæ incidunt ip-
              <lb/>
            ſis, BC, OD, Qf, R℟, ad eundem angulum ex eadem parte, ſunt
              <lb/>
            .</s>
            <s xml:id="echoid-s1770" xml:space="preserve">n. </s>
            <s xml:id="echoid-s1771" xml:space="preserve">anguli, BOD, Qf℟, æquales, quod & </s>
            <s xml:id="echoid-s1772" xml:space="preserve">de cæteris incidentibus
              <lb/>
            probabitur, ergo figurę, BODC, Qf℟R, quę capiunt omnes di-
              <lb/>
              <note position="right" xlink:label="note-0089-03" xlink:href="note-0089-03a" xml:space="preserve">Deſio. 10.
                <lb/>
              huius.</note>
            ctas incidentes, ſunt ſimiles, & </s>
            <s xml:id="echoid-s1773" xml:space="preserve">arum homologę ipſę incidentes, qua-
              <lb/>
            rum omnium regulæ ſunt, OD, f℟, & </s>
            <s xml:id="echoid-s1774" xml:space="preserve">ſunt ipſę figurę, BD, Q℟,
              <lb/>
            æquè ad eandem partem ipſis baſibus inclinatę, cum ſint in planis fi-
              <lb/>
              <note position="right" xlink:label="note-0089-04" xlink:href="note-0089-04a" xml:space="preserve">Lem. 1.</note>
            gurarum, oOS, sfp, ergo dicta ſolida ſunt etiam ſimilia iuxta de-
              <lb/>
            fin. </s>
            <s xml:id="echoid-s1775" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1776" xml:space="preserve">huius. </s>
            <s xml:id="echoid-s1777" xml:space="preserve">quod ſi plana, GOo, 8fs, non eſſent in ambitu ſi-
              <lb/>
            milium dictorum ſolidorum, facilè tamen oſtenderemus portiones
              <lb/>
            ſolidorum vltra eadem plana exiſtentes eſſe ſimiles, ac ipſarum, & </s>
            <s xml:id="echoid-s1778" xml:space="preserve">
              <lb/>
            oppoſitorum tangentium planorum iam dictorum incidentes repe-
              <lb/>
            riri in planis figurarum, BD, Q℟, cum eiſdem integrantes figuras
              <lb/>
            incidentes integrorum ſimilium ſolidorum, ac dictorum oppoſito-
              <lb/>
            rum tangentium, quod ſpeculanti facilè innoteſcet, hoc autem erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s1779" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div177" type="section" level="1" n="116">
          <head xml:id="echoid-head127" xml:space="preserve">LEMMA.</head>
          <p>
            <s xml:id="echoid-s1780" xml:space="preserve">CIrculi omnes, necnon femicirculi ſunt ſimiles iuxta meam deſi-
              <lb/>
            nitionem ſimilium planarum figurarum, & </s>
            <s xml:id="echoid-s1781" xml:space="preserve">eorum, & </s>
            <s xml:id="echoid-s1782" xml:space="preserve">tangen-
              <lb/>
            tium oppoſitarum, quæ ab extremitatibus diamertrorum ducuntur,
              <lb/>
            incidentes ſunt ipſi diametri.</s>
            <s xml:id="echoid-s1783" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1784" xml:space="preserve">Sint circuli, ABCD, ONQ, quorum diametri, AC, OQ, per
              <lb/>
            quorum extrema ducantur tangentes, FA, GC, HO, LQ. </s>
            <s xml:id="echoid-s1785" xml:space="preserve"/>
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