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

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          <p>
            <s xml:id="echoid-s753" xml:space="preserve">
              <pb o="26" file="0046" n="46" rhead="GEOMETRIÆ"/>
            ductæ, reperitur tamen earumdem portiones, quæiacent inter ip-
              <lb/>
            ſas, GL, BF, ex eadem parte, eodem ordine ſumptas, eſſe, vtip-
              <lb/>
            ſas, BF, GL, nam quia, DK, eſt æqualis ipſi, HN, &</s>
            <s xml:id="echoid-s754" xml:space="preserve">, BF, ipſi,
              <lb/>
            GL, vt, BF, ad, GL, ita eſt, DK, ad, HN, & </s>
            <s xml:id="echoid-s755" xml:space="preserve">ita eſſe oſtende-
              <lb/>
            mus, DE, ad, HM, DC, ad, HI, &</s>
            <s xml:id="echoid-s756" xml:space="preserve">, DP, ad, HO, nam iſtæ
              <lb/>
            ſunt æquales. </s>
            <s xml:id="echoid-s757" xml:space="preserve">Idem demonſtrabitur in cæteris, quæ ſimiliter ad ean-
              <lb/>
              <note position="left" xlink:label="note-0046-01" xlink:href="note-0046-01a" xml:space="preserve">Def.10.</note>
            dem partem diuidunt ipſas, BF, GL, igitur figuræ, APK, ZON,
              <lb/>
            ſunt ſimiles: </s>
            <s xml:id="echoid-s758" xml:space="preserve">Et quia earum homologæ, tum, PC, OI, tum, EK,
              <lb/>
            MN, ſunt ęquales, quod etiam de cæteris oſtendetur eodem pacto,
              <lb/>
            ſunt enim ſemper parallelogrammorum oppoſita latera, ideò figu-
              <lb/>
            ræ, APK, ZON, nedum erunt ſimiles, ſed etiam æquales, & </s>
            <s xml:id="echoid-s759" xml:space="preserve">re-
              <lb/>
              <note position="left" xlink:label="note-0046-02" xlink:href="note-0046-02a" xml:space="preserve">Aequales
                <lb/>
              homolo-
                <lb/>
              gas argue
                <lb/>
              reęquales
                <lb/>
              ſimiles fi-
                <lb/>
              guras, &è
                <lb/>
              contra,
                <lb/>
              patebit
                <lb/>
              infra in
                <lb/>
              Cor.25.
                <lb/>
              huius, ab
                <lb/>
              hac inde
                <lb/>
              pendẽter.
                <lb/>
              D. Defin.
                <lb/>
              10.</note>
            gulæ homologarum erunt ipſæ oppoſitæ tangentes, & </s>
            <s xml:id="echoid-s760" xml:space="preserve">ipſę, BF, G
              <lb/>
            L, earum incidentes. </s>
            <s xml:id="echoid-s761" xml:space="preserve">Quia verò figuræ, APK, ZON, ſunt in pla-
              <lb/>
            nis æquidiſtantibus ita conſtitutæ, vt earum incidentes ſint paralle-
              <lb/>
            læ, & </s>
            <s xml:id="echoid-s762" xml:space="preserve">homologæ figurarum, ZON, APK, ſunt ad eandem par-
              <lb/>
            tem incidentium poſitę, & </s>
            <s xml:id="echoid-s763" xml:space="preserve">item homologæ partes incidentium, B
              <lb/>
            F, GL, vt ipſæ, BD, GH, ſunt ad eandem partem pariter conſti-
              <lb/>
            tutæ, ideò figuræ, APK, ZON, nedum erunt ſimiles, & </s>
            <s xml:id="echoid-s764" xml:space="preserve">æqua-
              <lb/>
            les, ſed etiam ſimiliter poſitæ, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s765" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div95" type="section" level="1" n="69">
          <head xml:id="echoid-head80" xml:space="preserve">COROLLARIV M.</head>
          <p style="it">
            <s xml:id="echoid-s766" xml:space="preserve">_M_Anifeſtum eſt autem, quia plana oppoſita tangentia cylindrici,
              <lb/>
            PN, ducta ſunt vtcumque, & </s>
            <s xml:id="echoid-s767" xml:space="preserve">eorum, & </s>
            <s xml:id="echoid-s768" xml:space="preserve">oppoſitarum baſium
              <lb/>
            productarum communes ſectiones ſunt regulæ homologarum earumdem,
              <lb/>
            quod ſi duxerimus duo alia oppoſita tangentia plana, habebimus etiam
              <lb/>
            earumdem figurarum homologas, regulis adbuc communibus ſectionibus
              <lb/>
            horum tangentium planorum poſtremò ductorum, & </s>
            <s xml:id="echoid-s769" xml:space="preserve">earumdem baſium
              <lb/>
            productarum, quæ communes ſectiones cum primò dictis angulos æqua-
              <lb/>
            les continebunt, nam quæ exiſtent ex. </s>
            <s xml:id="echoid-s770" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s771" xml:space="preserve">in plano figuræ, APK, erunt
              <lb/>
              <note position="left" xlink:label="note-0046-03" xlink:href="note-0046-03a" xml:space="preserve">_10. Vnde-_
                <lb/>
              _cimi Ele._</note>
            parallelæ exiſtentibus in plano figuræ, ZON, igitur in oppoſitis cylin-
              <lb/>
            dricorumbaſibus homologas babebimus etiam cum quibuſuis rectis lineis
              <lb/>
            æquales angulos cum duabus quibuſuis homologarum earumdem inuen-
              <lb/>
            tis regulis continentibus, quæ igitur cum regulis homologarum oppoſi-
              <lb/>
            tarum baſium cylindrici angulos ad eandem partem continent æquales,
              <lb/>
            ſunt & </s>
            <s xml:id="echoid-s772" xml:space="preserve">ipſæ homologarum earumdem regulæ, neonon earundem oppoſi-
              <lb/>
            tarum baſium, & </s>
            <s xml:id="echoid-s773" xml:space="preserve">oppoſitarum tangentium æquè ad prædictas inclinata-
              <lb/>
            rum, etiam incidentes licebit, vt ſupra, inuenire.</s>
            <s xml:id="echoid-s774" xml:space="preserve"/>
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