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

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            <s xml:id="echoid-s733" xml:space="preserve">
              <pb o="25" file="0045" n="45" rhead="LIBER I."/>
            duo plana oppoſita tangentia cylindricum, PN, parallela cuidam
              <lb/>
              <note position="right" xlink:label="note-0045-01" xlink:href="note-0045-01a" xml:space="preserve">Coroll. 1.
                <lb/>
              huius.</note>
            per latera tranſeunti, quorum, & </s>
            <s xml:id="echoid-s734" xml:space="preserve">oppoſitarum baſium productarum
              <lb/>
            communes ſectiones ſint ex vna parteipſæ, VF, XL, ex alia verò,
              <lb/>
            AB, ZG, quæ tangent vel in latere, ſiue lateribus, vt in, VX, AZ,
              <lb/>
              <note position="right" xlink:label="note-0045-02" xlink:href="note-0045-02a" xml:space="preserve">9. Huius.</note>
            vel in planis, quæ erunt parallelogramma, ſint autem dicta plana, & </s>
            <s xml:id="echoid-s735" xml:space="preserve">
              <lb/>
            communes ſectiones, indefinitè producta, & </s>
            <s xml:id="echoid-s736" xml:space="preserve">in qualibet dictarum
              <lb/>
              <figure xlink:label="fig-0045-01" xlink:href="fig-0045-01a" number="19">
                <image file="0045-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0045-01"/>
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            communium ſectionum, vt
              <lb/>
            in, AB, ſumpto vtcumque
              <lb/>
            puncto, B, ducatur vſque
              <lb/>
            ad oppoſitam tangentem
              <lb/>
            vtcumque in earum plano
              <lb/>
            recta, BF, illi incidens in,
              <lb/>
            F, & </s>
            <s xml:id="echoid-s737" xml:space="preserve">per, B, ducatur in pla-
              <lb/>
            no tangente ipſa, BG, pa-
              <lb/>
            rallela vni laterum cylin-
              <lb/>
            drici, PN, per ipſas autem,
              <lb/>
            FB, BG, intelligatur ex-
              <lb/>
            tenſum planum, quod ſe-
              <lb/>
            cet aliud planum tangens
              <lb/>
            in recta, FL, & </s>
            <s xml:id="echoid-s738" xml:space="preserve">planum
              <lb/>
            per, ZG, XL, ductum in
              <lb/>
            recta, GL, erunt igituripſę,
              <lb/>
            BE, GL, parallelæ, vt & </s>
            <s xml:id="echoid-s739" xml:space="preserve">
              <lb/>
            ipſæ, BG, FL, & </s>
            <s xml:id="echoid-s740" xml:space="preserve">erit, FG,
              <lb/>
            parallelogrammum. </s>
            <s xml:id="echoid-s741" xml:space="preserve">Du-
              <lb/>
            catur nunc intra dicta op-
              <lb/>
            poſita tangentia plana eiſdem ęquidiſtans planum, quod erit ductum
              <lb/>
            perlatera, cylindricumque, PN, ſecabit, ſit ductum perlatera, P
              <lb/>
              <note position="right" xlink:label="note-0045-03" xlink:href="note-0045-03a" xml:space="preserve">Ex Lem.
                <lb/>
              ſeq.</note>
            O, CI, EM, KN, & </s>
            <s xml:id="echoid-s742" xml:space="preserve">productum ſecet planum, FG, in recta, D
              <lb/>
            H, & </s>
            <s xml:id="echoid-s743" xml:space="preserve">planum, quod tranſit per, AB, VF, in recta, PD, & </s>
            <s xml:id="echoid-s744" xml:space="preserve">quod
              <lb/>
            tranſit per, ZG, XL, in recta, OH: </s>
            <s xml:id="echoid-s745" xml:space="preserve">erit ergo, DH, parallela
              <lb/>
            ipſi, BG, &</s>
            <s xml:id="echoid-s746" xml:space="preserve">, BG, eſt parallela vni laterum cylindrici, ergo &</s>
            <s xml:id="echoid-s747" xml:space="preserve">, D
              <lb/>
            H, erit parallela ipſi, KN, EM, CI, PO, & </s>
            <s xml:id="echoid-s748" xml:space="preserve">erunt ipſa, PI, CM,
              <lb/>
            EN, KH, FH, DG, parallelogramma, & </s>
            <s xml:id="echoid-s749" xml:space="preserve">eorum latera oppo-
              <lb/>
            ſita inter ſe ęqualia, nempè, FD, ipſi, LH, & </s>
            <s xml:id="echoid-s750" xml:space="preserve">DB, ipſi, HG, D
              <lb/>
            K, ipſi, HN, DE, ipſi, HM, DC, ipſi, HI, &</s>
            <s xml:id="echoid-s751" xml:space="preserve">, DP, ipſi, H
              <lb/>
            O, ſunt igitur ipſæ, BF, GL, ductæ inter oppoſitas tangentes fi-
              <lb/>
            gurarum, APK, ZON, ad eundem angulum ex eadem parte,
              <lb/>
            quia angulus, BFV, eſt æqualis angulo, GLX, nam, BF, eſt pa-
              <lb/>
            rallela ipſi, GL, &</s>
            <s xml:id="echoid-s752" xml:space="preserve">, FV, ipſi, LX, & </s>
            <s xml:id="echoid-s753" xml:space="preserve">ſunt ipſæ, BF, GL, ſimili-
              <lb/>
              <note position="right" xlink:label="note-0045-04" xlink:href="note-0045-04a" xml:space="preserve">10. Vnde-
                <lb/>
              cimi Ele.</note>
            ter ad eandem partem diuiſæ in punctis, D, H, per rectas, PD, O
              <lb/>
            H, parallelas ipſis oppoſitis tangentibus, quæ cum ſint </s>
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