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

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          <p>
            <s xml:id="echoid-s649" xml:space="preserve">
              <pb o="21" file="0041" n="41" rhead="LIBER I."/>
            Dico, RO, eſſe parallelam lateri cylindrici, FG. </s>
            <s xml:id="echoid-s650" xml:space="preserve">Iungantur, CE.
              <lb/>
            </s>
            <s xml:id="echoid-s651" xml:space="preserve">
              <note position="right" xlink:label="note-0041-01" xlink:href="note-0041-01a" xml:space="preserve">33. p. Pri-
                <lb/>
              mi Elem.
                <lb/>
              p. 16. Vn-
                <lb/>
              dec. Elem.
                <lb/>
              10. Vnde-
                <lb/>
              cimi Ele.</note>
            MN, quoniam ergo, CE, MN, coniungunt extrema laterum cy
              <lb/>
              <figure xlink:label="fig-0041-01" xlink:href="fig-0041-01a" number="15">
                <image file="0041-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0041-01"/>
              </figure>
            lindrici, CM, EN, quæ ſunt æqualia, & </s>
            <s xml:id="echoid-s652" xml:space="preserve">
              <lb/>
            parallela, erunt & </s>
            <s xml:id="echoid-s653" xml:space="preserve">ipſæ æquales, & </s>
            <s xml:id="echoid-s654" xml:space="preserve">paralle-
              <lb/>
            læ, ſunt etiam parallelę ipſæ, CR, MO, er-
              <lb/>
            goangulus, ECR, erit æqualis angulo, N
              <lb/>
            MO, eodem pacto oſtendemus angulum, C
              <lb/>
            ER, eſſe æqualem angulo, MNO, vnde
              <lb/>
              <note position="right" xlink:label="note-0041-02" xlink:href="note-0041-02a" xml:space="preserve">26. Primi
                <lb/>
              Elem.</note>
            etiam, CR, MO, erunt æquales, & </s>
            <s xml:id="echoid-s655" xml:space="preserve">funt pa-
              <lb/>
            rallelæ, ergo eas iungentes, quæ ſunt, RO,
              <lb/>
            CM, erunt ęquales, & </s>
            <s xml:id="echoid-s656" xml:space="preserve">parallelę, eſt autem,
              <lb/>
            CM, latus cylindrici, FG, ergo, RO, com-
              <lb/>
            munis ſectio duorum planorum dictum cy-
              <lb/>
            lindricum ſecantium, erit eiuſdem lateribus
              <lb/>
            parallela. </s>
            <s xml:id="echoid-s657" xml:space="preserve">Idem oſtendemus, ſi ſectio contingat fieri intra cylindri
              <lb/>
            cum, ſiautem fiat in ſuperficie, patet non poſſe fieri, niſi in latere
              <lb/>
            cylindrici, nam plana ſecantia ducuntur per latera, quodfibet autem
              <lb/>
            latus eſt cęteris eiuſdem cylindrici lateribus æquidiſtans, & </s>
            <s xml:id="echoid-s658" xml:space="preserve">ideò vbi-
              <lb/>
            cumq; </s>
            <s xml:id="echoid-s659" xml:space="preserve">contingat ſectionem fieri ſemper communis ſectio planorum
              <lb/>
            perlatera cylindrici ductorum ſe inuicem ſecantium, eſt parallela la-
              <lb/>
            teribus cylindrici. </s>
            <s xml:id="echoid-s660" xml:space="preserve">Idem ſequetur de tangentibus planis, quod erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s661" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div84" type="section" level="1" n="63">
          <head xml:id="echoid-head74" xml:space="preserve">THEOREMA V. PROPOS. VIII.</head>
          <p>
            <s xml:id="echoid-s662" xml:space="preserve">SI quilibet cylindricus ſecetur planis parallelis perlatera
              <lb/>
            ductis conceptæ in cylindrico figuræ erunt parallelo-
              <lb/>
            gramma æquiangula.</s>
            <s xml:id="echoid-s663" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s664" xml:space="preserve">Sit quilibet cylindricus, BF, planis ſectus
              <lb/>
              <figure xlink:label="fig-0041-02" xlink:href="fig-0041-02a" number="16">
                <image file="0041-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0041-02"/>
              </figure>
            parallelis per latera ductis, ſit autem vnius
              <lb/>
            in cylindrico, AF, concepta figuræ paral-
              <lb/>
            lelogrammum, BH, alterius autem paral-
              <lb/>
            lelogramma, AN, QF. </s>
            <s xml:id="echoid-s665" xml:space="preserve">Dico hæc eſſe
              <lb/>
            ęquiangula, quod enim ſint parallelogram-
              <lb/>
              <note position="right" xlink:label="note-0041-03" xlink:href="note-0041-03a" xml:space="preserve">ExCor. 6.
                <lb/>
              huius.</note>
            ma, patet, quia plana ſecantia ducuntur per
              <lb/>
            latera, quod verò fint æquiangula patet e-
              <lb/>
            tiam, nam in parallelogrammo, AN, la-
              <lb/>
            tus, AD, æquidiſtat lateri, BO, &</s>
            <s xml:id="echoid-s666" xml:space="preserve">, AP,
              <lb/>
            ipſi, BC, nam ſunt communes fectiones pla-
              <lb/>
            ni, ABCR, & </s>
            <s xml:id="echoid-s667" xml:space="preserve">æquidiftantium planorum,
              <lb/>
            AN, BH, & </s>
            <s xml:id="echoid-s668" xml:space="preserve">ideo angulus, PAD, æqua-
              <lb/>
              <note position="right" xlink:label="note-0041-04" xlink:href="note-0041-04a" xml:space="preserve">10. Vnde-
                <lb/>
              cimi Ele.</note>
            tur angulo, CBO, ergo parallelogramma, AN, BH, erunt </s>
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