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

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        <div xml:id="echoid-div1193" type="section" level="1" n="714">
          <pb o="519" file="0539" n="539" rhead="LIBER VII."/>
        </div>
        <div xml:id="echoid-div1194" type="section" level="1" n="715">
          <head xml:id="echoid-head748" xml:space="preserve">THEOREMA XIII. PROPOS. XIII.</head>
          <p>
            <s xml:id="echoid-s13419" xml:space="preserve">SI, expoſitis duabus quibuſcumq; </s>
            <s xml:id="echoid-s13420" xml:space="preserve">ſolidorum rectangu-
              <lb/>
            lorum deſcriptibilium regulis, ad vnum punctum cõ-
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            poſitis, iuxta eaſdem ſolidum rectangulum contineatur
              <lb/>
            ſub parallelogrammo, & </s>
            <s xml:id="echoid-s13421" xml:space="preserve">alia quacumq; </s>
            <s xml:id="echoid-s13422" xml:space="preserve">figura plana in
              <lb/>
            ambitu contenti ſolidi exiſtente, ipſum ſolidum rectangu-
              <lb/>
            lum erit cylindricus, & </s>
            <s xml:id="echoid-s13423" xml:space="preserve">figura plana ſuperius dicta erit il-
              <lb/>
            lius baſis. </s>
            <s xml:id="echoid-s13424" xml:space="preserve">Quod ſi etiam prædicta figura fuerit parallelo-
              <lb/>
            grammum, & </s>
            <s xml:id="echoid-s13425" xml:space="preserve">ambo in illius ambitu, contentum ijſdem
              <lb/>
            ſolidum rectangulum erit parallelepipedum.</s>
            <s xml:id="echoid-s13426" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13427" xml:space="preserve">Exponantur duæ inuicem perpendiculares regulæ, BC, CD, ſo-
              <lb/>
            lidorũ deſcriptib liũ ſub parallelogrammo, AC, & </s>
            <s xml:id="echoid-s13428" xml:space="preserve">figura plana qua
              <lb/>
            cumque, HDC, ſit autem deſcriptum ſolidum rectangulum ſub eiſ-
              <lb/>
              <figure xlink:label="fig-0539-01" xlink:href="fig-0539-01a" number="355">
                <image file="0539-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0539-01"/>
              </figure>
            dem contentum, AG
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            CH, iuxta regulas, B
              <lb/>
            C, CD, ita tamen vt
              <lb/>
            figura plana, HDC,
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            ſit in ambitu ipſius
              <lb/>
            contenti ſolidi. </s>
            <s xml:id="echoid-s13429" xml:space="preserve">Di-
              <lb/>
            co, AGCH, eſſe cy-
              <lb/>
            lindricum. </s>
            <s xml:id="echoid-s13430" xml:space="preserve">Quod. </s>
            <s xml:id="echoid-s13431" xml:space="preserve">n.
              <lb/>
            </s>
            <s xml:id="echoid-s13432" xml:space="preserve">AC, CG, GH, ſint
              <lb/>
            ſuperficies cylindra-
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            ceæ, quarum regula,
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            BC, manifeſtum eſt,
              <lb/>
            quod verò latera per
              <lb/>
            ſecantia para lela plana in ipſis deſignata ſint æqualia ipſi, BC, la-
              <lb/>
            teri parallelogrammi, AC, ex dictis etiam cõſtare poteſt, ſed maio-
              <lb/>
            ris dilucidationis gratia ſit ab aliquo dictorum ſecantium planorũ,
              <lb/>
            in ſolido, AGHC, productum rectangulum, IMON, eſt ergo, IN,
              <lb/>
            æqualis, MO, hoc eſt ipſi, BC, quo pacto idem de cæteris oſten-
              <lb/>
            demus, in parallelogrammo autem, GC, eadem verificantur, & </s>
            <s xml:id="echoid-s13433" xml:space="preserve">in
              <lb/>
            illi oppoſito, ſi contactus plani ipſi, GC, oppoſiti eſſent in plano,
              <lb/>
            vt manifeſtum eſt, ergo perinde eſt ac ſi latus æquale, BC, ambitũ
              <lb/>
              <note position="right" xlink:label="note-0539-01" xlink:href="note-0539-01a" xml:space="preserve">Def. 3. l. 1.</note>
            figuræ, HDC, extremo ſui puncto ſemper ipſi, BC, æquidiſtanter
              <lb/>
            percuriſſet ipſam ſuperficiem, ADBH, deſcribendo, erit ergo, A
              <lb/>
            GCH, cylindricus, cuius baſis eſt, HDC, figurá. </s>
            <s xml:id="echoid-s13434" xml:space="preserve">Præfatum qui-
              <lb/>
            dem ſolidum habet in ambitu figuras ipſum continentes, ſed ſi </s>
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