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

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        <div xml:id="echoid-div1001" type="section" level="1" n="597">
          <p>
            <s xml:id="echoid-s11004" xml:space="preserve">
              <pb o="422" file="0442" n="442" rhead="GEOMETRIÆ"/>
            ſimilare genitum ex figura, DAFEVC, iuxta communem regu-
              <lb/>
            lam, FE.</s>
            <s xml:id="echoid-s11005" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1003" type="section" level="1" n="598">
          <head xml:id="echoid-head623" xml:space="preserve">COROLL. XXII. SECTIO PRIMA.</head>
          <p>
            <s xml:id="echoid-s11006" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s11007" xml:space="preserve">22. </s>
            <s xml:id="echoid-s11008" xml:space="preserve">ſi in ſuperioris figura ſupponamus, FR, eſſe æqua-
              <lb/>
            lem ei, quæ tangens ſectionem, DAF, in, A, concluditur in-
              <lb/>
            ter, A, & </s>
            <s xml:id="echoid-s11009" xml:space="preserve">aſymptoton, ON, habetur cylindrum, DE, eſſe ſexquial-
              <lb/>
            terum tympani hyperbol ci, DAFEVC, & </s>
            <s xml:id="echoid-s11010" xml:space="preserve">hoc tympanũ eſſe qua-
              <lb/>
            druplum conorum, NOY, HOS, & </s>
            <s xml:id="echoid-s11011" xml:space="preserve">ſic eſſe ſolida ſimilaria ex
              <lb/>
            eiſdem figuris genita iuxta communem regulam, DC.</s>
            <s xml:id="echoid-s11012" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1004" type="section" level="1" n="599">
          <head xml:id="echoid-head624" xml:space="preserve">SECTIO II.</head>
          <p>
            <s xml:id="echoid-s11013" xml:space="preserve">IN Coroll. </s>
            <s xml:id="echoid-s11014" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11015" xml:space="preserve">habetur cylindrum, DE, ad tympanum hyperbo-
              <lb/>
            licum, DAFEVC, demptis conis oppoſitis, HOS, NOY, eſſe
              <lb/>
            vt quadratum, DC, ad quadratum, AV, & </s>
            <s xml:id="echoid-s11016" xml:space="preserve">in caſu præſentis Prop.
              <lb/>
            </s>
            <s xml:id="echoid-s11017" xml:space="preserve">eſſe eorum dupla, & </s>
            <s xml:id="echoid-s11018" xml:space="preserve">ſic ſolida ſimilaria, &</s>
            <s xml:id="echoid-s11019" xml:space="preserve">c.</s>
            <s xml:id="echoid-s11020" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1005" type="section" level="1" n="600">
          <head xml:id="echoid-head625" xml:space="preserve">SECTIO III.</head>
          <p>
            <s xml:id="echoid-s11021" xml:space="preserve">IN Coroll. </s>
            <s xml:id="echoid-s11022" xml:space="preserve">2. </s>
            <s xml:id="echoid-s11023" xml:space="preserve">diſcimus inuenire cylindrum deſcriptum à paral-
              <lb/>
            lelogrammo ſectionibus oppoſitis circumſcripto, vt ibi dicitur,
              <lb/>
            quod ad reliquum tympani hyperbolici, demptis oppoſitis conis,
              <lb/>
            habeatrationem datam, dummodo ea ſit maioris inæqualit. </s>
            <s xml:id="echoid-s11024" xml:space="preserve">idem
              <lb/>
            intellige de ſol dis ſimilaribus, &</s>
            <s xml:id="echoid-s11025" xml:space="preserve">c.</s>
            <s xml:id="echoid-s11026" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1006" type="section" level="1" n="601">
          <head xml:id="echoid-head626" xml:space="preserve">COROLLARIVM XXIII.</head>
          <p>
            <s xml:id="echoid-s11027" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s11028" xml:space="preserve">23. </s>
            <s xml:id="echoid-s11029" xml:space="preserve">aſſumpta eius figura, &</s>
            <s xml:id="echoid-s11030" xml:space="preserve">,
              <lb/>
              <figure xlink:label="fig-0442-01" xlink:href="fig-0442-01a" number="305">
                <image file="0442-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0442-01"/>
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            vt fiat exemplum, ea circa axim, RZ,
              <lb/>
            reuoluta, vt ex, FC, fiat cylindrus, FC, & </s>
            <s xml:id="echoid-s11031" xml:space="preserve">
              <lb/>
            ex, TN, cylindrus, TN, & </s>
            <s xml:id="echoid-s11032" xml:space="preserve">ex oppoſitis,
              <lb/>
            hyperbolis, FAD, EVC, oppoſitæ conoi-
              <lb/>
            des, FAD, EVC, & </s>
            <s xml:id="echoid-s11033" xml:space="preserve">ex, TAY, MVN, op-
              <lb/>
            poſitæ, conoides, TAY, MVN, patet er-
              <lb/>
            go cylindrum, FC, demotis oppoſitis co-
              <lb/>
            noidibus, FAD, EVC, ad cylindrum, TN,
              <lb/>
            demptis oppoſitis conoidibus, TAX, MV
              <lb/>
            N, eſſe vt parallelepipedum ſub, ZV, & </s>
            <s xml:id="echoid-s11034" xml:space="preserve">
              <lb/>
            baſirectangulo, VOZ, cum {1/3}. </s>
            <s xml:id="echoid-s11035" xml:space="preserve">quadrati,
              <lb/>
            ZV, ad parallelepipedum ſub, ZV, baſi
              <lb/>
            rectangulo, VOS, cum {1/3}. </s>
            <s xml:id="echoid-s11036" xml:space="preserve">quadrati, SV, &</s>
            <s xml:id="echoid-s11037" xml:space="preserve"/>
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