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

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            ſcripta ſequuntur Corollaria, in quibus exempla adbibebimus, veluti
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            Lib. </s>
            <s xml:id="echoid-s8701" xml:space="preserve">3. </s>
            <s xml:id="echoid-s8702" xml:space="preserve">effectum eſt, aſſumptis nempè omnibus figuris ſimilibus genitri-
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            cium figurarum, quæ ſint circuli, diametros in ipſis genitricibus figu-
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            ris, quibus ſunt erecti, ſitos babentes, quæ per reuolutionem figuraram
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            circa ſuos axes deſcribi facilè appræbendi poſsũt, propter quod in exẽ-
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            plis tantũmodò axes aſſumemus congruenter ipſarũ genitrium figurarũ
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            reuolutioni, licet exempla etiam aſſumptis diametris confiici poſſent
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            per deſcriptionem omnium ſimilium figurarum haud tamen per reuolu-
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            tionem factam. </s>
            <s xml:id="echoid-s8703" xml:space="preserve">Liceat autem Prop. </s>
            <s xml:id="echoid-s8704" xml:space="preserve">antecedentium reaſſamptas figu-
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            ras ſub ampliori forma quandoque proponere, bel ſub auguſtiori, pro-
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            ut expedire comperietur, ſeruata ſemper earundem ſimilitudine.</s>
            <s xml:id="echoid-s8705" xml:space="preserve"/>
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        <div xml:id="echoid-div830" type="section" level="1" n="491">
          <head xml:id="echoid-head511" xml:space="preserve">COROLLARIVM I.</head>
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            <s xml:id="echoid-s8706" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s8707" xml:space="preserve">21. </s>
            <s xml:id="echoid-s8708" xml:space="preserve">ergo ſi intelligantur tres figuræ, nempè parallelo-
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            grammum, AF, triangulus, EVF, & </s>
            <s xml:id="echoid-s8709" xml:space="preserve">parabola, VEF, circa com-
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              <figure xlink:label="fig-0366-01" xlink:href="fig-0366-01a" number="247">
                <image file="0366-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0366-01"/>
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            munem axem reuolui, qui ſuppona-
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            tur eſſe, EM, fiet ex, AF, cylindrus,
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            AF. </s>
            <s xml:id="echoid-s8710" xml:space="preserve">extriangulo, VEF, conus, VEF,
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            & </s>
            <s xml:id="echoid-s8711" xml:space="preserve">ex parabola, VEF, conoides para-
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            bolicum, VEF, vnde patebit cylindrũ,
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            AF, eſſe duplum conoidis, VEF, & </s>
            <s xml:id="echoid-s8712" xml:space="preserve">
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            hoc eſſe ſexquialterum coni, VEF; </s>
            <s xml:id="echoid-s8713" xml:space="preserve">& </s>
            <s xml:id="echoid-s8714" xml:space="preserve">
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            vniuerſaliſsimè, vt dictum eſt, ſoli-
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            dum ſimilare genitum ex, AF, ad ſibi
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            ſimilare genitum ex parabola, VEF, habere duplam rationem, hoc
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            verò ad ſibi ſimilare gentium ex triangulo, VEF, rationem ſexqui-
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            alteram, quod tamen, ne figuræ multiplicentur, ſeu nimis confun-
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            dantur (quod etiã impofteru obſeruabimus) vno tãtũ adhibito exẽ-
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            plo, reuolutionis figurarũ
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            genitriciũ circa ſuos axes, explicare volui.</s>
            <s xml:id="echoid-s8715" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div832" type="section" level="1" n="492">
          <head xml:id="echoid-head512" xml:space="preserve">COROLLARIVM II.</head>
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            <s xml:id="echoid-s8716" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s8717" xml:space="preserve">22. </s>
            <s xml:id="echoid-s8718" xml:space="preserve">aſſumpta eius figura, fiat exemplum per reuolutio-
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              <figure xlink:label="fig-0366-02" xlink:href="fig-0366-02a" number="248">
                <image file="0366-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0366-02"/>
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            nem parabolæ, FCH, circa axẽ,
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            CG, dimiſsis parallelogrammis, AH,
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            RM, fient igitur in hac reuolutione
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            conoidea parabolica ex, FCH, OCM,
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            parabolis, quæ fint, FCH, OCM; </s>
            <s xml:id="echoid-s8719" xml:space="preserve">vn-
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            de patebit conoides parabolicum,
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            FCH, ad conoides parabolicũ, OCM,
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            eſſe, vt quadratũ, GG, ad </s>
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