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

Table of handwritten notes

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              <pb o="481" file="0501" n="501" rhead="LIBER VI"/>
            ſub rectangulo, AkE, cum {2/3}. </s>
            <s xml:id="echoid-s12331" xml:space="preserve">quadrati, kE, ſic igitur erit reſiduu@
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            cylindri, BF, dempto cono, DAF, ad reſiduum cylindri, CF, dem-
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            pto fruſto, DMIF; </s>
            <s xml:id="echoid-s12332" xml:space="preserve">cætera autem ex ſuis Propoſitionibus patent,
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            quæ explicanda proponebantur.</s>
            <s xml:id="echoid-s12333" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1133" type="section" level="1" n="678">
          <head xml:id="echoid-head708" xml:space="preserve">COROLL. GENERALE.</head>
          <p style="it">
            <s xml:id="echoid-s12334" xml:space="preserve">_L_Icet autem in ſuperioribus bu ius Libri Propoſitionibus tantum.
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            </s>
            <s xml:id="echoid-s12335" xml:space="preserve">modo cylindros, conos, ſphæras, ſphæroides, conoides paraboli-
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            cas, & </s>
            <s xml:id="echoid-s12336" xml:space="preserve">byperbolicas, apices ſphærales, atque anulos, apices parabo-
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            licos, & </s>
            <s xml:id="echoid-s12337" xml:space="preserve">ſemianulos, ac cætera conſimilia ſolida fuerimus contempla-
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            ti, quorum omnia planà ſunt omnes figuræ ſimiles figurarum, quæ eo-
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            rundem genitrices appellantur, ſcilicet in his ſolidis, aſſumptis tan-
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            tum ſimilibus figuris, quæ ſint circuli, vel ellipſes; </s>
            <s xml:id="echoid-s12338" xml:space="preserve">tamen manifeſtum
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            eſt, ſi vice circulorum, vel ellipſium alia fuiſſent aſſumptæ ſimiles fi-
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            guræ, quod eadem circa talia ſolida Theoremata, vel Problemata ſi-
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            milia præpoſitis conſtruere potuiſſemus. </s>
            <s xml:id="echoid-s12339" xml:space="preserve">Vnde ex .</s>
            <s xml:id="echoid-s12340" xml:space="preserve">g. </s>
            <s xml:id="echoid-s12341" xml:space="preserve">veluti in Prop. </s>
            <s xml:id="echoid-s12342" xml:space="preserve">
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            26. </s>
            <s xml:id="echoid-s12343" xml:space="preserve">buius inuenimus ſphæram æqualem dato cylindro, ita ſi vice cy-
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            lindri habuiſſemus cylindricum, cuius baſis fuiſſet triangulum æqui-
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            laterum, poteramus vice ſphæræ inuenire ſolidum, cylindrico dato ſi-
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            milare, genitum ex circulo, cuius nempè omnia plana ſuiſſent omnes
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            figuræ ſimiles, ideſt omnia triangula æquilatera, circuli, qui erat ſphæ-
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            ræ, & </s>
            <s xml:id="echoid-s12344" xml:space="preserve">eſt buius ſolidi genitrix figura, & </s>
            <s xml:id="echoid-s12345" xml:space="preserve">eodem modo in cæteris banc
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            commutationem proſequi, aſſumptis quibuſcumque ſimilibus figuris
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            genitricium figurarum, ex quibus dicta ſolida ad inuicem ſimilaria
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            genita dicuntur, quam varietatem, vt & </s>
            <s xml:id="echoid-s12346" xml:space="preserve">alia quamplurima tum Pro-
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            blemata, tum Theoremata, quæ ex bactenus oftenſis deduci poſſent,
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            quaq; </s>
            <s xml:id="echoid-s12347" xml:space="preserve">Lectoris induſtria relinquuntur, cuiq; </s>
            <s xml:id="echoid-s12348" xml:space="preserve">licebit iuxta propoſit am
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            methodum facilè meditari, & </s>
            <s xml:id="echoid-s12349" xml:space="preserve">propterea circa bæc non amplius im-
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            morandum mibieſſe cenſui.</s>
            <s xml:id="echoid-s12350" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1134" type="section" level="1" n="679">
          <head xml:id="echoid-head709" xml:space="preserve">Finis Sexti Libri.</head>
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