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

Table of handwritten notes

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        <div xml:id="echoid-div684" type="section" level="1" n="400">
          <head xml:id="echoid-head418" xml:space="preserve">SECTIO III.</head>
          <p>
            <s xml:id="echoid-s6932" xml:space="preserve">VLterius habemus faſcias ſolidas cylindricas genitas exempligr.
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            </s>
            <s xml:id="echoid-s6933" xml:space="preserve">ab eodem rectangulo, AR, dum ſit reuolutio ſemel circa, T
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            X, & </s>
            <s xml:id="echoid-s6934" xml:space="preserve">ſemel circa parallelam, AC, ad anulos latos ellipticos altera
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            parte ſtrictiores genitos in reuolutionibus ab ellipſi, BDMG, ha-
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            bere eandem rationem ſcilicet quam habet, AR, ad ellipſim, BDM
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            G, & </s>
            <s xml:id="echoid-s6935" xml:space="preserve">ideò inter ſe dictos anulos eſſe, vt dictas faſcias, dictæ autem
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            faſciæ ſolidæ cylindricæ ſunt, vt reſidua, demptis à quadratis ſemi-
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            diametrorum baſium integrorum cylindrorum quadratis ſemidiame-
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            trorum baſium cylindrorum, quas dictæ faſciæ complectuntur, & </s>
            <s xml:id="echoid-s6936" xml:space="preserve">
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            ideò dicti anuli inter ſe eandem rationem habebunt, quam dicta qua-
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            dratorum reſidua.</s>
            <s xml:id="echoid-s6937" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div685" type="section" level="1" n="401">
          <head xml:id="echoid-head419" xml:space="preserve">SECTIO IV.</head>
          <p>
            <s xml:id="echoid-s6938" xml:space="preserve">IN Corollario huius tandem dicitur, quòd ſi, BDMG, non
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            eſſet ellipſis, tum in Schemate huius, tum Theorematis antece-
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            dentis, ſed alia vtcunque ſigura habens tamen prædictas conditiones
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            ibi appoſitas, quod de eadem dicta quoque de ellipſi, BDMG, ve-
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            riſicarentur, noſque hic colligimus, quod omnia ſupradicta æquè,
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            ac deſolidis genitis ab ellipſi, BDMG, de genitis abipſa figura pa-
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            riter veriſicarentur. </s>
            <s xml:id="echoid-s6939" xml:space="preserve">Poſſumus autem vocare ſolida deſcripta per
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            reuolutionem factam circa, CR, à ſigura, BDMG. </s>
            <s xml:id="echoid-s6940" xml:space="preserve">Solida anu-
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            laria ſtricta altera parte latiora: </s>
            <s xml:id="echoid-s6941" xml:space="preserve">quæ verò ſiunt ab eadem per reuolu-
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            tionem circa, TX. </s>
            <s xml:id="echoid-s6942" xml:space="preserve">Solida anularia lata altera parte ſtrictiora.</s>
            <s xml:id="echoid-s6943" xml:space="preserve"/>
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        <div xml:id="echoid-div686" type="section" level="1" n="402">
          <head xml:id="echoid-head420" xml:space="preserve">SCHOLIVM.</head>
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            <s xml:id="echoid-s6944" xml:space="preserve">POſſent quidem plura alia circa bæc ſolida conſiderari; </s>
            <s xml:id="echoid-s6945" xml:space="preserve">bt ſi ſecentur
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            planis parallelis, ad axem, circa quem ſit reuolutio, exiſtentibus
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            rectis, quam inter ſerationem babeant reſecta ſegmenta. </s>
            <s xml:id="echoid-s6946" xml:space="preserve">Item reſtat
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            contemplandum ſolidum, quod naſceretur ex reuolutione dimidiæ elli-
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            pſis circa non axem, ſed diametrum, vel diametro parallelam; </s>
            <s xml:id="echoid-s6947" xml:space="preserve">quæ vo-
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            luta circa diametrum ſolidum deſcribit referens ſiguram Pyri; </s>
            <s xml:id="echoid-s6948" xml:space="preserve">circa,
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            berò parallelam diametro portionem maiorem ab ellipſireſecantem, de-
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            ſcribit quoddam ſolidum latius ex vna parte, quam ex alia, referens ſi-
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            guram Mali paradiſi, vt vulgò dicitur, circa berò parallelam </s>
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