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

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            <s xml:id="echoid-s4422" xml:space="preserve">Sit ergo expoſitum quodcumq; </s>
            <s xml:id="echoid-s4423" xml:space="preserve">parallelogrammum, AC, & </s>
            <s xml:id="echoid-s4424" xml:space="preserve">tri-
              <lb/>
            angulum, FGH, in quibus pro regulis ſumantur latera, BC, GH.
              <lb/>
            </s>
            <s xml:id="echoid-s4425" xml:space="preserve">Dico ſolidum quodcumq; </s>
            <s xml:id="echoid-s4426" xml:space="preserve">ſimilare genitum ex parallelogrammo, A
              <lb/>
            C, (iuxta regulam, BC,) eſſe cylindricum, cuius baſis erit a, BC,
              <lb/>
            deſcripta figura, & </s>
            <s xml:id="echoid-s4427" xml:space="preserve">latus, vtrumuis ipſorum, AB, LC, laterum re-
              <lb/>
            gulæ, BC, inſiſtentium; </s>
            <s xml:id="echoid-s4428" xml:space="preserve">Et genitum ex triangulo, FGH, iuxta
              <lb/>
            regulam, GH, eſſe conicum, cuius baſis erit à, GH, deicripta fi-
              <lb/>
            gura, & </s>
            <s xml:id="echoid-s4429" xml:space="preserve">latus vtrumuis duorum, FG, FH, regulæ, GH, inſiſten-
              <lb/>
            tium. </s>
            <s xml:id="echoid-s4430" xml:space="preserve">Deſcribantur à regulis, BC, GH, figuræ vtcunque planæ,
              <lb/>
            BCE, GHP, æqualiter inclinatę planis, AC, FGH, deinde per
              <lb/>
            circuitum figuræ, BCE, feratur latus, AB, cui ſit æqualelatus, E
              <lb/>
            X, quodque puncto, A, deſcribat circuitum figuræ, AXL, & </s>
            <s xml:id="echoid-s4431" xml:space="preserve">per
              <lb/>
            circuitum figuræ, GHP, feratur vtrumuis laterum, FG, FH, in-
              <lb/>
              <figure xlink:label="fig-0200-01" xlink:href="fig-0200-01a" number="118">
                <image file="0200-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0200-01"/>
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            definitè productum verſus fi-
              <lb/>
            guram, GHP, cuius portio
              <lb/>
            inter, F, & </s>
            <s xml:id="echoid-s4432" xml:space="preserve">punctum, P, fit,
              <lb/>
            FP, erit ergo ſolidum quod
              <lb/>
            clauditur ſuperficie cylindri-
              <lb/>
              <note position="left" xlink:label="note-0200-01" xlink:href="note-0200-01a" xml:space="preserve">Ex def. 3.
                <lb/>
              324. lib. 1.</note>
            ca, deſcripta latere, AB, & </s>
            <s xml:id="echoid-s4433" xml:space="preserve">
              <lb/>
            duabus figuris, ALX, BC
              <lb/>
            E, cylindricus; </s>
            <s xml:id="echoid-s4434" xml:space="preserve">& </s>
            <s xml:id="echoid-s4435" xml:space="preserve">quod c au-
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            ditur ſuperficie conica de-
              <lb/>
            ſcripta altero laterum, FG,
              <lb/>
            FH, indefinitè producto, & </s>
            <s xml:id="echoid-s4436" xml:space="preserve">
              <lb/>
            figura, GHP, erit conicus.
              <lb/>
            </s>
            <s xml:id="echoid-s4437" xml:space="preserve">Dico autem ſolidum ſimilare genitum ex, AC, iuxta regulam, BC,
              <lb/>
            cuius omnia plana ſint omnes figuræ ipſius, AC, ſimiles figuræ, B
              <lb/>
            CE, eſſe hunc cylindricum, ACE, nam quælibet earum, quæ di-
              <lb/>
            cuntur omnes figuræ ſimiles parallelogrammi, AC, regula, BC,
              <lb/>
              <note position="left" xlink:label="note-0200-02" xlink:href="note-0200-02a" xml:space="preserve">A. def. 8.
                <lb/>
              huius.</note>
            ſimiles inquam figuræ, BCE, eſt etiam ſimiliter poſita, ac, BCE,
              <lb/>
            deſcripta latere homologo ipſi, BC, igitur eius perimeter erit in ſu-
              <lb/>
            perficie cylindrica deſcripta latere, AB, ſi enim aliquid eius eſſet in-
              <lb/>
            tra, vel extra illam ſuperficiem, aliquid eius eſſet intra, vel extra com-
              <lb/>
            munem ſectionem talis aſſumptę figurę, & </s>
            <s xml:id="echoid-s4438" xml:space="preserve">ſuperficiei cylindricę, ta-
              <lb/>
            lis autem communis ſectio eſt perimeter figuræ ſimilis, & </s>
            <s xml:id="echoid-s4439" xml:space="preserve">ſimiliter
              <lb/>
            poſitę, ac, BCE, (quia ſi cylindricus plano ſecetur baſi æquidiſtan-
              <lb/>
              <note position="left" xlink:label="note-0200-03" xlink:href="note-0200-03a" xml:space="preserve">Corol. 12.
                <lb/>
              lib. 1.</note>
            te concepta figura erit ſimilis, & </s>
            <s xml:id="echoid-s4440" xml:space="preserve">ſimiliter poſita, ac baſis) ergo ha-
              <lb/>
            beremus duas figuras ab eodem latere homologo deſcriptas, ſimiles
              <lb/>
            æquales, & </s>
            <s xml:id="echoid-s4441" xml:space="preserve">ſimiliter poſitas, & </s>
            <s xml:id="echoid-s4442" xml:space="preserve">non congruentes, quod eſt abſur-
              <lb/>
              <note position="left" xlink:label="note-0200-04" xlink:href="note-0200-04a" xml:space="preserve">Corollar.
                <lb/>
              25. l. 1.</note>
            dum, congruent igitur, erit ergo aſſumpta figura, quæ eſt vna ea-
              <lb/>
            rum, quę dicuntur omnes figurę parallelogrammi, AC, ſimiles ipſi,
              <lb/>
            BCE, regula, BC, & </s>
            <s xml:id="echoid-s4443" xml:space="preserve">eſt vnum eorum, quæ dicuntur omnia </s>
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