Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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<
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<
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">parallelogrammum, AC, & </
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xml:space
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angulum, FGH, in quibus pro regulis ſumantur latera, BC, GH.
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</
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<
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<
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xml:space
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">ſimilare genitum ex parallelogrammo, A
<
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C, (iuxta regulam, BC,) eſſe cylindricum, cuius baſis erit a, BC,
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deſcripta figura, & </
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<
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xml:space
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">latus, vtrumuis ipſorum, AB, LC, laterum re-
<
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gulæ, BC, inſiſtentium; </
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<
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xml:space
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">Et genitum ex triangulo, FGH, iuxta
<
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regulam, GH, eſſe conicum, cuius baſis erit à, GH, deicripta fi-
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gura, & </
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<
s
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xml:space
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">latus vtrumuis duorum, FG, FH, regulæ, GH, inſiſten-
<
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tium. </
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<
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xml:space
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">Deſcribantur à regulis, BC, GH, figuræ vtcunque planæ,
<
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BCE, GHP, æqualiter inclinatę planis, AC, FGH, deinde per
<
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circuitum figuræ, BCE, feratur latus, AB, cui ſit æqualelatus, E
<
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X, quodque puncto, A, deſcribat circuitum figuræ, AXL, & </
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<
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xml:space
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circuitum figuræ, GHP, feratur vtrumuis laterum, FG, FH, in-
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definitè productum verſus fi-
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guram, GHP, cuius portio
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inter, F, & </
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<
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FP, erit ergo ſolidum quod
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clauditur ſuperficie cylindri-
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xml:space
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">Ex def. 3.
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324. lib. 1.</
note
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ca, deſcripta latere, AB, & </
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<
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<
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duabus figuris, ALX, BC
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E, cylindricus; </
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<
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ditur ſuperficie conica de-
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ſcripta altero laterum, FG,
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FH, indefinitè producto, & </
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<
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figura, GHP, erit conicus.
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</
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<
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xml:space
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">Dico autem ſolidum ſimilare genitum ex, AC, iuxta regulam, BC,
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cuius omnia plana ſint omnes figuræ ipſius, AC, ſimiles figuræ, B
<
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CE, eſſe hunc cylindricum, ACE, nam quælibet earum, quæ di-
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cuntur omnes figuræ ſimiles parallelogrammi, AC, regula, BC,
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huius.</
note
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ſimiles inquam figuræ, BCE, eſt etiam ſimiliter poſita, ac, BCE,
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deſcripta latere homologo ipſi, BC, igitur eius perimeter erit in ſu-
<
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perficie cylindrica deſcripta latere, AB, ſi enim aliquid eius eſſet in-
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tra, vel extra illam ſuperficiem, aliquid eius eſſet intra, vel extra com-
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munem ſectionem talis aſſumptę figurę, & </
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<
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lis autem communis ſectio eſt perimeter figuræ ſimilis, & </
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<
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poſitę, ac, BCE, (quia ſi cylindricus plano ſecetur baſi æquidiſtan-
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xml:space
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lib. 1.</
note
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te concepta figura erit ſimilis, & </
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<
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">ſimiliter poſita, ac baſis) ergo ha-
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beremus duas figuras ab eodem latere homologo deſcriptas, ſimiles
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æquales, & </
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<
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<
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25. l. 1.</
note
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dum, congruent igitur, erit ergo aſſumpta figura, quæ eſt vna ea-
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rum, quę dicuntur omnes figurę parallelogrammi, AC, ſimiles ipſi,
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BCE, regula, BC, & </
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