Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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na ſolidi ſimilaris geniti ex, AC, iuxta regulam, BC, erit, inquam,
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aſſumpta figura etiam vnum eorum, quæ dicuntur omnia plana cy-
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lindrici, ACE, regula, BCE, quod etiam de cæteris ſimili modo
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oſtendetur, ergo ſolidum ſimilare genitum ex, AC, iuxta regulam,
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BC, & </
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<
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">cylindricus, ACE, habebunt omnia plana (regula, BCE,
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aſiumpta) communia, ergo ſolidum ſimilare genitum ex, AC, iux-
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ta regulam, BC, erit idem cylindrico, ACE, cuius baſis eſt figura,
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BCE, & </
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<
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<
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">Similiter oſtendemus ſo-
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lidum ſimilare genitum ex triangulo, FGH, iuxta regulam, GH,
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eſſe dem conico, FGHP, cuius latus alterum laterum, FG, FH,
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& </
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<
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">baſis eſt figura, GHP, conſimili via ſupradictæ procedentes, quę
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erant demonſtranda.</
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">COROLLARIVM I.</
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">_H_Inc manifeſtum eſt, ſi figuræ deſcriptæ à, BC, GH, ſint circuli,
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quod ſolidum ſimilare genitum ex, AC, erit cylindrus, & </
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<
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tum ex triangulo, FGH, conus ſiue recti, ſiue ſcaleni, ſi verò deſ criptæ
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figuræ ſint rectilineæ, genitum ex, AC, erit priſma, ex, FGH, autem
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pyramis, ſiue recta, ſiue ſcalena cętera autem nomine communi vo-
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cantur ſolida ſimilaria genita ex eiſdem fig. </
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<
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">iuxta regulas, intellige,
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BC, GH.</
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">_S_I intra triangulum, FGH, ducamus ipſi, GH, parallelam vtcunq;
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">quæ ſit, DI, abſcindens à triangulo, FGH, trapezium, DH, oſten-
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demus eodem modo, quo ſupra, ſolidum ſimilare genitum ex trape-
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zio, DH, iuxta regulam, GH, eſſe fruſtum ſolidi ſimilaris geniti ex
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triangulo, FGH, iuxta eandem regulam, ideſt fruſtum conici, FGHP,
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_
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_l. I._</
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.</
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">cont, cum figura deſcripta à GH, eſt circulus, vel fruſtum pyra-
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midis rectæ, ſiue ſcalenæ, cum illa eſi figura rectilinea, quæ facilè
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oſtendentur.</
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">_T_Andem patet vice verſa, ſi quiuis cylindricus, vel conicus, vel
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eius fruſium, intelligatur ſecari per latera, de illo plano ſecante
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_2. & Cor._
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_l. I._</
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conceptam in ſecto ſolido figuram eſſe genitricem earumdem per deſcri-
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ptionem ſimitium figurarum, & </
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ſdem figuris geni@ricibus iuxta regulas communes ſectiones </
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