Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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bus, quæ ſunt regulæ homologarum earundem, poſſunt reperiri duæ in-
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cidentes earundem, quarum altera ſit iam ducta; </
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cumque inuentæ ſunt duæ incidentes, KN, HP, quarum altera fuit,
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HP. </
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eas terminatarum, portiones, eodem ordine ſumpcæ, ſunt proportiona-
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les, ſunt enim, vt ipſæ incidentes, ideò per homologarum productarum,
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talia extremaſemper tranſeunt aliquæ incidentes.</
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">planis parallelis, cum
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omnibus eiuſdem lateribus coincidentibus, conceptæ
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in ipſo figuræ erunt inter ſe ſimiles, & </
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">Sit conicus, cuius baſis, FHG, ver-
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0058-01
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tex, A, ſecetur autein vtcumque planis
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parallelis, quæ cum omnibus eiuſdem la-
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teribus coincidant, & </
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ipſo figuræ, DME, BNC. </
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eſſe ſimiles, & </
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quia planum figuræ, DME, coincidit
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omnibus lateribus conici, AFHG, ideo
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eſt etiam conicus ipſe, ADME, ſecatur
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autem plano eius baſi, DME, æquidi-
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ſtante, eo ſcilicet, quod producit figu-
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ram, BNC, ergo figura, BNC, erit ſi-
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milis baſi, DME, & </
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ſita, quod erat demonſtrandum.</
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<
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">SI quilibet conicus ſecetur plano per verticem, ſiue ab
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eodem tangatur in plano, nempe in triangulo, veltrian-
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gulis, ſecetur autem alijs planis vtcumq; </
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<
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">baſi parallelis, com-
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munes ſectiones, quæ ab eodem plano ſecante ſiunt in dictis
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planis baſi parallelis, erunt homologę lineę, vel latera figu-
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rarum, quæ ab eiſdem æquidiſtantibus planis in eodem co-
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nico producuntur.</
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