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

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126106GEOMETRIÆ guræ, ABC, productis ſi opus ſit, idem intellige in recta, EM, cuius
omnia puncta dicuntur eiuſdem obliqui tranſitus, eius nempè, qui
in tali inclinatione fit.

Pro intelligentia Defin. _8._ ſupponatur in figura plana propoſita,
ABC, vtcunque recta, BC, quæ deſcribat figuram planam, BC,

68[Figure 68] eleuatam ſuper, ABC, ſin-
gulæ autem lineæ, quæ di-
cuntur omnes lineæ figuræ,
ABC, ſumptæ regula, B
C, recti tranſitus, ſi figu-
ra, BC, ſit erecta figuræ,
ABC, veleiuſdem obliqui
tranſitus (qui nempè in in-
clinatione deſcriptæ figuræ
ad planum, ABC, fit, ſi figura, BC, ſit inclinata ad figuram, AB
C,) deſcribere intelligantur figuras planas ſimiles ſimiliter poſitas,
& æquidiſtantes ipſi figuræ, BC, ita vt deſcribentes ſint deſcripta-
11_D. Defin._
_10. lib.1._ rum figurarum lineæ, vel later a bomologa, quarum figurarum ali-
quæ ſint ipſæ, BC, PF, LH, iſtæ igitur omnes ſimul ſumptæ vocan-
22_A. Def. 8._
_huius._ tur, omnes figuræ ſimiles ipſius figuræ, ABC, ſumptæ regula figura,
BC, vellinea, aut latere, BC.

Solidum, cuius omnes dictæ figuræ ſimiles ipſius, ABC, ſunt
omnia plana, dicitur, ſolidum ſimilare genitum ex figura plana, A
BC, iuxta regulam ipſam figuram, vel lineam, BC, & ipſa figu-
33_B. Def. 8._
_huius._ ra, ABC, appellatur genitrix eiuſdem ſolidi, quod eſſe intelliga-
tur ipſum, ABC.

Si verò adſit alia figura plana, cuius omnes lineæ, quædam re-
gula ſumptæ, deſcribant ſimiles figuras planas, & ſimiliter poſitas,
omnes vni cuidam æquidiſtantes, & ſimiles figuræ, BC, & æquè
44_C. Def. 8._
_huius._ eleuatas ſuper plana genitricium figur arum, ſolida ſimilaria genita
ex iſtis figuris, iuxta dictas regulas vocabuntur vlterius inter ſe,
vel ad inuicem ſimilaria, licet cum dicemus, ſolida ſimilaria geni-
ta ex talibus, & talibus figuris, & hoc etiam ſine alio addito, in-
telligemus ſemper ea eſſe inter ſe, vel ad inuicem ſimilaria, etiam
ſinon exprimatur, hoc autem niſi aliter explicetur.

Pro declarandis D. & E. Defin. _8._ exponantur duæ figuræ in

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