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

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123103LIBER II.

A. VIII.

11A.

PRopoſita quacunque plana figura, & in ea ducta vtcun-
que recta linea vſque ad ambitum hinc inde terminata,
ſi ipſa recta linea deſcribere quamcumque figuram planam
intelligatur, non exiſtentem in plano propoſitę figurę, ac de-
inde reliquæ earum, quæ dicuntur omnes lineæ propoſitæ fi-
guræ, ſumptę regula iam ducta linea (& recti tranſitus ſi de-
ſcripta figura ſit erecta plano propoſitę, veleiuſdem obliqui
tranſitus, ſi illi ſit inclinata, eius nempè tranſitus, qui fit in
tali inclinatione) deſcribere intelligantur figuras planas ſi-
miles, ac ſimiliter poſitas, & æquidiſtantes primò deſcriptę,
ita vt omnes deſcribentes ſint deſcriptarum ſigurarum lineę,
vel latera homologa; omnes deſcriptæ figuræ ſimul ſumptæ
dicentur. Omnes figuræ planæ ſimiles talis propoſitæ figurę,
ſumptæ regula earum vna, vel regula etiam ipſa linea, vel
latere deſcribente; vt ſi deſcriptæ figuræ eſſent quadrata, hæ
dicerentur. Omnia quadrata talis propoſitæ figuræ, vel ſi eſ-
ſent triangula ęquilatera dicerentur. Omnia triangula ęqui-
latera eiuſdem.

22B.

Solidum, cuius omnes deſcriptæ figuræ ſimiles ſunt om-
nia plana, dicetur: Solidum ſimilare genitum ex propoſita fi-
gura iuxta eandem regulam, iuxta quam ſumptæ omnes di-
ctæ figuræ ſimiles fuerunt, quæ igitur ex figuris propoſitis,
vt ſic generantur, dicentur abſque alio addito: Solida ſimi-
laria genita ex propoſitis figuris iuxta regulas omnium ſimi-
lium figurarum, quæ ipſorum euadunt omnia plana, propo-
ſitæ autem figuræ, eorundem genitrices figuræ vocabuntur.

33C.

Cum verò duarum genitricium vtcunq: figurarum omnes
deſcriptæ figuræ nedum ſimiles erunt: quę reperientur in ea-
rum vnaquaque, ſed etiam quæ ſunt vnius, inuenientur ſimi-
les omnibus figuris ſimilibus alterius propoſitæ figuræ, fue-
rint autem in vtroque ſolido figuræ æquè eleuatæ ſuper pla-
na genitricium figurarum, tunc ſolida genita ex propoſitis

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