Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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<
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note
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xml:space
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">PRopoſita quacunque plana figura, & </
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<
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xml:space
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">in ea ducta vtcun-
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que recta linea vſque ad ambitum hinc inde terminata,
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ſi ipſa recta linea deſcribere quamcumque figuram planam
<
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intelligatur, non exiſtentem in plano propoſitę figurę, ac de-
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inde reliquæ earum, quæ dicuntur omnes lineæ propoſitæ fi-
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guræ, ſumptę regula iam ducta linea (& </
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<
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xml:space
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">recti tranſitus ſi de-
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ſcripta figura ſit erecta plano propoſitę, veleiuſdem obliqui
<
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tranſitus, ſi illi ſit inclinata, eius nempè tranſitus, qui fit in
<
lb
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tali inclinatione) deſcribere intelligantur figuras planas ſi-
<
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miles, ac ſimiliter poſitas, & </
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>
<
s
xml:id
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xml:space
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">æquidiſtantes primò deſcriptę,
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ita vt omnes deſcribentes ſint deſcriptarum ſigurarum lineę,
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vel latera homologa; </
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<
s
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xml:space
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">omnes deſcriptæ figuræ ſimul ſumptæ
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dicentur. </
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<
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xml:space
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">Omnes figuræ planæ ſimiles talis propoſitæ figurę,
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ſumptæ regula earum vna, vel regula etiam ipſa linea, vel
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latere deſcribente; </
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<
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xml:space
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">vt ſi deſcriptæ figuræ eſſent quadrata, hæ
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dicerentur. </
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ſent triangula ęquilatera dicerentur. </
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latera eiuſdem.</
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<
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xml:space
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head
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<
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xml:space
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">B.</
note
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<
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<
s
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xml:space
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">Solidum, cuius omnes deſcriptæ figuræ ſimiles ſunt om-
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nia plana, dicetur: </
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<
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">Solidum ſimilare genitum ex propoſita fi-
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gura iuxta eandem regulam, iuxta quam ſumptæ omnes di-
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ctæ figuræ ſimiles fuerunt, quæ igitur ex figuris propoſitis,
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vt ſic generantur, dicentur abſque alio addito: </
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<
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xml:space
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laria genita ex propoſitis figuris iuxta regulas omnium ſimi-
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lium figurarum, quæ ipſorum euadunt omnia plana, propo-
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ſitæ autem figuræ, eorundem genitrices figuræ vocabuntur.</
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<
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xml:space
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">C.</
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<
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xml:space
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">C.</
note
>
<
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<
s
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xml:space
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">Cum verò duarum genitricium vtcunq: </
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<
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deſcriptæ figuræ nedum ſimiles erunt: </
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<
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rum vnaquaque, ſed etiam quæ ſunt vnius, inuenientur ſimi-
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les omnibus figuris ſimilibus alterius propoſitæ figuræ, fue-
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rint autem in vtroque ſolido figuræ æquè eleuatæ ſuper pla-
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na genitricium figurarum, tunc ſolida genita ex propoſitis </
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