Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

Sint cylindrici quicunque, AH, KY; ſeu conici in ijſdem baſibus,
& altitudinibus (vt vna vice vtriuſq; demonſtrationem abſoluamus)
NLH, VXY, ſimiles iuxta definit. 7. huius. Dico eoſdem etiam
eſſe ſimiles iuxta definit. 11. Quoniam ergo vtraque prædicta ſolida
ſunt ſimilia, erunt baſes, LH, XY, ſimiles, ducantur earum oppo-
ſitę tangentes, quę ſint homologarum regulę, ipſę, LD, HG, X f,
Y l, quarum, & prædictarum ſimi-
lium figurarum incidentes ſint ipſæ,
DG, f l, quæ etiam pro regulis alia-
rum homologarum ſumi poterunt,
ſint ergo duę quæcunque homologę
parallelę incidentibus, D G, fl, ip-
ſæ, LH, XY, ſi ergo per has, & la-
tera cylindricorum, vel conicorum
iam dictorum extendantur plana, ab
ijs producentur in cylindricis ſimilia
parallelogramma, & in conicis ſimi-
lia triangula, quę etiam erunt ad ba-
ſes æquè ad eandem partem inclina-
ta. Extendantur ergo per oppoſitas
tangentes, LD, HG; Xf, Yl, pla-
na tangentia tam cylindricos, quam
conicos iam dictos, & hęc ſimul cum
planis baſium indefinitè producan-
tur ad partes incidentium, DG, fl,
& tandem per, DG, fl, cum ſint
parallelæ, extendantur plana ipſis,
AH, KY, parallela ſecantia iam pro-
ducta plana in rectis, DG, GE, E
B, BD, DE, fl, l & , & Z, Zf, f
& , erunt ergo parallelepipeda, AG,
Kl, & priſmata, LNGD, XVlf,
ergo erit parallelogrammum, BG,
ſimile ipſi, AH, & , Zl, ſimile, K
Y, quæ cum ſint inter ſe ſimilia, e-
tiam, BG, Zl, erunt ſimilia, ſic e-
tiam oſtendemus triangula, EDG,
& fl, eſſe ſimilia, ſub intellige iuxta
definitionem Euclidis, ergo erunt e-
tiam ſimilia iuxta defin. 10. Ducantur duo plana oppoſitis tangenti-
bus intermedia, ac parallela, altitudines dictorum ſolidorum reipectu
baſium, LH, XY, ſumptas, ſimiliter ad eandem partem diuidentia,

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