Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ omnia quadrata, EG, regula, FG, ſunt in ratione compoſita ex
ratione quadrati, BC, ad quadratum, FG, & ex ratione, DC, ad,
HG, ſiue, BC, ad, FG, . i. in ratione compoſita ex tribus rationi-
bus, BC, ad, FG, ideſt habent eandem rationem, quam, BC, ad
quartam propo tionalem duarum, quarum prima, BC, ſecunda eſt,
FG, . . ſunt in tripla ratione eius, quam habet, BC, ad, FG, quod
erat oſtendendum.

194.1.

Tux. diff. 1.
Sex. El.
0145-01
Ex def. 1.
Sex. El.
11. huius.
Defin. 11.
Quin. El.
Defin. 11.
Quin. El.

195. COROLLARIVM.

_H_Inc patet, quod eodem modo idem oſtendemus de omnibus quibuſ-
uis alijs figuris ſimilibus parallelogrammorum, AC, EG vice
quadratorum ſumptis, regulis eiſdem, ex ſuperioribus Corollarijs id de-
ducentes.

196. THEOREMA XIV. PROPOS. XIV.

SI duo parallelogramma fuerint in eadem altitudine con-
ſtituta, omnes figuræ ſimiles vnius ad omnes figuras ſi-
miles alterius, etiamſi ſint diffimiles primò dictis, regulis ba-
ſibus, iuxta quas altitudo ſumitur, erunt, vt figura deſcripta
à baſi parallelogrammi primò dicti ad figuram deſcriptam à
baſi parallelogrammi ſecundò dicti.

196.1.

A. Def. 8.
huius.

Sint parallelogramma in eadem altitudine conſtituta, AE, EC. Dico omnes figuras ſimiles parallelogrammi, AE, ad omnes figu-
ras ſimiles parallelogrammi, EC, etiamſi ſint diſſimiles prædictis,
eſſe vt figura deſcripta à, DE, ad figuram deſcriptam ab, EF, quæ
ſunt baſes, iuxta quas ſumitur dictorum paral-
lelogrammorum altitudo . ſ. ex. g. omnia qua-
drata, AE, ad omnes circulos, EC, eſſe vt
quadratum, DE, ad circulum deſcriptum ab,
EF. Ducta enim ipſa, HN, vtcunque paral-
lela, DF, reperiemus, vt figura, DE, ad fi-
guram, EF, ita eſſe figuram, HM, ad figu-
ram, MN, quia quæ deſcribuntur lateribus,
HM, DE, equalibus ſunt ęquales, veluti de
ſcriptę à lateribus, MN, EF, pariter ſunt æquales, & ideò, vt vnum
ad vnum, ſic omnia ad omnia . ſ. vt figura deſcripta à, DE, ad figu-
rain deſcriptam ab, EF, ſic erunt omnes figuræ ſimiles parallelo-

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