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

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142122GEOMETRIÆ poſitas, ex quibus ſumantur quotcunque partes æquales, AI, IH,
nempè æquales ipſi, CA, & , BP, æqualis ipſi, BC, & complean-
tur parallelogramma, AM, IK, BQ; ſunt igitur parallelogramma,
CF, AM, IK, in æqualibus altitudinibus, ac baſibus, & ideò ſin-
gulorum omnia quadrata regulis eiſdem baſibus, erunt æqualia, &
119. Huius pari ratione omnia quadrata parallelogrammorum, BQ, CQ, e-
runt ęqualia, regula, CD, altitudines autem parallelogrammorum,
CF, AM, IK, ſunt æquales ipſi, AO, & altitudines parallelogram-
morum, CE, BQ, ſunt æquales, nempè ipſi, CN, habemus ergo
æquèmultiplices primę, & tertiæ . ſ. compoſitum ex altitudinibus pa-
rallelogrammorum, CF, AM, IK, quod tam multiplex eſt altitu-

82[Figure 82] dinis, AO, quam compoſitum ex omnibus qua-
dratis, CF, AM, IK, multiplex eſt omnium
quadratorum parallelogrammi, CF, & ſic com-
poſitum ex altitudinibus parallelogrammorum,
CE, BQ, tam multiplex eſt altitudinis, CN,
ac compoſitum ex omnibus quadratis parallelo.
grammorum, BQ, CE, multiplex eſt omnium
quadratorum, CE; ideſt quam multiplicia ſunt
omnia quadrata parallelogrammi, HD, omnium quadratorum pa-
rallelogrammi, AD, tam altitudo parallelogrammi, HD, multi-
plex eſt altitudinis parallelogrammi, AD, ſiue tam ipſa, CH, mul-
tiplex eſt ipfius, CA, dum ſunt æquiangula, & quam omnia qua-
drata parallelogrammi, PD, multiplicia ſunt omnium quadratorum
parallelogrammi, BD, tam altitudo parallelogrammi, PD, mul-
tiplex eſt altitudinis, CN, vel tam, PC, multiplex eſt ipſius, CB:
Si autem multiplex primæ fuerit æquale multiplici ſecundæ, etiam
multiplex tertiæ erit æquale multiplici quartæ, ſi maius maius, & ſi
minus minus, nam ſi altitudo parallelogrammi, HD, fuerit æqua-
lis altitudini parallelogrammi, DP, omnia quadrata, HD, erunt
æqualia omnibus quadratis, DP, nam parallelogramma, HD, D
P, ſunt in eadem baſi, CD, ſi illa maior, & hæc maiora, & ſi mi-
22Exautec. nor minora, ergo prima ad ſecundam erit, vt tertia ad quartam,
335. Quinti
Elem. nempè vt altitudo parallelogrammi, AD, ad altitudinem paralle-
logrammi, DB, . ſ. AO, ad, CN, vel, AC, ad, CB, dum ſunt
æquiangula, ita erunt omnia quadrata, AD, ad omnia quadrata,
DB, ſunt ergo, vt altitudines ipſorum parallelogrammorum, vel
vt latera ęqualiter baſi inclinata, cum nempè parallelogramma ſunt
æquiangula: hæc autem etiam verificarentur ſi parallelogramma
eſſent in æqualibus baſibus, quod oſtendere opus erat.

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