Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ libet portiones extra figuram ad oppoſita latera terminan-
tes, & in eadem recta linea conſtitutæ integræ, & inter ſe
æquales: Omnia quadrata dicti parallelogrammi ad omnia
quadrata inſcriptæ figuræ, cum rectangulis bis ſub eadem
figura, & ſub dictarum portionum ijs omnibus, quę extra fi-
guram ad vnum dictorum laterum oppoſitorum eiuſdem pa-
rallelogrammi terminantur, erunt vt prædictum parallelo-
grammum ad inſcriptam figuram.

Sitigitur parallelogrammum, AN, & illi inſcripta vtcunq; figu-
ra, BDMO, & ſumpta pro regula, EN, ſit ducta vtcunque intra
parallelogrammum, AN, ipſa, DO, quę cadat etiam tota intra fi-
guram, BDMO, ſit etiam ducta alia vtcunque parallela ipſi, EN,
nempè, VR, portiones autem eiuſdem, VR, ſint extra figuram,
ad latera oppoſita, AE, CN, terminantes . ſ. VI, SR, quæ ſint in-
tegræ, & inter ſe æquales. Dico omnia quadrata, AN, ad omnia
quadrata figuræ, BDMO, cum rectangulis bis ſub figuræ, BDM
O, & ſub trilineis, BCO, ONM, . i. ſub omnibus portionibus, quę
terminant ad latus, CN, extra figuram, BDMO, conſtitutis, elie
vt, AN, ad figuram, BDMO: Omnia
enim quadrata, AN, ad rectangula ſub,
A N, & ſub figura, BDMO, ſunt vt, A
N, ad figuram, BDMO, ſed rectangula
ſub, AN, & ſub figura, BDMO, diui-
duntur in rectangula ſub eadem figura, B
D MO, & ſub trilineis, BAD, DEM,
ſub eadem, & ſub trilineis, BCO, ON
M, & in rectangula ſub eadem in eandem
figuram . ſ. in omnia quadrata eiuſdem fi-
guræ, BDMO, quia verò linearum æqui-
diſtantium, regulæ, EN, portiones, quæ
ſunt in eadem recta linea extra figuram adiacentes lateribus oppoſi-
tis, AE, CN, ſunt & integræ, & æquales, ideò ſicuti rectangu-
lum, VIS, eſt æquale rectangulo, ISR, ita rectangula ſub figura,
B DMO, & trilineis, BAD, DEM, erunt æqualia rectangulis
ſub eadem figura, BDMO, & ſub trilineis, BCO, ONM, ſunt
ergo rectangula ſub, AN, & ſub figura, BDMO, æqualia om-
nibus quadratis figuræ, BDMO, cum rectangulis bis ſub eadem,
& ſub trilineis, BCO, ONM; omnia autem quadrata, AN, ad
rectangula ſub, AN, & ſub figura, BDMO, ſunt vt, AN, ad fi-
guram, BDMO; ergo omnia quadrata, AN, ad omnia quadra-

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