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

124[Figure 124] V, in parallelepipedo, AM, rectan-
11Coroll. 6.
lib. I. gulum, EO, & in parallelepipedo,
NP, rectangulum, RV, per pla-
2210. Lib. 1. num igitur, EV, diuiduntur paral-
lelepipeda, AM, NP, in paralle-
pipeda, AR, BM, NQ, OP, eſt
autem totum parallelepipedum, A
P, æquale parallelepipedis, AR, B
M, NQ, OP, & eſt parallelepipe-
dum, AR, ſub, DS, SO, ideſt ſub,
DS, TV, & parallelepipedum, B
M, ſub, ER, RG, hoc eſt ſub, D
S, QH, & parallelepipedum, NQ,
eſt ſub, ST, TV, & , OP, eſt ſub,
RQ, QH, hoc eſt ſub, ST, QH,
ergo parallelepipedum, AP, ideſt
ſub, DT, TH, eſt æquale paralle-
lepipedis ſub, DS, & , TV, & ſub,
DS, VP, & ſub, ST, TV, & ſub,
ST, QH, ideſt parallelepipedis ſub
fingulis partibus altitudinis, & ſingulis partibus baſis content@s.

SCHOLIV M.

_C_Ontineri autem parallelepipedum voco ſub tribus rectis eiuſdem
angulum ſolidum continentibus, quarum dua qualibet rectum
angulum conſtituunt, ſiue ſub earum quauis, & parallelogrammo re-
ctangulo ſub reliquis duabus; ita vt, cum dico parallelepipedum ſub
tali recta linea, & tali rectangulo, ſiue ſub talibus tribus rectis lineis,
intelligam illud parallelepipedum habere angulum ſolidum rectis an-
gulis conſtitutum, veluti in iſtis Theorematibus ipſum aſſumo, igitur
patet nos ex tribus rectis parallelepipedum continentibus quamlibet
poſſe pro altitudine ſumere, & rectangulum ſub reliquis duabus pro
baſi.

THEOREMA XXXVI. PROPOS. XXXVI.

SI recta linea in vno puncto ſecta ſit vtcumq; parallelepi-
pedum ſub tota linea, & quadrato vnius factarum par-
tium erit æquale parallelepipedo ſub tali parte, &

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