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

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220200GEOMETRIÆ

THEOREMA II. PROPOS. II.

SI à circulo, vel ellipſi per lineam ad eorum axim, vel dia-
metrum ordinatim applicatam vtcunque portio abſcin-
datur, ſit autem parallelogrammum in eadem altitudine cum
dicta portione, ſed in baſi æquali ſecundę diametro, & regula
baſis ipſius portionis: Omnia quadrata dicti parallelogram-
miad omnia quadrata dictę pottionis erunt, vt rectangulum
ſub dimidia eiuſdem axis, vel diametri, & ſub eiuſdem dimi-
diæ tripla, ad rectangulum ſub axi, vel diametro abſciſſæ
portionis, & ſub compoſita ex axe, vel diametro reliquę por-
tionis, & dimidia totius axis, vel diametri.

Sit igitur circulus, vel ellipſis, BVOR, eius axis, vel diameter,
BO, ordinatim ad ipſum applicata, VR, vtcumq; abſcindens por-
tionem, VBR, ſit verò ſecunda diameter, CF, & producta, VR,
ita vt, PN, ſit æqualis ipſi, CF, & , PM, ipſi, CA, in baſi, PN,
& altitudine portionis, VBR, ſit parallelogrammum, DN, & cir-
ca axim, vel diametrum, BM. Dico ergo omnia quadrata paralle-
logrammi, DN, regula, VR, ad omnia quadrata portionis, VBR,
eſſe vt rectangulum ſub, BA, & tripla, AO, ad rectangulum ſub, B

133[Figure 133] M, & ſub compoſita ex, MO, OA; iun
gantur, VB, PB; Omńia ergo quadrata
ſemiportionis, BCVM, ad omnia qua-
drata trianguli, BVM, ſunt vt, AO, O
M, ad, OM, . i. ſumpta, BM, commu-
11Exant. ni altitudine, vt rectangulum ſub, BM,
MOA, ad rectangulum, BMO, omnia
225. Lib.2. autem quadrata trianguli, BVM, ad
33PerB.Co.
rollar.22.
lib.2. omnia quadrata trianguli, BPM, ſunt
vt quadratum, VM, ad quadratum, P
M, velad quadratum, CA, . i. vt rectan-
44Ex 40. l.1.
& eiuſdẽ
Scholio. gulum, OMB, ad rectangulum, OAB, ergo ex æquali, & conuer-
tendo omnia quadrata trianguli, BPM, ad omnia quadrata ſemi-
portionis, BVM, erunt vt rectangulum, BAO, ad rectangulum
5524. Lib. 2. ſub, BM, & , MOA, & antecedentium tripla. ſ. omnia quadrata
parallelogrammi, DM, ad omnia quadrata ſemiportionis, BVM,
668. Lib.2. vel omnia quadrata parallelogrammi, DN, ad omnia quadrata
portionis, VBR, erunt vt rectangulum ſub, BA, & tripla,

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