Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

335. COROLLARIVM.

_P_ATET autem omnia quadrata, HT, ad omnia quadrata figure,
BMCP, eſſe pariter, vt quadratum, BP, ad rectangulum ſub,
BP, PA, vna cum rectangulo ſub, PA, & ſub exceſſu, quo dupla,
EI, ſuperat, EF, cum, {2/3}, quadrati, BA. Et quoniam, iuncta, BM,
oſtenſum eſt omnia quadrata, HP, ad omnia quadrata trapezij, MB,
PC, eſſe vt quadratum, BP, adrectangulum, BPA, vna cum {1/3}, qua-
drati, AB, ideò eadem omnia quadrata, HP, ad reſiduum omnium
quadratorum figuræ, quæ eiſdem, MCPB, & curua, MB, contine-
tur, demptis ab ijſdem omnibus quadratis trapezij, BMCP, erunt vt
idem quadratum, BP, ad rectangulum ſub, AP, & ſub exceſſu du-
pla, EI, ſuper, EF, vnacum, {2/3}, quadrati, BA.

335.1.

_28. Lib. 2._

336. THEOREMA XVIII. PROPOS. XIX.

EXpoſita adhuc figura Propof. 15. & intra circulum, vel
ellipſim, MBEG, ducta, RV, vtcunq; regulę, DF,
parallela, diuidente ipſum circulum, vel ellipſim in duas vt-
cunque portiones, SMT, SET. Dico omnia quadrata
portionis, SMT, cumrectangulis bis ſub eadem portione,
& ſub quadrilineo, MTVN, ad omnia quadrata portionis,
SET, cum rectangulis bis ſub eadem portione, & ſub tri-
lineis, TGV, GEF, eſſe vt portio, SMT, ad portionem,
SET.

Quoniam . n. rectangula ſub portione, SMT, & parallelogram-
mo, HV, ad omnia quadrata, HV, ſunt vt portio, SMT, ad
parallelogrammum, HV, rectangula verò ſub, SMT, & paralle-
logrammo, HV, diuiduntur in rectangula ſub, SMT, & ſub, SM
T, ideſt in omnia quadrata, SMT, & in rectangula ſub, SMT, & ſub quadrilineis, HRSM, MTVN, ideſt bis ſub, SMT, & ſub
quadrilineo, MTVN; namcum, ME, ſit diameter, bifariam di-
uidit tum ordinatim applicatas in parallelogrammo, HF, tum in
circulo, vel ellipſi, MBEG, & ideò exceſſus earundem linearum
hinc inde relinquuntur æquales, vndein quadrilineis, HRSM, M
TVN, lineæ in eadem rectitudine ſumptæ ſunt æquales, ideò om-
nia quadrata portionis, SMT, & rectangula ſub eadem, & ſub qua-

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