Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER III. collectis) ad omnia quadrata figuræ, LCFEG, demptis omnibus
quadratis trilineorum, CLT, EGY, erunt vt parallelepipedum ſub
altitudine, KL, baſi parallelogrammo, KG, ad cylindricum ſub
altitudine, KL, baſi portione, TCFEY, vna cum, {1/6}, cubi, RV,
in circulo. In ellipſi autem, vt idem parallepipedum ad eundem cy-
lindricum, vna cum ea parte cubi, RV, vel parallelepipedi ſub, R
V, & rhombo, RZ, ad quam eiuſdem cubi, vel parallelepipedis ſex-
ta pars ſit, vt quadratum, CE, ad quadratum, FH: Omnia autem
quadrata, AG, ad omnia quadrata, KG, ſunt vt parallelepipedum
ſub altitudine, AL, baſi parallelogrammo, AG, ad parallelepipe-
dum ſub altitudine, LK, baſi parallelogrammo, KG, ergo ex ęqua-
li pariter omnia quadrata, AG, ad omnia quadrata figurę, LCFE
G, demptis omnibus quadratis trilineorum, CLT, EGY, erunt in
circulo, vt parallelepipedum ſub altitudine, AL, vel, FI, baſi au-
tem parallelogrammo, AG, ad cylindricum ſub altitudine, LK, vel,
MI, baſi autem portione, TCFEY, vna cum, {1/6}, cubi, RV, vel,
TY. In ellipſi verò erunt, vt parallelepipedum ſub altitudine, FI,
baſi autem parallelogrammo, AG, ad cylindricum ſub altitudine,
MI, baſi autem ipſa portione, TCFEY, vna cum ea parte cubi,
RV, vel, TY, ſiue parallelepipedi ſub altitudine, TY, & baſi rhom-
bo, RZ, ad quam eiuſdem cubi, vel parallelepipedi ſexta pars ſit, vt
quadra@um, CE, ad quadratum, FH; quod oſtendere oportebat.

342.1.

G. B. Cor.
4. Gen.
34. l. 2.
A. 23. l. 2.
36. Lib. 2.

343. THEOREMA XXII. PROPOS. XXIII.

EXpoſita figura circuli Theorematis ſuperioris, & in eo
ſumpta vtcunq; portione minori, RFV, cæteris, prout
ſtant, ſuppoſitis. Dico omnia quadrata, Δ V, ad omnia qua-
drata portionis, RFV, eſſe, vt ſexquialtera, FM, ad reli-
quum diametri, MH, maioris portionis, ab eodem dempta
recta linea, ad quam tripla, MN, ſit, vt parallelogrammum,
Δ V, ad portionem, RFV.

Rectangula enim ſub, Δ V, VT, ad omnia quadrata, RZ, ſunt vt
vnum ad vnum. i. vt rectangulum, FMI, ad quadratum, VZ, vel
ad quadratum, RV, omnia item quadrata, RZ, ſunt ſexcupla re-
ctangulorum ſub portione, RFV, & quadrilineo, RTHYV, ideſt
ſunt ad illa, vt quadratum, RV, ad ſui, {1/6}, ergo ex æquali rectan-
gula ſub, Δ V, VT, ad rectangula ſub portione, RFV, & quadri-
lineo, RTHYV, erunt vt rectang. FMI, ad, {1/6}, quadrati, RV,

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