Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

578. COROLLARIVM IV.

IN Prop. 4. iterum aſſumpta figura Coroll. 2. patebit cylindrũ,
SF, ad fruſtum hyperbolicum, HD
FG, ab eo dempto cylindro, HQ, eſſe
vt rectangulum, OEN, ad rectangulum
ſub compoſita ex {1/3}. EM, integra, MN,
& {1/2}. NO. Conum verò, DMF, ad idẽ
fruſtum, dempto cylindro, HQ, eſſe vt
rectangulum, OEN, ad rectangulum ſub
compoſita ex, EX, & dupla, NM: & ſic
eſſe quæcunq; ſolida ſimilaria genita ex
eiſdem figuris . ſ. parallelogrammo, SF,
fruſto hyperbolæ, HDFG, dempto ſo-
lido ſimilari genito ex, HQ, & triangu-
lo, DMF, iuxta communem regulam,
DF.

578.1.

0434-01

579. COROLLARIV M V.

IN Prop. 5. aſſumpta iterum figura Prop. 2. dimiſsis rectis, CP,
RQ, Lk, & triangulo, DM, & , vt fiat ſolitum exemplum, ea
reuoluta circa axem, NE, vt ex, A
F, fiat cylindrus, AF, ex hyperbola,
DNF, conois, DNF, quæ ſolida
ſint ſecta plano, SZ, baſi, DF, ęqui-
diſtante, patet cylindrum, AF, dẽ-
pta conoide, DNF, ad cylindrum,
SF, dempto fruſto conoidis, DHG
F, eſſe vt parallelepipedum ſub cõ-
poſita ex, XE, EN, & ſub quadrato,
NE, ad parallelepipedum ſub com-
poſita ex, XE, EN, NM, & ſub qua-
drato, ME; & ſic eſſe quodlibet
ſolidum ſimilare genitum ex, AF,
dempto ſolido ſimilari genito ex
hyperbola, DNF, ad ſibi ſimilare
genitum ex, SF, dempto ſolido ſimilari genito ex fruſto hyperbo-
læ, DHFG, iuxta communem regulam, DF.

579.1.

0434-02

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