434414GEOMETRIÆ
COROLLARIVM IV.
IN Prop.
4.
iterum aſſumpta figura Coroll.
2.
patebit cylindrũ,
293[Figure 293]
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.
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.
COROLLARIV M V.
IN Prop.
5.
aſſumpta iterum figura Prop.
2.
dimiſsis rectis, CP,
RQ, Lk, & triangulo, DM, & , vt fiat ſolitum exemplum, ea
294[Figure 294]
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.
RQ, Lk, & triangulo, DM, & , vt fiat ſolitum exemplum, ea
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.