433413LIBER V.
COROLLARIVM II.
INProp.
2.
aſſumpta eius figura, dimiſſis parallelogrammis, A
Z, CG, & rectis, CH, RG, LK, vt fiat noſtrum exemplum re-
291[Figure 291]
uoluatur figura circa manentem axim,
NE, vt fiat ex parallelogrammo, SF, cy,
lindrus, SF, ex triangulo, DMF, conus-
DMF, & ex hyperbolis, DNF, HNG,
conoides hyperbolicæ, DNF, HNG,
patet ergo ex hac Propoſ. conoidem, D
NF, ad conoidem, HNG, abſciſſam pla-
no, HG, æquidiſtanteipſi plano, DF,
eſſe vt parallelepipedũ ſub, XE, & qua-
drato, EN, ad parallelepipedum ſub, X
M, & quadrato, MN, & ſic eſſe quod-
libet ſolidum ſimilare genitum ex hy-
perbola, DNF, ad ſibi ſimilare genitũ
ex hyperbola, HNG, iuxta communem
regulam, DF.
Z, CG, & rectis, CH, RG, LK, vt fiat noſtrum exemplum re-
NE, vt fiat ex parallelogrammo, SF, cy,
lindrus, SF, ex triangulo, DMF, conus-
DMF, & ex hyperbolis, DNF, HNG,
conoides hyperbolicæ, DNF, HNG,
patet ergo ex hac Propoſ. conoidem, D
NF, ad conoidem, HNG, abſciſſam pla-
no, HG, æquidiſtanteipſi plano, DF,
eſſe vt parallelepipedũ ſub, XE, & qua-
drato, EN, ad parallelepipedum ſub, X
M, & quadrato, MN, & ſic eſſe quod-
libet ſolidum ſimilare genitum ex hy-
perbola, DNF, ad ſibi ſimilare genitũ
ex hyperbola, HNG, iuxta communem
regulam, DF.
COROLLARIVM III.
IN Prop.
3.
patet in ſuperioris figura, in qua eius exemplum
conſtructum eſt, cylindrum, SF, ad fruſtum conoidis, HDFG,
eſſe vt rectangulum, OEN, ad rectangulum ſub, OE, & , NM,
vna cum rectangulo ſub compoſita ex {1/2}. NO, & {1/3}. ME, & ſub, M
E. Et conum, DMF, ad idem fruſtum eſſe, vt rectangulum, OE
N, ad rectangulum ſub, OE, & tripla, NM, vna cum rectangulo
ſub compoſita ex, NX, & , ME, & ſub, ME; & ſic eſſe ſolida ſi-
milaria quæcunq; genita ex eiſdem figuris, parallelogrammo nẽ-
pè, SF, fruſto hyperbolæ, HDFG, & triangulo, DMF, iuxta cõ.
munem regulam, DF.
conſtructum eſt, cylindrum, SF, ad fruſtum conoidis, HDFG,
eſſe vt rectangulum, OEN, ad rectangulum ſub, OE, & , NM,
vna cum rectangulo ſub compoſita ex {1/2}. NO, & {1/3}. ME, & ſub, M
E. Et conum, DMF, ad idem fruſtum eſſe, vt rectangulum, OE
N, ad rectangulum ſub, OE, & tripla, NM, vna cum rectangulo
ſub compoſita ex, NX, & , ME, & ſub, ME; & ſic eſſe ſolida ſi-
milaria quæcunq; genita ex eiſdem figuris, parallelogrammo nẽ-
pè, SF, fruſto hyperbolæ, HDFG, & triangulo, DMF, iuxta cõ.
munem regulam, DF.