441421LIBER V.
COROLLARIVM XX.
IN Prop.
20.
expoſita eius figura, &
vt fiatſolitum exemplum;
ea circa axim, FE, reuoluta, vt ex, BE, fiat cylindrus, BC, &
303[Figure 303]
ex oppoſitis hyperbolis, BND, AM
C, fiant conoides, BND, AMC, quę
pariter dicantur; Conoides oppoſitę,
Pitet cylindrum, BC, ad reliquum,
demptis ab eodem oppoſitis cono@di-
bus, AMC, BND, eſſe vt rectangulũ,
NEO, ad rectangulum, NOE, bis,
cum {2/3}. quadrati, ME; & ſic eſſe quod-
libet lolidum ſimilare genitum ex, B
E, ad reliquum, demptis ab e@dem
ſolid@s ſimilaribus gen tis ex ſemihy-
perbolis, BNF, AME, vel ſic ſolidum
quodlibet ſimilare genitum ex, BC, ad
relliquum ab eodem, dempt@s ſolidis
ſimilaribus genitis ex hyperbolis op-
poſitis, BND, AMC, iuxta commu-
nem regulam, AC.
ea circa axim, FE, reuoluta, vt ex, BE, fiat cylindrus, BC, &
C, fiant conoides, BND, AMC, quę
pariter dicantur; Conoides oppoſitę,
Pitet cylindrum, BC, ad reliquum,
demptis ab eodem oppoſitis cono@di-
bus, AMC, BND, eſſe vt rectangulũ,
NEO, ad rectangulum, NOE, bis,
cum {2/3}. quadrati, ME; & ſic eſſe quod-
libet lolidum ſimilare genitum ex, B
E, ad reliquum, demptis ab e@dem
ſolid@s ſimilaribus gen tis ex ſemihy-
perbolis, BNF, AME, vel ſic ſolidum
quodlibet ſimilare genitum ex, BC, ad
relliquum ab eodem, dempt@s ſolidis
ſimilaribus genitis ex hyperbolis op-
poſitis, BND, AMC, iuxta commu-
nem regulam, AC.
COROLLARIVM XXL
IN Prop.
21.
expoſita eius figura, &
ea circa axim, LX, reuo-
luta, vt ex, DX, fiat cylindrus, DE, & ex figura, DAFEVC,
304[Figure 304]
ſolidum, DAFEVC,
quod vocetur: @ym-
panum hyperbolicũ:
& ex triangulis, HL
O, OXN, oppoſit
coni, HOS, NOY,
patet cylindrum, D
E, adtympanum, D
AFEVC, eſſe vt qua-
dratum, FE, ad qua
dratum, AV, cum1.
quadrat@ HS,. Ve (vt aliter ibiexplicatur) vt quadratum, RZ,
ad quadratum, AV, vna cum rectangulo ſub, AZ, & rexquitertia,
ZV; & ſic eſſe quod@bet ſolidum ſimilare genitum ex, DE, ad
luta, vt ex, DX, fiat cylindrus, DE, & ex figura, DAFEVC,
quod vocetur: @ym-
panum hyperbolicũ:
& ex triangulis, HL
O, OXN, oppoſit
coni, HOS, NOY,
patet cylindrum, D
E, adtympanum, D
AFEVC, eſſe vt qua-
dratum, FE, ad qua
dratum, AV, cum1.
quadrat@ HS,. Ve (vt aliter ibiexplicatur) vt quadratum, RZ,
ad quadratum, AV, vna cum rectangulo ſub, AZ, & rexquitertia,
ZV; & ſic eſſe quod@bet ſolidum ſimilare genitum ex, DE, ad
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