444424GEOMETRIÆ
drum, FC, in figura Coroll.
23.
demptis oppoſitis conoidibus, F
AD, EVC, ad tympanum hyperbolicum genitum ex figura, EVC
DAF, in figura Coroll. 24. ſcilicet ad tympanum hyperbolicum,
EVCDAF, habere rationem compoſitam ex ratione rectanguli,
AOZ, bis cum {2/3}. quadrati, VZ, ad rectangulum, AZO, & ex ra-
tione rectanguli ſub, DC, vel, RZ, & ſub, EC, ad quadratum, A
V, cum {1/3}. quadrati, KI, vel cum rectangulo ſub, AZ, & ſexqui.
tertia, ZV, & ſic eſſe quodlibet ſolidum ſimilare genitum ex, FC,
de@nptis ſolidis ſimilaribus genitis ex oppoſitis hyperbolis, FAD,
EVC, iuxta communem regulam, EC, ad ſolidum ſimilare ſibi
genitum ex figura, EVCDAF, iuxta regulam, CD.
AD, EVC, ad tympanum hyperbolicum genitum ex figura, EVC
DAF, in figura Coroll. 24. ſcilicet ad tympanum hyperbolicum,
EVCDAF, habere rationem compoſitam ex ratione rectanguli,
AOZ, bis cum {2/3}. quadrati, VZ, ad rectangulum, AZO, & ex ra-
tione rectanguli ſub, DC, vel, RZ, & ſub, EC, ad quadratum, A
V, cum {1/3}. quadrati, KI, vel cum rectangulo ſub, AZ, & ſexqui.
tertia, ZV, & ſic eſſe quodlibet ſolidum ſimilare genitum ex, FC,
de@nptis ſolidis ſimilaribus genitis ex oppoſitis hyperbolis, FAD,
EVC, iuxta communem regulam, EC, ad ſolidum ſimilare ſibi
genitum ex figura, EVCDAF, iuxta regulam, CD.
COROLLARIVM XXVII.
IN Prop.
27.
conſpecta figura Coroll.
21.
intelligantur deſcri-
ptæ ſectiones, BIG, kMP, quæ dicuntur coniugatæ ſectioni-
bus, DAF, CVE, ex quibus in reuolutione genitæ fuerint oppoſi-
tæ conoides, B G, kMP, patet igitur cylindrum, DE, ad tympa-
num hyperbolicum, DAF, EVC, demptis oppoſitis conoidibus,
BIG, KMP, eſſe vt parallelepipedum ſub, ZC, & ſub quadrato, Z
Q (quæ habetur extenſa, ZC, ad aſymptoton producta . ſ. ad, OS,
cu@occurrat in, Q,) a@ parallele ipedum bis ſub, XM, & quadra-
to, MO, cum cubo, MO, & amplius {1/3}. eiuſdem cubi; & ſic eſſe
quodlibet ſolidum ſimilare genitum ex, FC, ad ſibi ſimlare g@nitũ
ex figura, DAFEVC, demptis ſolidis ſimilaribus genitis ex oppo-
ſitis hyperbolis, BIG, KMP, iuxta cõmunẽ regulam, FE, vel, AV.
ptæ ſectiones, BIG, kMP, quæ dicuntur coniugatæ ſectioni-
bus, DAF, CVE, ex quibus in reuolutione genitæ fuerint oppoſi-
tæ conoides, B G, kMP, patet igitur cylindrum, DE, ad tympa-
num hyperbolicum, DAF, EVC, demptis oppoſitis conoidibus,
BIG, KMP, eſſe vt parallelepipedum ſub, ZC, & ſub quadrato, Z
Q (quæ habetur extenſa, ZC, ad aſymptoton producta . ſ. ad, OS,
cu@occurrat in, Q,) a@ parallele ipedum bis ſub, XM, & quadra-
to, MO, cum cubo, MO, & amplius {1/3}. eiuſdem cubi; & ſic eſſe
quodlibet ſolidum ſimilare genitum ex, FC, ad ſibi ſimlare g@nitũ
ex figura, DAFEVC, demptis ſolidis ſimilaribus genitis ex oppo-
ſitis hyperbolis, BIG, KMP, iuxta cõmunẽ regulam, FE, vel, AV.
IN Prop.
28.
illius aſſumpta figu-
307[Figure 307]
ra, eadem reuoluatur circa axẽ,
& Y, vel, GZ, ſit autem reuolutio
circa, & Y; patet ergo cylindrum ge-
nitum ex, TV, nempè, TV, ad reli-
quum, ab eodem demptis ſolidis ge
nitis ex quatuor hyperbolis coniu-
gatis, BFH, PIQ, AEC, MON, eſſe
vt cubus, ZV, vel, SY, ad parallele-
pipedum ſub, QV, & quad. ZV, vna
cum parallelepipedo ſub, ZQ, & ſub
compoſito ex {1/3}. quadrati, ZQ, &
qua@rato, SO, ab his tamen dempto
parallelepipedo ſub, SO, & quadra
to, OY, cum {1/3}. cubi, OY, & ſic
& Y, vel, GZ, ſit autem reuolutio
circa, & Y; patet ergo cylindrum ge-
nitum ex, TV, nempè, TV, ad reli-
quum, ab eodem demptis ſolidis ge
nitis ex quatuor hyperbolis coniu-
gatis, BFH, PIQ, AEC, MON, eſſe
vt cubus, ZV, vel, SY, ad parallele-
pipedum ſub, QV, & quad. ZV, vna
cum parallelepipedo ſub, ZQ, & ſub
compoſito ex {1/3}. quadrati, ZQ, &
qua@rato, SO, ab his tamen dempto
parallelepipedo ſub, SO, & quadra
to, OY, cum {1/3}. cubi, OY, & ſic