442422GEOMETRIÆ
ſimilare genitum ex figura, DAFEVC, iuxta communem regu-
lam, FE.
lam, FE.
COROLL. XXII. SECTIO PRIMA.
IN Prop.
22.
ſi in ſuperioris figura ſupponamus, FR, eſſe æqua-
lem ei, quæ tangens ſectionem, DAF, in, A, concluditur in-
ter, A, & aſymptoton, ON, habetur cylindrum, DE, eſſe ſexquial-
terum tympani hyperbol ci, DAFEVC, & hoc tympanũ eſſe qua-
druplum conorum, NOY, HOS, & ſic eſſe ſolida ſimilaria ex
eiſdem figuris genita iuxta communem regulam, DC.
lem ei, quæ tangens ſectionem, DAF, in, A, concluditur in-
ter, A, & aſymptoton, ON, habetur cylindrum, DE, eſſe ſexquial-
terum tympani hyperbol ci, DAFEVC, & hoc tympanũ eſſe qua-
druplum conorum, NOY, HOS, & ſic eſſe ſolida ſimilaria ex
eiſdem figuris genita iuxta communem regulam, DC.
SECTIO II.
IN Coroll.
1.
habetur cylindrum, DE, ad tympanum hyperbo-
licum, DAFEVC, demptis conis oppoſitis, HOS, NOY, eſſe
vt quadratum, DC, ad quadratum, AV, & in caſu præſentis Prop.
eſſe eorum dupla, & ſic ſolida ſimilaria, & c.
licum, DAFEVC, demptis conis oppoſitis, HOS, NOY, eſſe
vt quadratum, DC, ad quadratum, AV, & in caſu præſentis Prop.
eſſe eorum dupla, & ſic ſolida ſimilaria, & c.
SECTIO III.
IN Coroll.
2.
diſcimus inuenire cylindrum deſcriptum à paral-
lelogrammo ſectionibus oppoſitis circumſcripto, vt ibi dicitur,
quod ad reliquum tympani hyperbolici, demptis oppoſitis conis,
habeatrationem datam, dummodo ea ſit maioris inæqualit. idem
intellige de ſol dis ſimilaribus, & c.
lelogrammo ſectionibus oppoſitis circumſcripto, vt ibi dicitur,
quod ad reliquum tympani hyperbolici, demptis oppoſitis conis,
habeatrationem datam, dummodo ea ſit maioris inæqualit. idem
intellige de ſol dis ſimilaribus, & c.
COROLLARIVM XXIII.
IN Prop.
23.
aſſumpta eius figura, &
,
305[Figure 305]
vt fiat exemplum, ea circa axim, RZ,
reuoluta, vt ex, FC, fiat cylindrus, FC, &
ex, TN, cylindrus, TN, & ex oppoſitis,
hyperbolis, FAD, EVC, oppoſitæ conoi-
des, FAD, EVC, & ex, TAY, MVN, op-
poſitæ, conoides, TAY, MVN, patet er-
go cylindrum, FC, demotis oppoſitis co-
noidibus, FAD, EVC, ad cylindrum, TN,
demptis oppoſitis conoidibus, TAX, MV
N, eſſe vt parallelepipedum ſub, ZV, &
baſirectangulo, VOZ, cum {1/3}. quadrati,
ZV, ad parallelepipedum ſub, ZV, baſi
rectangulo, VOS, cum {1/3}. quadrati, SV, &
reuoluta, vt ex, FC, fiat cylindrus, FC, &
ex, TN, cylindrus, TN, & ex oppoſitis,
hyperbolis, FAD, EVC, oppoſitæ conoi-
des, FAD, EVC, & ex, TAY, MVN, op-
poſitæ, conoides, TAY, MVN, patet er-
go cylindrum, FC, demotis oppoſitis co-
noidibus, FAD, EVC, ad cylindrum, TN,
demptis oppoſitis conoidibus, TAX, MV
N, eſſe vt parallelepipedum ſub, ZV, &
baſirectangulo, VOZ, cum {1/3}. quadrati,
ZV, ad parallelepipedum ſub, ZV, baſi
rectangulo, VOS, cum {1/3}. quadrati, SV, &
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