9474GEOMETRIÆ
quæ in cylindricis producant figuras, IM, RT, in conicis verò, O
M, ST, ſecent verò plana tangentia in rectis, IC, MF, Od; r ℟,
Tp, So, iſtæ ergo erunt ad inuicem parallelæ, & tangent figuras,
1116. Vnd.
Elem. IM, RT, OM, ST, eadem verò planaſecent plana, BG, Zl, in
22Corol. 9.
50[Figure 50]
rectis, CF, ℟ p.
Quod ergo figuræ,
33Corol. 18. IM, RT, vel, OM, ST, ſint ſimi-
les baſibus, & ijſdem ſimiliter poſitę
44@2. Et 19.
huius. iam oſtenſum fuit, ex quo fit, vt &
ipſarum, & quarumcunq; ſic in prę-
fatis ſolidis producibilium ſimilium
figurarum homologæ duabus qui-
buſdam regulis, vt ex. gr. ipſis, HG,
Yl, ſemper æquidiſtent. Reliquum
eſt autem, vt probemus, CF, ℟ p,
vel, dF, op, eſſe prædictarum in-
cidentes. Cumergo duę, IC, CF,
duabus, LD. DG, ęquidiſtentan-
5510. Vnd.
Elem. guli, ICF, LDG, æquales erunt,
ſic etiam probabimus eſſe æquales,
R ℟ p, Xfl, cum verò, IC, ſit e-
tiam æqualis, LD, & R ℟, ipſi,
Xf, necnon, CF, ipſi, DG, & ,
℟ p, ipſi, fl, erit, IC, ad, R ℟, vt,
CF, ad, ℟ p, & incidunt ipſis, IC,
MF, R ℟, Tp, ad eundem angu-
lum ex eadem parte, ergo, CF, ℟
p, erunt incidentes ſimilium figura-
rum, IM, RT, & oppoſitarum tan-
66@4. huius. gentium, IC, MF; R ℟, Tp, ea-
dem ratione demonſtrabimus, dF,
op, eſſe incidentes ſimilium figura-
rum, OM, ST, & oppoſitarum tan-
gentium, Od, MF; So, Tp, eſt
autem, dF, ad, op, vt, dE, ad,
o & , ſcilicet, vt, DE, ad, f & , nam,
DE, f & , ſunt ſimiliter ad eandem
partem diuiſæ in punctis, do, (ete-
77@7. Vnd.
Elem. nim altitudines dictorum ſolidorum per plana, IF, Rp, ſimiliter ad
eandem partem diuiduntur) ergo, dF, op, æquidiſtantes oppoſitis
tangentibus, BE, DG, Z & , fl, ſunt homologæ figurarum ſimi-
lium, EDG, & fl, quarum & oppoſitarum tangentium incidentes
erunt ipſæ, ED, & f. Eodem modo oſtendemus, CF, ℟ p,
M, ST, ſecent verò plana tangentia in rectis, IC, MF, Od; r ℟,
Tp, So, iſtæ ergo erunt ad inuicem parallelæ, & tangent figuras,
1116. Vnd.
Elem. IM, RT, OM, ST, eadem verò planaſecent plana, BG, Zl, in
22Corol. 9.
33Corol. 18. IM, RT, vel, OM, ST, ſint ſimi-
les baſibus, & ijſdem ſimiliter poſitę
44@2. Et 19.
huius. iam oſtenſum fuit, ex quo fit, vt &
ipſarum, & quarumcunq; ſic in prę-
fatis ſolidis producibilium ſimilium
figurarum homologæ duabus qui-
buſdam regulis, vt ex. gr. ipſis, HG,
Yl, ſemper æquidiſtent. Reliquum
eſt autem, vt probemus, CF, ℟ p,
vel, dF, op, eſſe prædictarum in-
cidentes. Cumergo duę, IC, CF,
duabus, LD. DG, ęquidiſtentan-
5510. Vnd.
Elem. guli, ICF, LDG, æquales erunt,
ſic etiam probabimus eſſe æquales,
R ℟ p, Xfl, cum verò, IC, ſit e-
tiam æqualis, LD, & R ℟, ipſi,
Xf, necnon, CF, ipſi, DG, & ,
℟ p, ipſi, fl, erit, IC, ad, R ℟, vt,
CF, ad, ℟ p, & incidunt ipſis, IC,
MF, R ℟, Tp, ad eundem angu-
lum ex eadem parte, ergo, CF, ℟
p, erunt incidentes ſimilium figura-
rum, IM, RT, & oppoſitarum tan-
66@4. huius. gentium, IC, MF; R ℟, Tp, ea-
dem ratione demonſtrabimus, dF,
op, eſſe incidentes ſimilium figura-
rum, OM, ST, & oppoſitarum tan-
gentium, Od, MF; So, Tp, eſt
autem, dF, ad, op, vt, dE, ad,
o & , ſcilicet, vt, DE, ad, f & , nam,
DE, f & , ſunt ſimiliter ad eandem
partem diuiſæ in punctis, do, (ete-
77@7. Vnd.
Elem. nim altitudines dictorum ſolidorum per plana, IF, Rp, ſimiliter ad
eandem partem diuiduntur) ergo, dF, op, æquidiſtantes oppoſitis
tangentibus, BE, DG, Z & , fl, ſunt homologæ figurarum ſimi-
lium, EDG, & fl, quarum & oppoſitarum tangentium incidentes
erunt ipſæ, ED, & f. Eodem modo oſtendemus, CF, ℟ p,