Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

379359LIBER IV. uicẽ, vt ſemianulos ſtrictos parabolicos ex parabolis, DBF, NBC,
genitos in reuolut. circa, CF, & ſic ſolida ſimiliaria, & c. & vtroſq;
ſemianulos parabolicos, ſiue latos, ſiue ſtrictos eſſe ad inuicom, vt
cubi dictarum parabolarum baſium, DF, NO, & ſic etiam ſolida
ſimilaria, & c.

IN Prop. 41. viſis adhuc fig. Cor. 10. & 12. ſuperiorum, patet
ſemibaſim columnarem ſtrictam parabolicam genitam in re-
uolutione ex figura, CBDF, ad ſemibaſim columnarem latam pa-
rabol cam genitam ex figura, CBNP, eſſe vt parallelepipedum
ſub, BE, & {1/2} {7/4}. quadrati ipſius, DF, ad parallelepipedum ſub, BX,
& his ſpatijs. ſ@ quadrato, XP, {1/2}. quadrati, NX, & rectangulo ſub
ſexquitertia, NX, & ſub, XP; & ſic etiam eſse quodlibet ſolidum
ſimilare genitum ex figura, CBDF, ad ſolidum ſibi ſimilare genitũ
ex figura, CBNP, iuxta communem regulam, DF, patet inſuper
ſemibaſim columnarem latam parabolicam genitam in reuolutio-
ne circa, HM, ex figura, DBHM, ad ſemibaſim columnarem latã
parabolicam genitam ex figura, HBNV, eſse vt parallelepipedum
ſub, BE, & his ſpatijs . ſ. quadrato. ME, {1/2}. quadrati, ED, & rectã-
gulo ſub ſexquitertia, DE, & ſub, EM, ad parallelepipedum ſub, B
X, & his ſpatijs . ſ. quadrato, VX, {1/2}. quadrati, XN, & rectangulo
ſub ſexquitertia, NX, & ſub, XV; & ſic etiam eſſe ſolidum ſimila-
re quodcunq; genitum ex figura, HBDM, ad ſolidum ſibi ſimila-
re genitum ex figura, HBNV, iuxta communem regulam, DM.

IN Prop. 42. aſſumpta figura, quæ ad ipſum pertinet . ſ. paralle-
logrãmo, AF, & ſruſto parab læ maiori illi incluſo . ſ. EBHF,

259[Figure 259] vt fiat noſtrum exẽ
plũ reuoluatur, AF,
eirca manẽtẽ axim,
CF, fiat autem ex,
AF, cylindrus, AN,
& ex figura, HBCF,
ſolidum, HBON,
quod vocetur: ſemi-
baſis collumnaris
media parabolica, & extenſo plano, AF, macſimiè producatur