Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER V. ſolidum ſimilare quodcunque genitum ex parallelogrammo, TV,
ad ſibi ſimilare genitum ex figura, TBFHRVQIPX, demptis ſo-
lidis ſimilaribus genitis ex oppoſitis hyperbolis, AEC, MON, iux-
ta communem regulam, RV; eadem verò eſſe oſtendemus ſum-
pta pro regula ipſa, VX, & reuolutione facta circa axem, GZ.

606.1.

0444-01

607. SECTIO POSTERIOR.

IN Coroll. colligitur cylindrum, TV, ad cylindrum, TP, & , HV,
cum tympano, BFHQIP, eſſe vt cubus, YS, ad parallelepipedũ
ſub, KY, & quadrato, YS, vna cum parallelepido ſub, KS, & com-
poſito ex quadrato, SO, & {1/3}. quadrati, SK; & ſic ſolida ſimilaria ex
elſdem figuris genita iuxta ibi aſſumptam regulam, RV.

608. COROLL. XXIX. SECTIO PRIOR.

IN Propoſ. 29. viſa eius figura, eaque reuoluta circa axem, & Y,
vt in anteced. conſpicitur, patet ſolidum in reuolutione de-
ſcriptum a figura reſidua, demptis à parallelogrammo, T V, qua-
tuor hyperbolis, BFH, PIQ, AEC, MON, ad ſolidum deſ@riptum
in reuolutione ex figura reſidua, demptis à parallelogrammo, βΩ,
quatuor hyperbolis, 9F7, ΦΙΛ, L E ſ, ΣΟ3, eſſe vt parallelepipe-
dum ſub QV, & quadrato, VZ, vna cum parallelepipedo ſub, QZ,
& compoſito ex quadrato, SO, & {1/3}. quadrati, QZ, ab his dempto
parallelepipedo ſub, SO, & quadrato, OY, & {1/3}. cubi, OY, ad paral-
lelepipedum ſub, ΛΩ, & quadrato, Ω4, vna cum parallelepipedo
ſub, Λ4, & compoſito ex quadrato, SO, & {1/3}. quadrati, Λ4, dempto
parallelepido ſub, SO, & quadrato, O6, cum {1/3}. cubi, O6: Sic etiam
patet eſſe quodlibet ſolidum ſimilare genitum ex figura, TBFHR
VQIPX, demptis ſolidis ſimilaribus genitis ex opoſitis hyperbolis,
AEC, MON, ad ſibi ſimilare genitũ ex figura, B9F72ΩΛΙΦΛ, dem-
ptis ſolidis ſimilaribus genitis ex oppoſitis hyperbolis, LEF, ΣΟ3,
iuxta communem regulam, RV.

609. SECTIO POSTERIOR.

IN Coroll. colligitur eadem ſolida, genita nempè ex figuris,
TBFHRVQIPX β9F72ΩΛ ΙΦΔ, iuxta communem regulam,
RV, nihil ab eis dempto, eſſe vt dicta parallelepipeda, nihil pari-
@er ab eiſdem dempto.

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