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

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284264GEOMETRI Æ
COROLL. VI. SECTIO PRIOR.
IN Propoſ. ſexta, & eiuſdem figura apparet ſolidum ſimilare ge-
177[Figure 177] nitum ex circulo, vel ellipſi, ABC
D, ſiue ſit ſphæra, vel ſphæroides, vel
tantum ſolidum ſimilare, ad ſolidum ſibi
ſimilare genitum ex altera portionum, B
AD, BCD, vtramuis, vtex, BAD,
ſiue hoc ſit portio ſphæræ, vel ſphæroi-
dis, vel tantum ſolidum ſimilare genitum
ex, BAD, eſſe vt parallelepipedum ſub
altitudine, XC, baſi quadrato, CA, ad
parallelepipedum ſub altitudine, XE, baſi
quadrato, EA, vel vt cubus, AC, ad pa-
rallelepipedum ſub altitudine tripla, EC,
baſi quadrato, AE, cum cubo, AE.
SECTIO POSTERIOR.
VNde colligitur in Corollario ſolidum ſimilare genitum ex por-
tione, BAD, ad ſibi ſimilare genitum ex portione, BCD,
eſſe vt parallelepipedum ſub altitudine, XE, baſi quadrato, EA, ad
parallelepipedum ſub altitudine, OAE, baſi quadrato, EC, qua-
liacunque ſint illa ſolida ſimilaria, ſiue ſit, AC, axis, ſiue tantum
diameter.
COROLLARIVM VII.
IN Propoſ. ſeptima colligitur ſoli-
178[Figure 178] dum ſimilare genitum ex portio-
ne, BAF, ad ſibi ſim lare genitum ex
portione, CAD, ſiue hæciolida ſint
portiones ſphærę, vel ſphæroidis, ſiue
tantum ſolida ſimilaria, ſiue, AN,
ſit axis, ſiue tantum diameter, eſſe vt
parallelepipedum ſub altitudine, XE,
baſi quadrato, EA, ad parallelepipe-
dum ſub altitudine, XM, baſi qua-
drato, MA, vt exemplificaturin præ-
ſenti ſigura more ſolito.

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