Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE CENTRO GRAVIT. SOLID.
bere proportionem, quam ſpacium g h ad dictã
figuram, hoc modo demonſtrabimus.
Intelligatur circulus, uel ellipſis x æqualis figuræ rectili-
neæ in g h ſpacio deſcriptæ:
& ab x conſtituatur conus, uel
Figure: /permanent/library/4E7V2WGH/figures/0141-01 not scanned
[Figure 95]
coni portio, altitudinẽ habens eandẽ, quã cylindrus uel cy
lindri portio c e.
Sit deinde rectilinea figura, in quay eade,
quæ in ſpacio g h deſcripta eſt:
& ab hac pyramis æquealta
conſtituatur.
Dico conũ uel coni portionẽ x pyramidiy æ-
qualẽ eſſe.
niſi enim ſit æqualis, uel maior, uel minor erit.
Sit primum maior, et exuperet ſolido z. Itaque in circu
lo, uel ellipſi x deſcribatur figura rectilinea;
& in ea pyra-
mis eandem, quam conus, uel coni portio altitudinem ha-
bens, ita ut portiones relictæ minores ſint ſolido z, quem-
admodum docetur in duodecimo libro elementorum pro
poſitione undecima.
erit pyramis x adhuc pyramide y ma
ior.
& quoniam piramides æque altæ inter ſe ſunt, ſicuti ba
6. duode-
cimi.
ſes;
pyramis x ad piramidem y eandem proportionem ha-
bet, quàm figura rectilinea x ad figuram y.
Sed ſigura recti

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