Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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FED. COMMANDINI
fruſtum a d. Sed pyramis q æqualis eſt fruſto à pyramide
abſciſſo, ut dem onſtrauimus.
ergo & conus, uel coni por-
tio q, cuius baſis ex tribus circulis, uel ellipſibus a b, e f, c d
conſtat, &
altitudo eadem, quæ fruſti: ipſi fruſto a d eſt æ-
qualis.
atque illud eſt, quod demonſtrare oportebat.

THEOREMA XXI. PROPOSITIO XXVI.

Cvivslibet fruſti à pyramide, uel cono,
uel coni portione abſcisſi, centrum grauitatis eſt
in axe, ita ut eo primum in duas portiones diui-
ſo, portio ſuperior, quæ minorem baſim attingit
ad portionem reliquam eam habeat proportio-
nem, quam duplum lateris, uel diametri maioris
baſis, vnà cum latere, uel diametro minoris, ipſi
reſpondente, habet ad duplum lateris, uel diame-
tri minoris baſis vnà cũ latere, uel diametro ma-
ioris:
deinde à puncto diuiſionis quarta parte ſu
perioris portionis in ipſa ſumpta:
& rurſus ab in-
ferioris portionis termino, qui eſt ad baſim maio
rem, ſumpta quarta parte totius axis:
centrum ſit
in linea, quæ his finibus continetur, atque in eo li
neæ puncto, quo ſic diuiditur, ut tota linea ad par
tem propinquiorem minori baſi, eãdem propor-
tionem habeat, quam fruſtum ad pyramidẽ, uel
conum, uel coni portionem, cuius baſis ſit ea-
dem, quæ baſis maior, &
altitudo fruſti altitudini
æqualis.

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