Valerio, Luca, De centro gravitatis solidorvm libri tres

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1cylindri AE ſubſeſquialterum: coni igitur ABC duplum.
Manifeſtum eſt igitur propoſitum.
PROPOSITIO XIII.
Omnis minor ſphæræ portio, ad cylindrum,
cuius baſis æqualis eſt circulo maximo, altitudo
autem eadem portioni, eam habet proportionem,
quam exceſſus, quo tripla ſemidiametri ſphæræ
excedit tres deinceps proportionales, quarum ma
xima eſt ſphæræ ſemidiameter, media vero quæ
inter centra ſphæræ & baſis portionis interijci­
tur; ad ſemidiametri ſphæræ triplam.
Sit ſphæræ, cuius centrum D, ſemidiameter BD, mi­
nor portio ABC, cuius axis BG ſegmentum ſemidiame­
tri BD, baſis autem circulus, cuius diameter AC. Sitque
EF, cylindrus, cu­
ius axis, ſiue alti­
tudo eadem BG:
baſis autem æqua­
lis circulo maxi­
mo, cuius ſemidia­
meter BD. Dico
portionem ABC,
ad cylindrum EF
eam habere pro­
79[Figure 79]
portionem, quam exceſſus, quo tripla ipſius BD, ſupe­
rat tres BD, DG; & minorem extremam ad ipſas, quæ
ſit M; ad ipſius BD triplam. vertice enim D, baſi cylin­
dri EF, cuius diameter FH deſcribatur conus FDH, cu­
ius intelligatur fruſtum FHKL abſciſsum plano, quod ab-

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