Valerio, Luca - De centro gravitatis solidorum

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PROPOSITIO XXXIX.

Omnis coni centrum grauitatis axim ita diui
dit, vt ſegmentum ad verticem ſit reliqui triplum.

Sit conus ABC, cuius vertex B, axis autem BD, cu
ius BE, ſit tripla ipſius ED. Dico punctum E, eſse co
ni ABC, centrum grauitatis. Si enim cono ABC, pyramis
inſcribatur, cuius baſis inſcripta circulo AC, æquilatera ſit,
& æquiangula, eius centrum grauitatis erit idem quod &
figuræ centrum, ſed centrum
talis figuræ circulo inſcriptæ
idem eſt, quod centrum cir
culi, vt colligitur ex demon
ſtrationibus quarti Elemen
torum; inſcriptæ igitur pyra
midis erit axis BD, & cen
trum grauitatis E. talis au
tem ea pyramis inſcribi po
teſt, vt à cono deficiat mino
ri ſpacio quantacumque ma
gnitudine propoſita; igitur
ABC, coni centrum graui
tatis erit E. Quod demonſtrandum erat.

55[Figure 55]

PROPOSITIO XXXX.

Omnis fruſti conici centrum grauitatis idem
eſt in axe centro grauitatis fruſti pyramidis baſim
habentis æquilateram, & æquiangul am in ſcriptæ
cono, ab ſciſſi eodem plano, quo coni fruſtum.

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