Valerio, Luca, De centro gravitatis solidorum, 1604

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1
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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