Valerio, Luca - De centro gravitatis solidorum

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Sit coni fruſtum ABCD, cuius axis EF, fruſto autem
ABCD, intelligatur inſcriptum fruſtum pyramidis inſcri
ptæ cono AHD, à quo abſciſsum eſt fruſtum ABCD,
baſim habentis æquilateram, & æquiangulam inſcriptam
circulo AD: quare eius centrum grauitatis, & figuræ erit
punctum F, vt diximus in præcedenti, axis autem FH, ſi
cut etiam pyramidis abſciſsæ vna cum cono BHC, axis
EH, quare & reliqui fruſti pyramidis axis erit EF, igi
tur in EF, ſit fruſti inſcripti fruſto ABCD, centrum gra
uitatis G. Dico punctum G, eſse centrum grauitatis fru
ſti ABCD. Ponatur enim
FL, pars quarta ipſius FH,
necnon EK, pars quarta ip
ſius EH: punctum igitur K,
eſt centrum grauitatis pyra
midis, & coni BHC, ſicut
& punctum L, pyramidis, &
coni AHD. cum igitur fru
ſti pyramidis fruſto ABCD,
inſcripti ſit centrum grauita
tis G; erit vt GL, ad LK,
ita pyramis BHC, ad pyra
midis fruſtum fruſto ABCD,
inſcriptum: ſed vt pyramis
BHC, ad pyramidis fruſtum
fruſto ABCD, inſcriptum,

56[Figure 56]
ita eſt diuidendo, conus BHC, ad fruſtum ABCD, pro
pter eandem triplicatam communium conis, & pyramidi
bus ſimilibus laterum homologorum proportionem; vt igi
tur GL, ad LK, ita erit conus BHC: ad fruſtum ABCD:
ſed coni BHC, centrum grauitatis erat K, & coni AHD,
centrum grauitatis L; fruſti igitur ABCD, centrum gra
nitatis erit G. Quod demonſtrandum erat.

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