Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRA VIT. SOLID.
"/>
ad portiones ſolidas maiorem habet proportioné, quàm
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n l ad l m: </
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<
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">& </
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<
s
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xml:space
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">diuidendo fruſtum pyramidis ad dictas por-
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tiones maiorem proportionem habet, quàm n m ad m l.
<
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</
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<
s
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xml:space
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">fiat igitur ut fruſtum pyramidis ad portiones, ita q m ad
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m l. </
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<
s
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xml:space
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">Itaque quoniam à fruſto coni, uel coni portionis a d,
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cuius grauitatis centrum eſtm, aufertur fruſtum pyrami-
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lb
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dis habens centruml; </
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<
s
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xml:space
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">erit reliquæ magnitudinis, quæ ex
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portionibus ſolidis conſtat; </
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<
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xml:space
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">grauitatis cẽtrum in linea l m
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producta, atque in puncto q, extra figuram poſito. </
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<
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xml:space
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">quod
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fieri nullo modo poteſt. </
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<
s
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xml:space
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">relinquitur ergo, ut punctum l ſit
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fruſti a d grauitatis centrum. </
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<
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xml:space
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">quæ omnia demonſtranda
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proponebantur.</
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<
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">THEOREMA XXII. PROPOSITIO XXVII.</
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ſolidorum in ſphæra deſcripto-
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rum, quæ æqualibus, & </
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nentur, centrum grauitatis eſt idem, quod ſphæ-
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ræ centrum.</
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<
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">Solida eiuſmodi corpora regularia appellare ſolent, de
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quibus agitur in tribus ultimis libris elementorum: </
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xml:space
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autem numero quinque, tetrahedrum, uel pyramis, hexa-
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hedrum, uel cubus, octahedrum, dodecahedrum, & </
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hedrum.</
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</
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<
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">Sit primo a b c d pyramis ĩ ſphæra deſcripta, cuíus ſphæ
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ræ centrum ſit e. </
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">Dico e pyramidis a b c d grauitatis eſſe
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centrum. </
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<
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">Si enim iuncta d e producatur ad baſim a b c in
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f; </
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<
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">ex iis, quæ demonſtrauit Campanus in quartodecimo li
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bro elementorum, propoſitione decima quinta, & </
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ſeptima, erit f centrum circuli circa triangulum a b c de-
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ſcripti: </
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<
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xml:space
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">atque erit e f ſexta pars ipſius ſphæræ axis. </
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<
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xml:space
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">quare
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ex prima huius conſtat trianguli a b c grauitatis centrum
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eſſe punctum f: </
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xml:space
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">idcirco lineam d f eſſe pyramidis axem.</
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