Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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<
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>Sit coni fruſtum ABCD, cuius axis EF, fruſto autem
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ABCD, intelligatur inſcriptum fruſtum pyramidis inſcri
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ptæ cono AHD, à quo abſciſsum eſt fruſtum ABCD,
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baſim habentis æquilateram, & æquiangulam inſcriptam
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circulo AD: quare eius centrum grauitatis, & figuræ erit
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punctum F, vt diximus in præcedenti, axis autem FH, ſi
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cut etiam pyramidis abſciſsæ vna cum cono BHC, axis
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EH, quare & reliqui fruſti pyramidis axis erit EF, igi
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tur in EF, ſit fruſti inſcripti fruſto ABCD, centrum gra
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uitatis G. </
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<
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>Dico punctum G, eſse centrum grauitatis fru
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ſti ABCD. </
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<
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>Ponatur enim
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FL, pars quarta ipſius FH,
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necnon EK, pars quarta ip
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ſius EH: punctum igitur K,
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eſt centrum grauitatis pyra
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midis, & coni BHC, ſicut
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& punctum L, pyramidis, &
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coni AHD. cum igitur fru
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ſti pyramidis fruſto ABCD,
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inſcripti ſit centrum grauita
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tis G; erit vt GL, ad LK,
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ita pyramis BHC, ad pyra
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midis fruſtum fruſto ABCD,
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inſcriptum: ſed vt pyramis
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BHC, ad pyramidis fruſtum
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fruſto ABCD, inſcriptum,
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ita eſt diuidendo, conus BHC, ad fruſtum ABCD, pro
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pter eandem triplicatam communium conis, & pyramidi
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bus ſimilibus laterum homologorum proportionem; vt igi
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tur GL, ad LK, ita erit conus BHC: ad fruſtum ABCD:
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ſed coni BHC, centrum grauitatis erat K, & coni AHD,
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centrum grauitatis L; fruſti igitur ABCD, centrum gra
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nitatis erit G. </
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<
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>Quod demonſtrandum erat. </
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