Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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trum grauitatis. </
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<
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>Si enim non eſt, erit aliud, eſto G: &
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iunctatur EG, producatur ad partes G, in infinitum vſ
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que ìn F. </
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<
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>Quoniam igitur E, eſt centrum grauitatis vnius
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partis AC, & G, totius AB; erit reliquæ partis CD, in
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linea GF centrum grauitatis: ſed & in puncto E; eiuſ
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dem igitur magnitudinis AB, duo centra grauitatis erunt.
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<
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>Quod fieri non poteſt; totius igitur AB, erit centrum gra
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uitatis idem E. </
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<
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>Manifeſtum eſt igitur propoſitum. </
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PROPOSITIO XIX.
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<
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grauitatis, & figuræ. </
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<
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>Sit triangulum rectilineum ABC, cuius centrum G.
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</
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<
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>Dico G, eſse centrum grauitatis trianguli ABC. </
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<
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fieri poteſt, ſit aliud punctum N, centrum grauitatis trian
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guli ABC, & per punctum G, ducantur rectæ AF, BD,
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CE, & DHE, ERF, FKD,
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K
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LH, & NG. </
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<
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niam igitur quæ ab angulis A, B, C, ductæ ſunt rectæ
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lineæ per G, ſecant bifariam latera AB, BC, CA; erit
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triangulum EDF, ſimile triangulo ABC, ob latera pa
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rallela vt ſunt EF, AC. </
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<
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>Et quoniam triangulum EDF,
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dimidium eſt cuius vis trium parallelogrammorum AF,
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BD, CE, æqualia inter ſe erunt ea parallelogramma
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omnifariam ſumpta, quorum centra grauitatis H, K, R;
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intelligantur autem tria parallelogramma AF, BD, CE,
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diſtincta penitus, ita vt inter ſe congruant ſecundum tria
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triangula DEF, inter ſe congruentia: trium igitur trian
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gulorum DEF, inter ſe congruentium & centra grauita
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tis inter ſe congruent in puncto M. </
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<
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ter duas parallelas EF, KH, ſecant ſe rectæ lineæ FH,
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LR, in puncto G; erit vt FG, ad GH, ita RG, ad GL; </
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