Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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dupla igitur RG, eſt ipſius GL. </
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<
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lo AGC, recta GD, ſecat AC, bifariam in puncto D;
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ipſi AC, parallelam KH, bifariam ſecabit in puncto L,
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duorum igitur æqualium parallelogrammorum AF, EG;
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ſimul, quorum centra grauitatis ſunt K, H, centrum gra
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uitatis erit L. </
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<
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>Sed duo parallelogramma AF, EC, ſi
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mul ſunt paralle
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logrammi BD, du
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plum; trium igitur
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parallelogrammo
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rum AF, EC,
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BD, ſimul: hoc
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eſt
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ABC,
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vnà cum duobus
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trium
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inter ſe congruen
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tium EDF, cen
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trum grauitatis e
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rit G. </
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<
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li ABC, ponitur
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centrum grauitatis N; producta igitur NG, occurret
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centro M, reliquæ partis, ideſt duorum triangulorum DEF;
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quare vt triangulum ABC, ad duo triangula DEF, ſi
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mul, ita erit MG, ad GN. </
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<
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>Sed triangulum ABC, eſt
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duplum duorum triangulorum EDF: igitur & MG, erit
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ipſius GN, dupla. </
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<
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>Rurſus quoniam vtriuslibet duorum
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triangulorum EDF, centrum grauitatis erat M; erit ſi
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militer poſitum M, in triangulo EDF, ac centrum N, in
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triangulo ABC, propter ſimilitudinem triangulorum:
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Sed propter hæc ſimiliter poſita centra, quia homologo
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rum laterum eſt vt AB, ad DF, ita NG, ad GM: &
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AB, eſt dupla ipſius EB, erit & NG, dupla ipſius GM.
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<
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>Sed GM, erat dupla ipſius GN: igitur GN, erit ſui ipſius
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quadrupla. </
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<
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>Quod eſt abſurdum. </
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<
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>Non igitur centrum </
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