Valerio, Luca - De centro gravitatis solidorum

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1dupla igitur RG, eſt ipſius GL. Et quoniam in triangu
lo AGC, recta GD, ſecat AC, bifariam in puncto D;
ipſi AC, parallelam KH, bifariam ſecabit in puncto L,
duorum igitur æqualium parallelogrammorum AF, EG;
ſimul, quorum centra grauitatis ſunt K, H, centrum gra
uitatis erit L. Sed duo parallelogramma AF, EC, ſi
mul ſunt paralle
logrammi BD, du
plum; trium igitur
parallelogrammo
rum AF, EC,
BD, ſimul: hoc
eſt trianguli ABC,
vnà cum duobus
trium triangulorum
inter ſe congruen
tium EDF, cen
trum grauitatis e
rit G. Sed triangu
li ABC, ponitur

27[Figure 27]
centrum grauitatis N; producta igitur NG, occurret
centro M, reliquæ partis, ideſt duorum triangulorum DEF;
quare vt triangulum ABC, ad duo triangula DEF, ſi
mul, ita erit MG, ad GN. Sed triangulum ABC, eſt
duplum duorum triangulorum EDF: igitur & MG, erit
ipſius GN, dupla. Rurſus quoniam vtriuslibet duorum
triangulorum EDF, centrum grauitatis erat M; erit ſi
militer poſitum M, in triangulo EDF, ac centrum N, in
triangulo ABC, propter ſimilitudinem triangulorum:
Sed propter hæc ſimiliter poſita centra, quia homologo
rum laterum eſt vt AB, ad DF, ita NG, ad GM: &
AB, eſt dupla ipſius EB, erit & NG, dupla ipſius GM.
Sed GM, erat dupla ipſius GN: igitur GN, erit ſui ipſius
quadrupla. Quod eſt abſurdum. Non igitur centrum

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