Valerio, Luca, De centro gravitatis solidorvm libri tres

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1E, in recta linea, quæ iungit centra D, G; tria igitur pun­
cta D, E, G, ſunt in eadem recta linea. in qua igitur ſunt
puncta D, E, in eadem eſt punctum G; ſed puncta D, E, ſunt
in recta DH; igitur & punctum G, erit in recta DH: ſed
extra ipſam DE, vt modo oſtendimus, in reliqua igitur
EH. Quod demonſtrandum erat.
PROPOSITIO XVIII.
Sit totum quoduis planum ſit vni parti concen
tricum ſecundum centrum grauitatis, & reliquæ
erit concentricum. Et ſi partes inter ſe ſint con­
centricæ, & toti erunt concentricæ.
Sit totum quoduis planum AB, quod cum vna parte
AC habeat commune centrum grauitatis E. Dico & re­
liquæ partis CD, eſse
idem centrum grauitatis
E. Si enim illud non
eſt, erit aliud; eſto F, &
EF iungatur. Quoniam
igitur partium AC, CD,
centra grauitatis ſunt E,
F; erit totius AB, in re­
cta EF, centrum graui­
tatis: ſed & in puncto E,
vnius ergo magnitudinis
duo centra grauitatis e­
runt. Quod eſt abſurdum;
26[Figure 26]
idem igitur E erit centrum grauitatis vtriuslibet partium
AC, CD. Sed vtriuslibet partium AC, CD, ſit cen­
trum grauitatis E. Dico idem E totius AB, eſse cen-

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