Valerio, Luca - De centro gravitatis solidorum

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PROPOSITIO XXIII.

Circuli, & Ellypſis idem eſt centrum grauita
tis, & figuræ.

Sit circulus, vel ellypſis ABCD, cuius centrum E.
Dico centrum grauitatis figuræ ABCD, eſse punctum E.
Ducantur enim duæ diametri ad rectos inter ſe angulos
AC, BD; in ellypſi autem ſint diametri coniugatæ.
Quoniam igitur omnes rectæ lineæ, quæ in ſemicirculo,
vel dimidia ellypſi diametro ducantur parallelæ bifariam
ſecantur à ſemidiametro, & quo à baſi remotiores, eo ſunt

34[Figure 34]
minores; erit centrum grauitatis ſemicirculi, ſiue dimidiæ
ellypſis ABC, in linea BE; ſicut & ſemicirculi, ſiue di
midiæ ellypſis ADC, centrum grauitatis in linea DE.
eſt autem BED, vna recta linea: in diametro igitur BD,
erit centrum grauitatis circuli, ſiue ellypſis ABCD.
Eadem ratione oſtenderemus idem centrum grauitatis eſse
in altera diametro AC: in communi igitur vtriuſque ſe
ctione puncto E. Quod demonſtrandum erat.

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