Commandino, Federico - Liber de centro gravitatis solidorum

Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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1

THEOREMA XII. PROPOSITIO XVI.

In ſphæra, & ſphæroide idem eſt grauitatis, &
figuræ centrum.

Secetur ſphæra, uel ſphæroides plano per axem ducto;
quod ſectionem faciat circulum, uel ellipſim abcd, cuius
diameter, & ſphæræ, uel ſphæroidis axis db; & centrum e.
Dico e grauitatis etiam centrum eſſe. ſecetur enim altero
plano per e, ad planum ſecans recto, cuius ſectio ſit circu
lus circa diametrum ac. erunt adc, abc dimidiæ portio
nes ſphæræ, uel ſphæroidis. & quoniam portionis adc gra
uitatis centrum eſi in linea d, & centrum portionis abc in
ipſa be; totius ſphæræ, uel ſphæroidis grauitatis centrum
in axe db conſiſtet, Quòd ſi portionis adc centrum graui
tatis ponatur eſſe f & fiat ipſi fe æqualis eg: punctum g por

39[Figure 39]

tionis abc centrum erit. ſolidis enim figuris ſimilibus &
æqualibus inter ſe aptatis, & centra grauitatis ipſarum in

ter se aptentur neceſſe eſt. ex quo fit, ut magnitudinis, quæ
ex utilique conſtat, hoc eſt ipſius ſphæræ, uel ſphæroidis gra
uitatis centrum ſit in medio lineæ fg uidelicet in e. Sphæ
ræ igitur, uel ſphæroidis grauitatis centrum eſt idem, quod
centrum figuræ.

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