Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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<
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">THEOREMA XII. PROPOSITIO XVI.</
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">In ſphæra, & ſphæroide idem eſt grauitatis, &
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figuræ centrum.</
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<
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">Secetur ſphæra, uel ſphæroides plano per axem ducto;
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quod ſectionem faciat circulum, uel ellipſim abcd, cuius
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diameter, & ſphæræ, uel ſphæroidis axis db; & centrum e. </
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">Dico e grauitatis etiam centrum eſſe. </
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<
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id
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plano per e, ad planum ſecans recto, cuius ſectio ſit circu
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lus circa diametrum ac. </
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<
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id
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">erunt adc, abc dimidiæ portio
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nes ſphæræ, uel ſphæroidis. </
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">& quoniam portionis adc gra
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uitatis centrum eſi in linea d, & centrum portionis abc in
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ipſa be; totius ſphæræ, uel ſphæroidis grauitatis centrum
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in axe db conſiſtet, Quòd ſi portionis adc centrum graui
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tatis ponatur eſſe f & fiat ipſi fe æqualis eg:
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g por
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tionis abc centrum erit. </
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<
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id
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">ſolidis enim figuris ſimilibus &
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æqualibus inter ſe aptatis, & centra grauitatis ipſarum in
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ter se aptentur neceſſe eſt. </
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<
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">ex quo fit, ut magnitudinis, quæ
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ex utilique
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cõſlat
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, hoc eſt ipſius ſphæræ, uel ſphæroidis gra
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uitatis centrum ſit in medio lineæ fg uidelicet in e. </
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<
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ræ igitur, uel ſphæroidis grauitatis centrum eſt idem, quod
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centrum figuræ.</
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