Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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in axe DN, erit centrum grauitatis. </
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<
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>Eadem ratione in
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quolibet reliquorum trium axium, pyramidis ABCD, ip
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ſius centrum grauitatis eſse oſtenderemus; communis igi
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tur ſectio quatuor axium pyramidis ABCD, quod eſt
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ipſius centrum E, erit centrum grauitatis pyramidis AB
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CD. </
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>Quod demonſtrandum erat. </
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COROLLARIVM.
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>Hinc manifeſtum eſt centrum grauitatis pyra
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midis triangulam baſim habentis eſſe in eopun
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cto, in quo axis ſic diuiditur, vt pars quæ ad ver
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icem ſit reliquæ tripla. </
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PROPOSITIO XXXII.
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<
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>Ominis pyramidis baſim pluſquam trilate
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ram habentis centrum grauitatis axim ita diui
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dit, vt pars, quæ eſt ad verticem ſit tripla re
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liquæ. </
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<
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>Sit pyramis ABCDE, cui vertex E, baſis autem
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quadrilatera ABCD, & eſto axis EF, ſegmentum EM,
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reliqui MF, triplum. </
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<
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>Dico punctum M, eſſe centrum
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grauitatis pyramidis ABCDE. </
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<
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>Ducta enim AC, ſit
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trianguli ABC, centrum grauitatis H, ſicut & K, trian
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guli ACD: & iungantur KH, HE, EK: Factaque vt
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EM, ad MF, ita EL ad LH, & EN ad N
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K
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, iun
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gatur LN. </
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<
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>Quoniam igitur EF eſt axis pyramidis
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ABCDE, erit baſis ABCD centrum grauitatis F. </
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