Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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ABC circumſcripta ad AE cylindrum: vtraque autem
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circumſcriptarum figurarum excedit ſibi inſcriptam mino
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ri ſpacio quantacumque magnitudine propoſita, vt igitur
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triangulum ABC, ad parallelogrammum AE, ita erit co
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noides ABC, ad cylindrum AE. </
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<
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>Sed triangulum ABC
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eſt parallelogrammi AE dimidium; igitur conoides ABC
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eſt cylindro AE dimidium: ſed cylindrus AE eſt coni
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ABC, triplum: igitur conoides ABC, erit coni ABC
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ſeſquialterum. </
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<
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PROPOSITIO XIX.
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>Omnis priſmatis triangulam baſim habentis
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centrum grauitatis rectam lineam, quæ cuiuſlibet
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trium laterum bipartiti ſectionem, & oppoſiti pa
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rallelogrammi centrum iungit, ita diuidit, vt
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pars, quæ attingit latus ſit dupla reliquæ. </
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<
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>Sit priſma, quale diximus AB
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CDEF, ſectoque vno ipſius la
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tere BF in puncto G, bifariam
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parallelogrammi oppoſiti ſit cen
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trum H, & iuncta GH, cuius
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pars GK ſit dupla reliquæ
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K
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H.
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<
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>Dico priſmatis ABCDEF, cen
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trum grauitatis eſſe K. </
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<
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ctum enim H ducatur NO ip
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ſi AE, vel CD parallela, quæ
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ipſas AC, ED, ſecabit
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:
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iunctisque BN, FO, ducatur per
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punctum
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K
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, ipſi FB, vel NO
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parallela LM. </
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<
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>Quoniam igitur eſt vt HK ad KG, ita
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NL ad LB, & OM ad MF, erit NL, ipſius LB, & OM </
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