Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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FG, GH, homologa ſunt lateribus GO, ON. nam
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dupla eſt FG, ipſius GO, & GH, ipſius ON; angulus
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igitur OGN, æqualis erit angulo GFH; parallela igi
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tur GN, ipſi FH, & propterſimilitudinem triangulorum
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dupla erit FH, ipſius GN. Rurſus, quoniam recta
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OP, ſecat latera oppoſita parallelogrammi BD, bifa
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riam in punctis O, P, ſecta, & ipſa bifariam in puncto N,
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erit punctum N, parallelogrammi BD, centrum graui
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tatis, atque ideo axis FN, pyramidis ABDEF. qua
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ratione erit quoque axis FH, pyramidis ABCF: ſed
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FL, eſt tripla ipſius LH; pyramidis igitur ABCF, cen
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trum grauitatis erit L. </
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>Rurſus quia eſt vt GK, ad KH,
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ita GR, ad LH, propter ſimilitudinem triangulorum,
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erit æqualis GR, ipſi LH: ſed eſt FH, quadrupla ip-,
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ſius LH, quadrupla igitur FH, ipſius GR: ſed FH
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erat dupla ipſius GN; quadrupla igitur FH, reliquæ
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NR, ac proinde GR, RN, æquales erunt: recta igitur
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FL, tripla erit vtriuſque ipſarum GR, RN, ſed vt FL,
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ad NR, ita eſt FM, ad MN, propter ſimilitudinem trian
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gulorum; recta igitur FM, erit ipſius MN, tripla, ſicut
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& LM, ipſius MR: ſed quia KH, eſt æqualis GK,
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erit & LK, æqualis RK; propter ſimilitudinem trian
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gulorum; cum igitur LK, ſit tripla ipſius MR, erit LK,
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ipſius KM, dupla; vt igitur eſt pyramis ABEDF, ad
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pyramidem ABCF, ita erit LK, ad KM; eſt autem M,
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centrum grauitatis pyramidis ABED, ſicut & L, pyrami
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dis ABCF; totius igitur priſmatis ABCDEF, centrum
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grauitatis erit K. </
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<
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