Valerio, Luca - De centro gravitatis solidorvm libri tres

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1FG, GH, homologa ſunt lateribus GO, ON. nam
dupla eſt FG, ipſius GO, & GH, ipſius ON; angulus
igitur OGN, æqualis erit angulo GFH; parallela igi
tur GN, ipſi FH, & propterſimilitudinem triangulorum
dupla erit FH, ipſius GN. Rurſus, quoniam recta
OP, ſecat latera oppoſita parallelogrammi BD, bifa
riam in punctis O, P, ſecta, & ipſa bifariam in puncto N,
erit punctum N, parallelogrammi BD, centrum graui
tatis, atque ideo axis FN, pyramidis ABDEF. qua
ratione erit quoque axis FH, pyramidis ABCF: ſed
FL, eſt tripla ipſius LH; pyramidis igitur ABCF, cen
trum grauitatis erit L. Rurſus quia eſt vt GK, ad KH,
ita GR, ad LH, propter ſimilitudinem triangulorum,
erit æqualis GR, ipſi LH: ſed eſt FH, quadrupla ip-,
ſius LH, quadrupla igitur FH, ipſius GR: ſed FH
erat dupla ipſius GN; quadrupla igitur FH, reliquæ
NR, ac proinde GR, RN, æquales erunt: recta igitur
FL, tripla erit vtriuſque ipſarum GR, RN, ſed vt FL,
ad NR, ita eſt FM, ad MN, propter ſimilitudinem trian
gulorum; recta igitur FM, erit ipſius MN, tripla, ſicut
& LM, ipſius MR: ſed quia KH, eſt æqualis GK,
erit & LK, æqualis RK; propter ſimilitudinem trian
gulorum; cum igitur LK, ſit tripla ipſius MR, erit LK,
ipſius KM, dupla; vt igitur eſt pyramis ABEDF, ad
pyramidem ABCF, ita erit LK, ad KM; eſt autem M,
centrum grauitatis pyramidis ABED, ſicut & L, pyrami
dis ABCF; totius igitur priſmatis ABCDEF, centrum
grauitatis erit K. Quod demonſtrandum erat.

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