Valerio, Luca - De centro gravitatis solidorvm libri tres

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1lo KLM: ſed triangulum FGH, eſt ſimile triangulo
ABC, & triangulum KLM, ſimile eidem triangulo
ABC; triangulum ergo FGH, ſimile erit triangulo KLM:
ſed & æquale propter æqualitatem laterum homologo
rum. Similiter oſtenderemus reliquum ſolidum LKM
GFH continentia triangula bina oppoſita æqualia
inter ſe, & ſimilia, & parallela; octaedrum eſt igitur
LKMGFH. Dico iam punctum P, quod eſt cen
trum pyramidis ABCD, eſse centrum octaedri LK
MGFH. Quoniam enim DP, ponitur tripla ipſius PE,
& DO, eſt æqualis
OE (ſiquidem planum
trianguli KLM, plano
trianguli ABC, paralle
lum ſecat proportione
oens rectas lineas, quæ
ex puncto D, in ſubli
mi pertinent ad ſubie
ctum planum trianguli
ABC) erit OP, ipſi
PE, æqualis. Et quo
niam BH eſt dupla
ipſius QH, quarum
BE eſt dupla ipſius

16[Figure 16]
EH, ſiquidem E eſt centrum trianguli ABC; erit reli
qua EH reliquæ EQ dupla: & quia eſt vt LD ad DB,
ita LN ad BH, propter ſimilitudinem triangulorum, &
eſt LD, dimidia ipſius BD, erit & LN, dimidia ipſius
BH: ſed QH eſt dimidia ipſius BH; æqualis igitur LN
ipſi QH. Iam igitur quia eſt vt BE ad EH, ita
LO ad ON: ſed BE, eſt dupla ipſius EH; dupla igi
tur LO, erit ipſius ON: ſed & QH erat dupla ipſius
QE; vt igitur LN ad NO, ita erit HQ ad QE: &

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