Valerio, Luca - De centro gravitatis solidorvm libri tres

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1tiam partem quadrati DE. Abſciſsis enim æqualibus EL
ipſi BC, & FM ipſi AC, & EG, ipſi AB, conſtituantur
priſmata ABCLEG, AGMFCL, ANHDGM, &
pyramis ADGM, & iungatur ML. Quoniam igitur ob pa
rallelas EF, GM, & DF, GL, ſimilia inter ſe ſunt trian
gula DEF, DGM, EGL, duplicatam inter ſe habebunt
laterum ho mologorum DE, DG, GE, proportionem,
hoc eſt eandem, quæ totidem eſt quadratorum ex ipſis DE,
DG, GE, prout inter ſe reſpondent: vt igitur DG qua
dratum ad quadratum DE, ita eſt triangulum DGM
ad triangulum DEF: eademque ratione vt quadratum
GE ad DE quadratum, ita trian
gulum EGL ad triangulum D
EF: & vt prima cum quinta ad
ſecundam, ita tertia cum ſexta ad
quartam: videlicet, vt duo qua
drata DG, GE, ad quadratum
DE, ita duo triangula DGM,
EGL, ad triangulum DEF. &
conuertendo, & per conuerſionem
rationis, vt quadratum DE ad
rectangulum DGE bis, ita trian
gulum DEF, ad parallelogram

143[Figure 143]
mum GF: & conuertendo, vt rectangulum DGE bis, ad
quadratum DE, ita GF parallelogrammum ad triangu
lum DEF: & antecedentium dimidia, vt rectangulum
DGE ad quadratum DE, ita triangulum GML ad
triangulum DEF; hoc eſt priſma, cuius baſis triangulum
GLM, altitudo eadem priſmati HKF ad priſma HKF.

Rurſus, quoniam eſt vt quadratum EG ad quadratum
ED, ita triangulum EGL ad triangulum DEF; erit ſi
militer vt quadratum EG ad quadratum ED, ita priſma
BGL ad priſma HKF: ſed vt rectangulum DGE ad
quadratum DE, ita priſma erat, cuius baſis triangulum G

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