Valerio, Luca, De centro gravitatis solidorvm libri tres

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1ABC tres ad diametrum ordinatim applicatæ AD,
FH, MO. Quoniam igitur tres rectæ OB, BH, BD
ſeſe qualiter excedunt, quarum minima BO, maxi­
ma eſt BD, minor erit proportio BO ad BH, quàm
BH ad BD; hoc eſt NP ad GK, quàm GKad AC.
ſed vt OB ad BH hoc eſt NO ad GH, vel NP ad
GK ita eſt quadra­
tum MO ad quadra­
tum FH, hoc eſt eo­
no dis ſectionum cir­
culus MQ ad circu­
lum FL: eademque
ratione vt GK ad
AC ita circulus FL
ad circulum AC; mi
nor igitur proportio
erit circuli MQ ad
circulum FL quàm
124[Figure 124]
circuli FL ad circulum AC. Similiter autem oſtende­
remus ternas quaslibet alias ita factas ſectiones trianguli,
& parabolæ ABC inter ſe & baſi parallelas proportio­
nales eſse, & minorem proportionem vtrobique minimæ
ad mediam, quàm mediæ ad maximam. Sed E eſt cen­
trum grauitatis trianguli ABC, igitur per vigeſimamter­
tiam huius centrum grauitatis conoidis ABC erit idem E.
Quod demonſtrandum erat,
PROPOSITIO XLII.
Omnis fruſti conoidis parabolici centrum gra
uitatis axim ita diuidit, vt pars, quæ minorem
baſim attingit ſit ad reliquam; vt duplum maioris

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