Valerio, Luca, De centro gravitatis solidorum, 1604

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1atque ideo & portionis baſibus parallelo; ſuper ſectionem,
quæ erit circulus maximus, cuius diameter LM, duo cylin­
dri deſcripti intelligantur, ad oppoſita portionis baſium pla
na terminati ex illis autem totus cylindrus compoſitus EF,
cuius baſis æqua­
lis circulo maxi­
mo LM. Deinde
in ſegmento GH
ſumpta OH, ter­
tia parte minoris
extremæ maiori
GH in proportio
ne, quæ eſt LG ad
GH; & in ſegmen
to GK, ſumatur
87[Figure 87]
NK, tertia pars minoris extremæ maiori GK, in propor­
tione, quæ eſt LG ad GK. Dico portionem ABCD
ad cylindrum EF, eſse vt NO ad KH. Sumptis enim
ijſdem, quæ in præcedentis ſumpſimus, demonſtrationem
ſimiliter oſtenderemus tam portionem LBCM ad cy­
lindrum EF, eſse vt OG ad KH, quam portionem LA
DM ad eundem EF cylindrum, vt NG ad eundem axim
KH, vt igitur prima cum quinta ad ſecundam, ita tertia
cum ſexta ad quartam: videlicet, vt NO ad KH, ita por
tio ABCD ad EF cylindrum. Quod demonſtrandum
crat.
PROPOSITIO XVIII.
Omne conoides parabolicum dimidium eſt
cylindri, coni autem ſeſquialterum eandem ipſi
baſim, & eandem altitudinem habentium.

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