Valerio, Luca, De centro gravitatis solidorum, 1604

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1
PROPOSITIO II.
In omni triangulo vnum dumtaxat punctum
eſt, in quo rectæ ab angulis ad latera incidentes
ſecant ſeſe in eaſdem rationes. & ſegmenta, quæ
ad angulos, ſunt reliquorum dupla. & prædictæ
incidentes ſecant trianguli latera bifariam.
Sit triangulum ABC, cuius duo quælibet latera AB,
AC, ſint bifariam ſecta in punctis D, E, & ductæ rectæ
lineæ BE, CFD, AFG. Dico CF duplam eſſe ipſius
FD, & AF, ipſius FG, & BF, ipſius FE. Et in nullo alio
puncto à puncto F tres rectas ab angulis ad latera inciden­
tes ſecare ſe ſe in eaſdem rationes. Et reliquum latus BC
ſectum eſſe bifariam in puncto G. Quoniam enim eſt vt BA
ad AD, ita CA ad AE: hoc eſt, vt triangulum ABC ad
triangulum ADC, ita triangulum idem ABC ad trian­
gulum AEB; æqualia
erunt triangula ADC,
AEB, & ablato trape­
zio DE communi re­
liquum triangulum BD
F reliquo triangulo C
EF æquale erit: ſed
triangulum ADF eſt
æquale triangulo BDF;
& triangulum AFE
triangulo EFC, pro­
pter æquales baſes, &
7[Figure 7]
communes altitudines; totum igitur triangulum AFB
toti AFC, triangulo æquale erit: ſed vt triangulum AFB

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