Valerio, Luca - De centro gravitatis solidorvm libri tres

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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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