Valerio, Luca - De centro gravitatis solidorum

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1tiones, ita vt ſegmenta, quæ ad angulos, eo
rum, quæ ad oppoſita triangula, ſint tripla; ex quo
puncto tota pyramis diuiditur in quatuor pyrami
des æquales. Et in nullo alio puncto quatuor re
ctæ lineæ ductæ ab angulis ad triangula oppoſita
pyramidis ſecant ſeſe in eaſdem rationes. Vocetur
autem punctum hoc centrum dictæ pyramidis.

Sit pyramis ABCD, cuius vertex A, baſis autem
triangulum BCD, axes AE, BM, CL, DN, vnde qua
tuor triangulorum, quæ ſunt circa pyramidem ABCD,
centra erunt grauitatis E, L, M, N. Dico quatuor li
neas AE, BM, CL, DN, ſecare ſe ſe in vno puncto in
eaſdem rationes, quas prædixi, & quæ ſequuntur. Nam ex
puncto A, ducatur recta ALH, quæ ob trianguli ABD,
centrum L, ſecabit latus BD, bifariam in puncto H; iun
cta igitur CE, & producta conueniet cum ALH, vt in
puncto H. eadem ratione iunctæ AM, BE, & productæ
conuenient in medio lateris CD, conueniant in puncto K,
necnon AN, DE, in medio ipſius BC, vt in puncto G.
Quoniam igitur ob triangulorum centra, eſt vt CE ad EH,
ita AL ad LH, dupla enim eſt vtraque vtriuſque, ſeca
bunt ſeſe rectæ AE, CL, inter eaſdem parallelas; quare
vt AF ad FE, ita erit CF ad FL, circum æquales angu
los ad verticem: triangula igitur AFL, CFE; & reci
proca, & æqualia inter ſe erunt. Cum igitur ſit vt AL ad
LH, ita CE ad EH, hoc eſt vt triangulum AFL ad
triangulum FLH, (ſi ducatur FH) ita triangulum CFE,
ad triangulum FEH, erunt inter ſe æqualia triangula
FEH, FLH. Quare vt triangulum AFH, ad triangu
lum FLH, hoc eſt vt AH ad HL, ita erit triangulum
AFH ad triangulum FEH, hoc eſt AF ad FE: ſed re
cta AH, eſt tripla ipſius LH; igitur & AF, erit ipſius FE,

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