Valerio, Luca - De centro gravitatis solidorum

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1EF. quæ ſuntin latera homologa duorum triangulorum
ABC, DEF. Ex definitione igitur, duo puncta G, H,
in triangulis ABC, DEF, ſimiliter poſita erunt. At
enim ſi fieri poteſt ſit aliud punctum K, in triangulo
DEF, ſimiliter poſitum puncto G. Vel igitur punctum
K in aliquo triangulorum, quorum eſt communis vertex
H, vel in aliquo eorundem latere cadet. cadat in latere
FH, & iungatur DK: triangulum ergo DFK, ſimile
erit triangulo ACG. Sed & triangulum EDF, ſimile
eſt triangulo BAC; vtraque igitur horum ad illorum ſi
bi reſpondens triangulorum duplicatam eorundem late
rum homologorum AC, DF, habebunt proportionem:
vt igitur eſt triangulum EDF, ad triangulum BAC, ita
erit triangulum DFK, ad triangulum ACG: & per
mutando, vt triangulum ACG, ad triangulum ABC,
ita triangulum DFK, ad triangulum EDF: eadem ra
tione, vt triangulum ACG, ad triangulum ABC, ita
erit triangulum DFH, ad triangulum DEF: vt igitur
triangulum DFK, ad triangulum EDF; ita erit trian
gulum DFH, ad triangulum EDF; triangulum ergo
DFK, triangulo DFH, æquale erit, pars toti, quod eſt
abſurdum: idem autem abſurdum ſequeretur, ſi punctum
K, poneretur in aliquo prædictorum triangulorum, vt in
triangulo DFH; Non igitur aliud punctum à puncto H,
in triangulo EDF, ſimiliter poſitum erit puncto G.
Quod demonſtrandum erat.

PROPOSITIO V.

Cuilibet figuræ planæ rectangulum æquale
poteſt eſſe.

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