Valerio, Luca, De centro gravitatis solidorum, 1604

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1
PROPOSITIO
PRIMA.
Si ſint quotcumque magnitu­
dines inæquales deinceps
proportionales; exceſſus, qui
bus differunt deinceps pro­
portionales erunt, in propor­
tione totarum magnitudi­
num.
Sint quotcumque inæquales magnitudines deinceps
proportionales AB, CD, EF, & G,
differentes exceſſibus BH, DK, FL, mi­
nima autem ſit G.
Dico BH, DK, FL,
deinceps proportionales eſse in proportio­
ne, quæ eſt AB, ad CD, ſeu CD, ad
EF.
Quoniam enim eſt vt AB, ad
CD, ita CD ad EF; hoc eſt vt AB, ad
AH, ita CD, ad CK, permutando
erit, vt AB, ad CD, ita AH, ad CK:
vt igitur tota AB, ad totam CD, ita
reliqua BH, ad reliquam DK.
Simili­
ter oſtenderemus eſse vt CD ad EF,
ita DK ad FL; vt igitur BH ad DK,
ita erit DK ad FL, in proportione, quæ
eſt AB ad CD, & CD ad EF.
Quod demonſtran­
dum erat.
6[Figure 6]

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