Valerio, Luca - De centro gravitatis solidorum

Valerio, Luca, De centro gravitatis solidorum, 1604

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1ducantur rectæ GBH, GAF, quæ cum KE, produ
cta conueniant in punctis F, H: & fiant parallelogramma
FL, AK. Quoniam igitur eſt vt N, ad R, ita BC, ad
CA, hoc eſt AD, ad DB, hoc eſt rectangulum AK, ad
rectangulum BK; erit permutando vt rectangulum AK,
ad N, ita rectangulum BK, ad R; ſed rectangulum BK,
eſt pars quarta ipſius R, ergo & rectangulum AK, erit
pars quarta ipſius N. Rurſus quia eſt vt GD, ad DK,
ita GA, ad AF, & GB, ad BH: ſed GD eſt æqualis
DK; ergo & GA, ipſi AF, & GB, ipſi BH, æquales
erunt & centra grauita
tis A, quidem rectangu
li MK, B, vero rectan
guli KL, & rectangulum
AK, pars quarta ipſius
MK, quemadmodum
& BK ipſius KL; ſed
N, rectanguli AK, qua
druplum erat, quemad
modum & R ipſius BK;
igitur rectangulum MK,
ſpacio N, & rectangulum
KL, ſpacio R, æquale
erit. Sed vt BC, ad CA,
ita eſt N, ad R; vt igi
tur BC, ad CA, ita

24[Figure 24]
rectangulum MK, ad rectangulum KL; ſed A eſt cen
trum grauitatis rectanguli MK, & B, rectanguli KL; to
tius ergo rectanguli FL, hoc eſt duorum rectangulorum
MK, KL, ſimul centrum grauitatis erit C. Sed rectan
gulo MK, æquale eſt ſpacium N; & rectangulo KL, ſpa
cium R. Igitur ſi pro rectangulo MK, ſit ſuſpenſum N
ſpacium ſecundum centrum grauitatis in puncto A, & pro
rectangulo KL, ſpacium R, ſecundum centrum graui-

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