Valerio, Luca - De centro gravitatis solidorvm libri tres

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1guli ABC, quatuor rectæ inter ſe parallelæ AD, BE,
CF, NM, tres autem magnitudines æquales habeant cen
tra grauitatis G, H, K, in tribus AD, BE, CF. Di
co trium magnitudinum ſimul, quarum centra grauitatis
G, H, K, eſſe in linea NM. Iungantur enim rectæ GH,
HK, GK, BNP; & per punctum P, recta PL, ipſi MN,
parallela, & iungatur LH. Quoniam igitur rectæ BP, LH,
iungunt duas parallelas LP, BH; erunt quatuor rectæ BH,
LP, BP, LH, in eodem plano. Et quoniam planum quadran
guli PH, ſecat planum trianguli ABC, à communi autem
ſectione BP, ſurgunt
duæ parallelæ PL, MN;
quarum PL, eſt in pla
no quadranguli PH,
erit etiam MN, in eo
dem plano quadranguli
PH: & ſecabit LH. ſe
cet in puncto O: qùare
vt LO, ad OH, ita erit
PN, ad NB, propter
parallelas: ſed PN, eſt
dimidia ipſius NB; er
go & LO, eſt dimidia ip
ſius OH. Eadem ratio
ne, quoniam AP, æqua

43[Figure 43]
lis eſt PC, erit & GL, æqualis LK. Duarum igitur
magnitudinum G, K, ſimul centrum grauitatis erit L: ſed
reliquæ magnitudinis, quæ ad H, eſt centrum grauitatis
H; & vt compoſitum ex duabus magnitudinibus G,
K, ad magnitudinem H, ita ex contraria parte eſt HO,
ad OL; Trium igitur magnitudinum G, H, K, ſimul cen
trum grauitatis erit O, & in linea MN. Quod demon
ſtrandum erat.

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