- ( 6Si ) 
Intelligatiir fuper figura P F A D H ere£lus Cylindricus re» 
(ftus & refeitus piano per P H tranfeunte, cum piano bafeos an- 
giilum femirediim comprehendente ; exponet iftud folidum, 
momentum figurse P F A D H fuper axe P H libratse : Hujufq; 
folidi live pr3edidi raomenti fluxio, (folida nempe ereda lliper 
PFfp 3c HDdh) producitur, ii momentum Huxionis, five 
fluxio momenti ipfiifs A ducatur in | A C datam. Nam per 
Corol. hujus Prop. HDdh = DdxAC: Quare ipfum mo« 
mentum fiuens producitur ducendo momentum Curvse FAD 
refpe61u axis P H, fuperiore CoroL determinatum, nempe C A 
xBD + CBxAD, ini AC: eritq; proinde | A Cx A C xBD 
+ |ACxCBxAD. Adeoque fi hoc applicetur ad figuram li-. 
bratam P F A D H five 2 C A x A D per hujus Prop. Corol. 
fiet diftantia centri gravitatis figure P F A D H ab axe P H 
C A X B D 
= (I — 1-5 C B =:) dimidiae reitae C E fuperius deter- 
AD 
minatse. 
8. Si per N pundhim ubi D T tangens Catenariam in D, fe- 
cat A R, ducatur re£ta parallela ipfi B C, occurrens re^tae per E 
ad A R parallels in O ; erit O centrum gravitatis curvse A D. 
Nam per Corol. 6, centrum gravitatis curvse AD eft in re6ta 
E O, fed demonftrabitur illud efle in N O re6ta5 & proinde erit 
ipfum O pun6lum. Intelligatur D A librari circa H L axem ; 
hujus momentum eft curva D A du6ta in diftantiam centri gra- 
vitatis ab H L : Et ejus proinde fluxio = D A x H h (H h eft 
fluxio diftantise axis librationis k gravitatis centro) ~ VraTTTa 
a X 
= a X. Ac proinde ipfum momentum Curvse 
V a a X -j- x2 
gravis D A circa axem H L libratse = a x. Et igitur diftantia 
centri gravitatis ab eodem axe eft a x applicata ad A Dj live 
A C X D Y 
— — — — . Sed quia D T tangit Catenariam, per CoroL 4. hii- 
A jK 
jus Prop, angulus B D T five D N Y = A C R, & anguli ad A 
& Y funt recti, quare in triangulis sequiangulis R A C, D Y N; 
R A . A C : : D Y , Y N. Unde Y N = , hoc eft Y N 
R A 
eft diftantia centri gravitatis Catenae A D ab axe H L, five cen- 
trum praediilum eft in re^la N 0. 
0. SI 
