X5* DE MOTV OSCILLATORIO 



§. 52. Ex viribus nutcm E/, F;;; , et Gn fcqucn- 

 tia emergunt momenta : Scilicct pro flexura B cft mo- 

 mcntum = R(G£-B£)= ^5^, pro flexura A cft 

 momcntum = R(G£-A*)-f-Q.(F/-A<7); et pro ip- 

 fo axe O eft momcntum =R.G < g , -+-Q.F/-f-P.E*. 

 At ex viribus Rg,S<r,etTT oriuntur momenta inpar- 

 tcm contrariam vrgentia ; erit autem pro flexura B mo- 

 mcntum = ^~ (B^-f- j^ ) ; pro flexura A momen- 

 tumeft = ^(AB-+-BG-f-^)-f-¥ / (AF-f- L ' F ) 

 dcniquc pro axe ipfo O eft momcntum = "/ (OA-f- 

 AB + BG + ^j+f^OA + AF+^+^ 

 (OE-I-qe)- Hinc igitur oricntur trcs lcquentcs acqiur 

 tiones R(G^-B^)=: R -^(BG-1-^ G ) 

 R(G£-A*) + Q(F/-Aa)= R ^ Gs (AB~f-BG-f-^) 



R.G^-HQ;F/-4-P.E^=5^fi(OAH-AB+BG-r-i7;) 



-F- f(OA + AF+ ;.V )-f- '■? (OE-f- j 

 Ex quibus tribus acquationibus primum puncta L ct M 

 ac dcinccps longitudo penduli fimplicis uochroni / deter- 

 minabitur. 



§. 53. Prima aequatio ob G^:B^=MG:MB abit 

 in hanc BG./=BG.MG-f-fcifc: Atque C a fecunda 

 prima auferatur remanebit iftaR(B£ Aa)-\-Qjyj-Aa) 



-^H--" f (AF+ri;). Eil autem B*-A*= 



atquc Gg = -j , ex quibus haec fecunda aequatio 



refultat , R.AB/+Q.AF/= s ^Vb ,JL ° -4-Q.AF. LF 



+0: 



