De motu corporum in tuho mohili circa axem fixum, 81 



^a, ipsum vero tubum in directione contraria sollicitet. Hujus vis P momentum ad tubum versus 



Pfx ds^ 



corpus l reducendum erit = Px, hinc tubus removebitur per spatiolum fcp='' — j ex quo 

 prodit spatiolum pn = — — • —• Deinde eadcm pressio P corpus, quod est in l, perducere debet ia 

 n, eritque i;r = — •— . Ex his rcsultat 



P(Jxa; -+- Mkk)ds^ , dxds V ds^ ds^Vp V ds^ Sfx ds^ 



AAMkhu P ~7 ~^ '^ ~fVu A ' 4u "*" Mkk ' liT 



eritque ergo pressio quaesita 



Pz= 



AMkk /AVpu 



Axx H- Mkk 



/ 4Vpu F Sfx\ 



\ f l^^mk/ 



23. Tubus ergo nunc sollicitabitur a virium momento Sf — Px, ex quo oritur acceleratio 

 motus rotatorii 



du Sff Pfx Sff Afx /4Vpu V 



/ 4Vp 



\ r 



seu 



I ds Mkk Mkk Mkk Axx-t-Mkk\ f A 



j , Sffds 4Auxdx Vfcds 



Axx-t-Mkk Axx-i-Mkk Axx -t- Mkk 



Corpus autem, quod in tubo descripturum fuisset motu insito spatiolum dx, nunc ex J in punctum 

 tubi ;r pervenit, descripsit ergo spatium 



P7r2 Aa^ , T ds^ xds^ 



^JP^^O:.^OP) = JP-^---=JP-^ — =dx^-^.^-^-^, 



hinc accelerationem accepit = — h- -^ = ^^ ex quo erit dp=— — *--y— Quod si celeritas 



xxu 



corporis vera ponatur debita altitudini v, ob v = p-\--—i erit 



j , xxdu "iuxdx Tdx Sxxds Vx^ds 4Mkkuxdx 



dV = ap-h- -y- H Y' ~ ~~a' ~*~ Axx-^Mkk ~*~ f{Axx -^ Mkk)'^ ff(Axx -*- Mkk) 



2k. Ex priori aequatione oritur 



4Auxdx Sffds Vfieds 



du-h 



Axx -t- Mkk Axx h- Mkk Axx -*- Mkk 



cujus prius membrum fit integrabile si multiplicetur per (Jxx-i-Mkky; erit enim ejus integrale 

 (Jxx -i- Mkky u, quod ponatur = Q. Hinc erit 



dQ = Sffds {Axx -f- Mkk) -h Vfxds {Axx -*- Mkk) ; 

 dividatur haec aequatio per ^YQ erit 



dQ Sffds Vfxds , ,. njn\^/ /"^/7»» . rVfxds 



wq^^w-u-^w-u' ""^^ i^^^-^^f'^)y^=j-wu-^j^' 



Quare si vires sollicitantcs 5" et F evancscant, erit {Axx-¥- Mkk^Yu quantitas constans. 



25. Ex prima et ultima aequatione si climinentur termini, in quibus nulla vis sollicitaus 

 occurrit, prodibit Adv -t- — — =^ Tdx -t- Sds -h ^- Hinc ergo intcgrando obtincbitur 



Av 



Mkku y-rrj rVxds ^^ , j (Axx-i-Mkk)u 



^*"* =/Tdx -H pp ^fSds = Ap 



ir 



Si ergo vires sollicitantes T, F, et S evanescant, erit 



L. Eoleri Op. posthuroa. T. II. 1 1 



