142 DE NOFO GENERE OSCILLATIONVM. 



§.31 Coefficientes qiiidem poteftatum parium ipfius 

 t (iitis regulariter progrediuiltur , at poteftatum impariura 

 exponentes ad has formas rediguntur. 



g P . ^ ~a-^^b e 



") ■ ^ 1.2.3. 205(^3-26) I.2.> 206 



4&^ 



V , tf^ — 4 



S ■ I . 2 . 3 • + 



5 . +a^6g(a— 2 6J 



_g3_^.6? 



I ' 2 ' 3 7. ku^d^^g (a— 2 6) 



a* — trti* 



'^ 1.2.3 9' i6a^b^^ia—2b) *n^ i . 2 . . . s . i6a+ 6+ 



etc. 



Qiiare fi feries a -f- g^ -f- y r + etc. in feries fimpli- 

 ces regiilares relbluatur , prodibit s z^ 



^ [^ ~~ TTTTTab "1- i.,.,.,. + a2^2 ~ "" 1 .2 . 3 . ••0 . .«^63 + etC.) 



■+^^^^^(v7^-,.,!' .,a,V2a6 + :TTTrr-;^vl^ - etc) 



. ab^/zab / t f^ tf_ 



"Trg{a-2b)\i2ub z.z.^' zab^j^ah "i 1.2. j .+.'; .+0^02 vTa6 — etC.J 



_ Q^6 /t_ __ t^ rs 



£(0-26) ta i.2.3.a^ ""l^ I • 2 . 3 . + . j . a5 etC.) 



quae feries cum fingulae fint fummabiles, obtinebitur loco 

 s fequens valor finitus ^ s zn a. cof A . y,^^ ^- '^Vzab . 



f A i , ab-\/zah r \ ^ "^ ^ r s. t 



iJ^^- A • vl^ + ^I^^^ ""' ^ • vT^ ~ g(a— 26J lin- A . -. 

 qnae aequatio fi conftantes « et S aliquantillum mutentur 

 ■plane congruit cum ea , quae fupra §.27. ope integra- 

 tionis efl: eruta. 



§.32. Retincamus aequationes fupra inuentas s =; 

 D cof A . vT^ + C fm. A . 17^ - ^{^) ^^"^- A i et 

 -V^ziz^Ts fin.A . v7^&-^ cof ATT^ + j^jycof A^ 

 in quibus caliis ambo ipeciales fupra tra(flati egregie con- 

 tinentur. Ponamus nunc autem initio quo ^ zn o , corpus 

 quieuiffe in C, ita \t tum fiierit tam j = o quam V^y 

 ^ o. Fiet itaque D zz: o ; et C :z: ||zi^) , quibus va- 



loribus 



