THEORriMATIS ANALYTICI. 245 



/ zr .t - P, pcr foLim variabilem ; dctcra.inari queat, 



prinuim enim patet cffe 



vi^ (a, X)— vjy (a, O + P^ v{>'(a, /) -i-^-ifl?K?,n ^ dd,p^'{,,t) 



1. !. 3.VdF 



ctc. 



dcindc vero intelligitur quum \|y (;, .v) fimilis fit 

 fiiniflio ipforum / et x\ ac \jy(a, a.) ell ipforum a 

 et .V, poftcriorem fun(flionis valorem in pnorcm 

 abire , fi vbique loco a introducatur t, praeterea 

 vero (emper notandum eft , poft peradas differentia- 

 tiones \bique loco /' fcnbi debere f. Sic exempli 

 cauflli fi fiierit t — x — t x^ atque hinc inueftigari 

 debcat valor ipfius t t x pcr t exprefTus, ftatim fiet 

 P-/A-,P'-/'/, \K^, x)zLltx, v{y(a,;)-aa/ et viy'(a,/)-aa, 

 Vnde prodibit 



a a .V =; a a r -h a a /''; -+- a a /'' / + aa f '* ; 4- etc. 

 ideoque- 



ttx-i + t'-\-t'^t*-\- etc. = ^, , 



qui valor omnino veritati eft confentaneus. 



XII. Vt iam de fingulari huius Theorematis 

 vfu , breuiter quaedam adferamus , examinemus 

 prinio , quoiriodo eius ope radicem cuiuscunque ae- 

 quationis algebraicae per feriem exprin^ere liceat, 

 in quem vfum, ipfum Thcorcma a Celeb. la Grange 

 inuentum effe conftat. Si igitur propofita fucrit 

 hacc acquatio algebraica ad rationalitatem perduda : 



x — a-i-bx^-^cx^-^dx^-^-ex*-^- eic. 



H h 3 quac- 



