Mifcettanea Curiofa. 1 9.1 



A Method of Extracting the Root 

 of an Infinite Equation. 



By A. De Moivre, F.R.S. 



THE ORE M. 



IF azrYb^cz}^^^ 6 , &c. jzs gy 

 +%~b> 5 -l~ty 4 fyy'-Vmy 6 , &c. then will 

 h^bAA 

 at be ss^-yH y 2 



.+ -> J 



v.* 



^rn — ib AC~ icAAB h- *L4 4 

 a 



l-ibBC-zbAD-^cABB—scAAC-^dA 1 B 



a ^ 

 m —ibBD — bCC—ibAE --- c £ 3 — 6<r^£C 

 — $cAAD — 6dAABB—4<iA 3 C—$eA+B 

 ~fA s 



+ — ! /, &C. 



a 



For the underftanding of this Series, and 

 in order to continue it as far as we pleafe \ 

 it is to be obferv'd, i. That every Capital 

 Letter is equal to the Coefficient of each 



pre- 



