Example III, 



Let us take the Equation s. 4 — 80 ^+1998 

 -—14937 & +50001=3 o, which Dv. Wallis 

 ufes Cap. (52 of his Algebra^ in the Refolution 

 of a very difficult Arithmetical Problem where 

 by Viet ah Method he has obtain'd the root moffc 

 accurately; and Mr. Raphfonbx'mgs it alfo as an 

 Example of his Method, Page 25, 25. Now 

 this Equation is of the form, which may have 

 feveral Affirmative Roots, and (which increa- 

 fes the difficulty) the Coefficients are very great 

 ip refpeft of the Refohend given. 



But that it may be the eafier manag'd, 

 let it be divided, and acccording to the 

 known Rules of Tointing, let — zA-\~ 8 z. 5 ~~ 

 20 z? L \~} 5 i ^0,5 (where the quantity z. is 4k 

 ofz in the Equation propofed) and for the 

 firft Suppofition, let azz 1. Then -\ 5<? — 

 2e z +4e 3 -e*-o,5t=:o j that is, if s=s 5?+W; 



hence etz\J \ ss+bt — S-fL is t=s\/ 37- 5, and fo 



£,£=21, 27*, Whence 'tis rnanifeft that 12,7 is 

 near the true Root of the Equation propofed. 

 Now Secondly, let us fuppofe *,t=M2, 7, and 

 then according to the directions of the'TabJg 

 of Powers, there arifes 



b $ t u 



—26014, 464.1 — 8193, 532^—967, 74? ? — 50, 8e 3 — e+ 



870, 640^-38709, 60^3048 e z -|-8o e 3 

 — 322257,42' — .50749,2 e — 1998 C* 

 -1-189699,9 -I-14937, c 

 ~ 5000. 



t 



t 



4 



G B 



That 



