I 



[ 229 ] . 



Nearly fimilar is the management of three biquadratic furds, 

 by all which it will appear that this method is much fhorter 

 than M. Fermat's ; the principal care to be taken is to keep 

 at . the fame fide two furds whofe . product will give a fimple 

 quadratic, and then uniting the terms that will admit of it pro- 

 ceed as before by involution and tranfpofition. 



When fradlions having furds in their denominators occur, 

 it is expedient to remove the furds out of the denominator 

 by multiplication, this is ufually done by the multiplication 

 of the denominator taken as a binomial or refidual ; if there 

 be four quadratic furds this is generally fuppofed the limit, 

 and that if a fifth term be added whether rational or not, 

 the denominator cannot be rendered rational, but fince the bi- 

 nomial or refidual here affords the fame convenience as the 

 tranfpofition in equations, a repeated multiplication will clear 

 the denominator of radicality. True it is that after multiplica- 

 tion by a binomial, if the denominator be refolvcd info parts 

 of one and four furds, there will come out fix furds and in 

 no cafe lefs than four and a rational, however by continuing 

 the operation a little farther the finnplification will appear, 



m 



&c. 



"^0+ ■^b -\- -^c -\^ '^d + V/r X Vtf -j- v'(5 — v^<: — ■^d — */e the deno- 

 minator which is the multiplier being refolved into parts of two 



and 



