[ 230 J 



and three furds, in which cafe fewer furds will come out in 

 the produd after uniting fuch as admit of it, than if the deno- 

 minator were refolved into parts of four and one, by retain- 

 ing at the fame fide of the binomial thofe furds whofe quan- 

 tities under the radical fign have a common divifor, in the next 

 multipHcation their produd coalefce and may be united, fo that 

 after four multipHcations the denominator is freed from radi- 

 cality as will beft appear by example. 



^a+ "^6+ ^c-\- -^d-i- '^e X "/a -^'/b—'/c— -^d— -^e 



-\- a -\- -^ab + •v^jc + ■>^ad+ ^ ae + '^bc + ^bd-Y ■^te — "^cd— '^ec — "^ed 

 + (5 + -^ab — ">/ ac — "^ad— -^ae — ^bc — '^bd—'^bc — -^cd— '^ec — "^ed 

 — c 

 -d 



a^b — c — d — e+z^ab ^ ^ ^ ^ ^ ^ — 2 '^cJ— 2 ^ce 2^/cd 



Let all the rationals equal r and the produd will be 

 r+ 2 '^ab — 2 ViTf — z-^cd— 2 ^ae 



r + 2 ^ab — 2 "^ce — 2 ^cd— 2 ^edx r + 2 ^ab — s/ce + 2 "^cd + 2 '^de 



r + 2r '/ab — 2r -^ce — 2r ^cd — zr ^ de — A- '^ahce — 4 -^ abed _ 4 '^ abde 

 ifOb + 2r >/ab — zr "^ce + i^e ^cd+ 4c ^Je — 4 '/abce + 4 '/abed + 4 ^ abcde 

 ifCe — \d ^ce + 2r '/cd — \c^ de 



\cd — \d'/ee — \e Vcd + zr Vde 



\de 



r' + i^b + 4C(? — \cd— ifde ■\- \r Vab — 4r — Sd'v^ce — 8 ■</abce 



Let 



