[ 76 ]■ 



but this remainder may be refolved into thofe parts. 



m" — ^bm^ -^ d b^ m"- — Afb^ m-\-b''\ 3 « = m — b." 3 n 

 vf- — %bm -Y b^X 6n^= m — b''. 6 «^ 

 + 3«' = 3«' 



n, is affirmative, and m^—b' and m — ^ '^ alfo affirmative therefore 

 the remainder affirmative. 



Let the roots be — ?n —m— b 



7?i^. e^ + ;//*. 2 w. ? + m- . nf- 

 — 2bm — 2bm — ibm =0 



^b' -^ b^ + b" 



e' + 2 m. e ■\- vi^ ■= 



e = — ?;; + •Jjtf — 7lf- 



therefore when two roots of the prppofed equation are equal, the 

 value I?, by which the roots are to be cncre;ifed will be one of the 

 equal roots, therefore the two laft terms of the transfarmed equation 

 will vaniffi, therefore reducible to a fimple equation, which will give 

 the remaining root e.g. x^ + 7 ^v" + 16 .v -f- i c = 



49 +112 +256 



•^ .e = ^•.•?^ + 4^ + 4= •.•£-=:— 2 +i/4 — 4 



48 — ic8 —352 



