15IMPLE EQUATIONS. 33I 



In like manner, if \/ 2A;+3+4=:8, then will \/ 2x-^^ 



sr8 — 4=4> 



And 2;v4-3=4'=^4> ^n^l 2;v=64 — 3 = 61, or x=z^-J 

 r=3oi-, 



RUtE j^i 



If that side of the equation, which contains the iin* 

 known quantity, be a complete power, it may be reduced 

 by extracting the root of the said power from both sides 

 of the equation. .• - - 



Thus, if a;*-}-6x4-9=:25, then will »+ 31=^/25= 5 j 

 or Ar = 5 — 3 = 2. 



And, if 3;*" — 9=21 + 3, then will 3;^* = 21 + 3+9 = 

 33, and;f* = y = ii, or;v=\/ii. 



2a;' 

 In like manner, if — *-l-ic=S2o, then will 2A;*-4-30 

 3 

 S=:6o, and /v*+-i5 = 3o, or a;* = 30 — 15= i5,or Ar=:\/i54 



RULE 6*. 



Any analogy, or proportion, may be convCftdd into an 

 equation, by making the product of the two mean terms 

 equal to that of the two extremes. 



Thus, if 3.V t 16 :: 5 ! 10, then will 3JvX 10= 16X5, 



and 30^:= 80, or ^ = -~= 2j. 



2X 2CX 



And, if — : a i: h : d then will =r^^, and 2cx:afi' 



3 3 



3(7^ 



2ahf or xi=— ^. 



2C 



A? 



2 

 4.V 



9C 



In like manner, if 12 — x : — :: 4 : i, then will 12— 



2 



4.V 

 X=:—=z 2.V, and 2;v+.t =: 1 2, or ;* =i y ~ 4... 



RULB 



