26 
COMPUTATIONS OF Z. COLBURN. 
On numerical 
computations, 
particularly 
those perform- 
ed by Z. Col- 
burn. 
Practical illustrations of the rule. 
The square of m+n+p -\-q, or 7654, is 58 , 58'37’l6 
Deduct m* ----- 49 
953 
Deduct 2mn + n* - - - 876 
82 
Deduct 2 (m + n) q - - - 76 
637 
Deduct 2 (m-j-rc) q - - - - 6 08 
29 
The root is already found ; but to prove 
correctness, deduct p 2 ----- 25 
Deduct 2 p q 
416 
400 
Deduct ^ 2 
16 
16 
The involution and evolution of similar numbers have only 
this difference ; one process consists of repeated multiplications 
and additions ; the other chiefly of multiplications and subtrac- 
tions. One extends the length of a chain, by adding link to 
link in progressive order; the other diminishes the length, 
detaching link from link by retrccessive reductions. 
To extract the cube root of - - 448 3997^2 264 
Deduct the cube of the first root 7 - 343 
mrnmm 
,10 5 
Deduct 3 times 7 9 say 15 and 3 times. 
7 X ,6 say 1,2— say 16 x 6. - * - - g6 
9 
Deduct 1,2 (already found) x,5— ,60and 
the cube of ,6 say ,2 - - - - - - ,8 
8,2 
- - - 80 
— Th» 
Deduct 1 6 (already found) x ,5 
