50 
SIE E. POLLOCK ON THE EELATION BETWEEN EOOTS OE 
361 
0,1, 6,18 
-2,1,10,16 
-4, 7,10,14 
_6, 9,10, 12 
441 
-8, 8,13, 12 
-10, 4,15,10 
441 
- 2 , 1 , 6,20 
-4,1,10,18 
-6, 7, 10,16 
-8, 9,10,14 
529 
-10, 8,13,14 
-12, 4, 15, 12 
529 
-8,10,13,14 
-2, 5,10,20 
625 
-2, 4,11,22 
&c. 
625 
10, 10, 13, 16 
-4, 5,10,22 
729 
4, 4,11.24 
&c. 
is to he remembered, that throughout this pcvper the root of any sguare maybe 
This relation among the roots belongs also to the numbers 
number: thus. 
49 - 4=45 
-2, 3, 4, 4 
0, 0, 3, 6 
49 - 2=47 
-3,2, 5,3 
49 
0, 2, 3, 6 
49 + 2=51 
—1, 3, 4,5 
49 + 4=53 
0, 1, 4, 6 
&c. 
81 - 4=77 
-4, 3, 4,6 
-2, 0, 3, 8 
81 - 2=79 
— 5, 2, 5, 5 
81 
-2, 2, 3,8 
81 + 2=83 
-3, 3, 4,7 
81 + 4=85 
-2, 1, 4,8 
»&c. 
The addition may proceed indefinitely, but the subtraction has to ImU : 
<10 from 49 and also from 81, the numbers become 19 and 61, uhich are te 
serit t to 19, 33, 51, &c. (2»»+l); and any 2 alternate terms ot that senes ufil 
become by contmued addition adjoining odd squares. f,,-ir+l and 
Aov 2 alternate terms of the series may be represented by ^.(« i) +t- 
2 and 2»»+4»+3; add 2«.- 2 to each, and they become 
( 2 „-l)’, and (2»+l)^ that is, adjoining odd squares^ 
If, instead of the odd squares, a series of the eien squares i- 
adioinins terms will have similar properties; thus, 
4+1=5 16+1=17 
0,0, 2,1 
+ 1 , 0 , 0,2 
-2, 0, 2, 3 
— 1, 0, 0, 4 
