in Involution and Evolution. 347 
(a+b)*e=2624400=3 (540)? x3 
(a+D)e= 14580=3(540) x3? 
o= 27 Hi 33 
2639007 
3131 4856, 3d resol. 
(a+b +c)*d=530728200=3 (5430)? x 6 
(a+b+c)d=  §86440=3(5430) x6? 
dz 216= 26. 6 
531314856 : 
pane 
In this operation, in order to obtain a new figure, the parts 
within the parenthesis always represent a number consisting of 
one place of figures more than the number of letters ; the first 
letter represents the highest place of figures; the second the next 
highest ; and so on, to the right-hand place, where a cipher is 
introduced. 
This number is therefore the number formed by the figures in 
the root obtained by the preceding periods with a cipher annexed 
to the right hand ; so that when the cipher is replaced by the new 
figure, the number formed will be the root of the proposed num- 
ber as far as the number of periods that are used. Thus a+0 
=940 and a+ +c¢c=5430. 
But this operation may be simplified, as in the following, which is 
performed according to the last example in the involution herein. 
The method of pointing off is the same as before directed; the 
only difference in finding a period of the root is expressed in the 
following short 
Rule.—Subtract the product of the new figure into the sum of 
the square of the increased quotient, the product of the increased 
quotient into the new figure, and the square of the new figure 
from the resolvend. 
a*=7500 ' 160°634°321°856 (5436 
ab — 600 a@—125 
as 16 4 ~ 
8116=D , 39634 
(a+1)*=874800_ eS ade gg 
bist) ox shiny , 3170321 
879669=D as wk, 
(a+b+c)? =88454700 1, 331314856 
(a+b+c)d = 97740 6 x D=531314846 
d= _ 36 ———s 
88552476 0 
The 
