344 Account of certain Improvements 
a=125 és 
“3a%b= 30000 
joat= 2400 
me 64 
3(a+b)*c= 2624400 
{xtne= 14580 
ee c= 27 
3(a+b+c)*d= 530728200 
3(a4+b+e)a= 586440 
od Saat ot OP 216 
160634321856 
The foregoing operations now exhibited, require several minor 
operations which are omitted. However, these operations will not 
be necessary in the following form, where it may be considered 
that in the first period a=50 and l=4; in the second period 
(a+b) =540 and c=3; and in the third period (a+)+ ¢) =5430 
and d=6. Here follows the operation : 
3a? =7500 
Ist, jou= 600 
e be= 16 : 
8116=D 
3(a+b)? =874800 
2d,< 3(a+b)c= 4866 
Stain Gr 9 
879669 =f) 
3(a+b+c)? =88454700 
bay) sacra 97740 
‘kkeeepe = 36 
= 2639007... 
6xD”= 531314856 
160634321856 = (5436)? 
It is evident that, 8(a+b+c¢+ &c.)?=3(a+b4&c.)? + 
2:3(a+b+ &c.)c+3c* for the square of a+l+c &c., consists of 
the squares of each quantity, and twice the sum of the products 
of every two; this square being multiplied by 3, will give three 
times the square of each letter, and six times the product of every 
two, Again: the square of a+l+Q&c. with one letter less, con- 
tains the squares of all the letters, except the one omitted; and 
twice their products,except those of the letter omitted : therefore 
when multiplied by 3, will contain the square of each letter three © 
times, 
