MATHEMATICAL PAPERS. 16; 
XV. On tbe Extraétion of Roots. By BENJAMIN WsT, 
Efquire, F. 4. A. In a Letter to Mr. Cares GAN- 
NETT, Rec. Sec. F. A. A. 
DEAR Sin, 
AVING a little leifure at his fine: I thought it a pro- 
per opportunity to fulfil my promife of fending you the 
fubftance of what I have done, refpe&ing the Roots. What I 
chiefly aimed at was, to render the method of extracting the 
roots of the odd powers eafier, and lefs burthenfome to the 
memory ; and, I think, I have not failed in my attempt. The 
method, followed by Ward and others, is excellent, but is at- 
tended with too much difficulty in getting the divifors ; efpe- 
cially for learners, who are not acquainted with the reafon of 
the rules.— That difficulty I have ftrove to remedy in the fol- 
lowing work. In the courfe of my teaching, fince I made 
this difcovery, I have not met with more trouble in teaching 
the third, fifth and feventh powers, than what is ufual in ex- 
tra&ing the fquare root. Methods, fimilar to thefe, m be 
found for extracting the roots of the even powers. - | 
I generally get the three firft figures in the drby thie firit 
operation, (if there are fo many in the root) tho' many times 
four or five may be got, if the firft figure in the root comes 
very near to the firft period of the refolvend. — 
As it is not neceffary to make a long introdu&tion, I fhali 
proceed to fhow in what manner I inveftigated the rules. The 
‘cube root being the firft in order, I fhall begin with that ; and 
in order thereto, let the refolvend be = 2 ; the firft figure in 
the root = r ; and the remaining figures in the root — e ; and 
