1815.) Scientific Intelligence. 43 
and not — ae . t, it would therefore be improper, in the present 
case, to use the sign —, and consequently Mr. L.’s equation 
fi 6 2 B3 
should have been + (+ em tt). = aby coe 4 = — S508 
its equal — (@ — =). /t-+ = -/i-3 _ — and then 
by proceeding as he has done we obtain — > ~ yee aoe + = 
: roy ; 
sf = —/ = — =. a Va = as the same as the root given above. But 
it ought not to be forgotten that Mr. L., notwithstanding the above 
oversight, has the merit of being the first who has pointed out the 
method of finding the cube roots of a linomial, by means of the 
three roots of the cubic equation with which that binomial is con- 
nected. 
If we take the equation employed by Mr. L., viz. 2° — 242= 
72, wherex = 6,¢=3+4+ / —3andv=3— VW on 3, the 
binomial and roots will be as follows: ” 36 = / 784 = 64 
VW 8, ‘vein ghe as the upper or under i is used. 
First root = ty/—— =32+1=40r2. 
Second root = On an or (= ae = f—3 
=—'(1-—;/-— 8). 
- aa: 13 eg 
Third root = — tar) = /- (= + av-—8 
—(l1+ v7 — 8). 
So that when the upper signs are used, we obtain the cube roots 
of 64; but when we use the under ones, the results are the cube 
roots of 8. Hence it appears that N. R. D. was not “ too posi- 
tive” when he said, ‘ it is not the cube root of 64, but of 8;” 
for he used the sign given by Mr. L., and then the quantity is a 
cube root of 8, as appears from the “above, The reason why Dr. 
3+ 7 —3)\ 
2 j 
+ (— / _ (+ — v7 —3)); instead of the quantity given 
Tiarks made it a cube root of 64, was his using — ( 
