354 Mr, Bromhead on the fluents of irrational functions . 
same variable, then dy, dz, dw, . . are expressions proportional to the derived func- 
tions of y, z,w,.. whatever may be the variable of which they are common func- 
tions. Hence ~ ~ ; and if y be a function of x, or =: p (x), then ~ — 
dz dx 
2|Lifi — D<p lx) and dy — dx . Dp (<r) . 
Moreover, since the derived functions are in the limiting ratio of the increments, so 
also are the fluxions. From this consideration we can in the applications of analysis, 
practically determine the ratio of the fluxions, when the derived functions are 
unknown. 
ERRATA. 
Page 72, line 20, for parts, read part. 
73, line 3, for between, read below. 
. — ■ 98, line 4 from bottom, dele the comma after A. 
- ■■ 101, line 6 from bottom, dele BH. 
— — 102, line 4, for axes, read axis. 
164, line 11, dele the comma between m and n. 
. — — 174, line 7, for consisted of, read consisted in. 
-, line last, for m, n, read m, m. 
1 9 1, line i3,forpp x, read p <px. 
213, line 14, for 4 (x, y), read <pf (x, y). 
214, line 10, dele ** in an infinite number of ways”. 
224, line 22, for /(«), read/(x)., 
226, line 24, for — x, read r= z. 
232, line 16, in tbe denominator, for 1— , read 1 + . 
-, line 18, ditto, ditto, for 1— -, read i±. 
251, line 9, for 
d-]f x. 
7) 
^4 ( x >~z) 
read - — 
dx dx 
-, line 11, for d in both numerator, read d a . 
line 13, for ( i-j read x p j — 
