*6o 
Dr. Waring oh 
B+ |X) i?+ (k+ l(5±Jf)C + iB) e+{!+ \b-±zx xD+|C)f’ + 
& c . = a ; find the value of e in a feries proceeding according to the 
dimenfions of 
A — \(b±ix) X X 
b + Zb: 
and x + e will be the abfcifs 
,, , z -X xB + f X 
required; X denotes the value of y, when the abfcifs =x. 
From the fame principles may the ordinate y, &c. be found. 
This problem may be refolved in the fame manner, when 
X denotes an infinite feries deduced from an equation exprefling 
the relation between the abfcifs and ordinate of the given 
curve. 
If the given area a be the difference between two areas 
SPM («') and SPQ=(3 (fig.2.) ; for « fubftitute «' -/3, and the 
operation will be the fame as the preceding. 
j. Given any equations, of which the increments of 
the quantities contained in them can be found from each other, 
and given approximate values of each of the unknown quan- 
tities, which nearly correlpond to each other ; to firm approxi- 
mations, which differ lefs from the quantities themfelves than 
the given ones. 
Suppofe each of the given approximate values to be in- 
creafed or diminifhed by fmall increments or decrements, as 
e, o, i, &c. which are the approximations to be found ; and 
from the given find the equations refulting from this hypo- 
thefis ; and from thefe may be deduced, by Ample equations, 
the approximations fought e , i, o. Sec. by neglecting in them all 
the pouters of f, o, i. See. except the Ample ones, and all the 
produfts of them multiplied into each other ; and confequently 
the equations deduced will contain only given quantities and 
fimple powers of the unknown e, i, o , &c. to be found. 
2 . When two or more (n) values of one (a?) of the unknown 
quantities are nearly equal to its given approximate ; then the 
^ equation 
