Of GREATEST ATTRACTION. 193 
Tue whole area of the curve, therefore, is 4 2°, or + AB’; for 
when ¢ is a right angle fing=1, ) Hence the area of the curve 
on both fides of AB is equal to the fquare of AB. 
2. THE value of x, when y is a maximum, is eafily found. For 
mst 
4 
Ba eee QOL 
when y, and therefore y* is a maximum, 24 
a 
TS : a 
3«*° =a, that isw= —= d 
= 4 
; : iS i 27 
HEwce, calling 4 the value of y when a maximum, 
2 ’ 1 
2 
= + 2 
Baa x ae “ae: as a (==) = 7% and pee s 
ar Ds hl vo N/ 27 27 
and therefore a:4:: \ 247 af 2, -or as II: 7 nearly. 
3. It is material to obferve, that the radius of curvature at A’ 
20.1 9S 2 Sneha a 
is infinite. For fince y°=a? «?—x, J — * — x... But’ when 
2 
x is very fmall, or y indefinitely near to A, - becomes the dia- 
meter of the circle having the fame curvature with ACB at A, 
2 4 
and when « vanithes, this value of y or ai — x, becomes infi- - 
x3 
Nite, becaufe of the divifor x? being in that cafe =o. The dia- 
meter, therefore, and the radius of curvature at A are infinite. 
In other words, no circle, having its centre in AB produced, 
and pafling through A, can be defcribed with fo great a radius, . 
but that, at the point A, it will be within thé curve o 
£ equal 
attraction. 
THE 
