Of GREATEST ATTRACTION. 193 



The whole area of the curve, therefore, is ^ a\ or 4- AB 2 \ for 

 when <p is a right angle fin<p= 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 



± -T 



when .y, and therefore / is a maximum, |^ 3 x =z 2x, or 



4. 1 . a a 



3 arzitf 3 , that is x= — — — - — . 



S ti V 2 7 

 Hence, calling £ the value of y when a maximum, 



2? <r 27 t v 2? t y m^ V27 



and therefore a : 6 : :\/ 2J. :\/ 2, -or &s 11 : J nearly. 



3. It is material to obferve, that the radius of curvature at A 



4. 

 is infinite. For fince /= ^ ^— x\ y — = ^7 — *.- But when 



# 3 



2 

 J 



a? is very fmall, or y indefinitely near to A, - becomes the dia- 

 meter of the circle having the fame curvature with ACB at A, 



4 

 y 7, a 3 . r. 



and when x vanifhes, this value of ■*-, or — , — *, becomes mn- 



X' L 



X 6 , 



1 



nite, becaufe of the divifor x 3 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 the curve of equal 

 attra&ion. 



The 



