Of GREATEST ATTRACTION. 19gr 
From C (Fig. 1.) draw CE perpendicular to AB; let AB=a, 
AE=x, EC=y. We have found AB?XAE=AC;, that is, a x= 
(«° + ys, or a* x= («+ ¥); which is an equation to a line 
of the 6th order. 
4.2 @ Tato 
To have y in terms of 2, a +y=a? w?, yma? x? — a, 
se | RAE 
and y = «*' a?—vx3, 
HENCE y=0, both when x=0, and whenx=a. Alfo if # 
be fuppofed greater than a, y is impoffible. No part of the. 
curve, therefore, lies beyond B. 
THE parts of ‘the curve on oppofite fides of the line AB, are 
fimilar and equal, becaufe the pofitive and negative values of y 
are equal. There is alfo another part of the curve on the fidé 
of A, oppofite to B, fimilar and equal'to ACB; for the values 
of y are the,fame whether x be pofitive or negative. 
IIT. 
THE curve may eafily be conftructed without having recourfe 
to the value of y juft obtained. 
Let AB=a, (Fig. 1.) AC=2z, and the angle BAC=¢. 
Then AE= AC x cofg = zcofg, and fo a’ zcofg =z, or 
a’ cof~ =x"; hence z=aN cof. 
From this formula a value of AC or z may be found, if 9 or. 
the angle BAC be given; and if it be required to find x in 
numbers, it may be conveniently calculated from this expref- 
fion. A geometrical conftruction may alfo be’ eafily derived 
from it. For if with the radius AB, a circle BFH be defcribed. 
from the centre A; if AC be produced to meet the circumfe- 
rence 
