192 ‘Of the SOLIDS 
ence in F, and if FG be drawn at right angles to AB, then 
AG GAME freee +t 
AB = cof¢, and fo % =axN oe —/ABx AG = AC, 
TuHeEREFORE, if from the centre A, with the diftance AB, a 
circle BFH be defcribed, and if a circle be alfo defcribed on the 
diameter AB, as AKB, then drawing any line AF from A, 
meeting the circle BFH in F, and from F letting fall FG per- 
pendicular on AB, interfecting the femicircle AKB in K; if AK 
be joined, and AC made equal to AK, the point C is in the 
curve. 
For AK = VAB x AG, from the nature of the femicircle, 
-and therefore AC = V AB x AG, which has been fhewn to be a 
property of the curve. In this way, any number of points of 
the curve may be determined; and the Solid of greatef attrac- 
tion will be defcribed, as already explained, by the revolution of 
this curve about the axis AB. 
2 
TVs 
To find the area of the curve ACB. 
1. Ler ACE, AFG (Fig. 2.) be two radii, indefinitely near to 
one another, meeting the curve ACB im C and F, and the 
circle, defcribed with the radius AB, in E and G. Let AG=2z 
as before, the angle BAC = 9, and AB=a. Then GE= ag, 
and the area AGE= 4a %, and fince AE’: AC’: : Sect. AEG : 
Sect. ACF, the fector ACF=+ 2’ Q- But 2? = a’ cof 9, (§ 111.), 
whence the fector ACF, or the fluxion of the area ABC=+4"@ cof Q 
and confequently the area ABC = +4 fing, to which no con- 
ftant quantity need be added, becaufe it vanithes when @= 0, or 
when the area ABC vanithes. 
THE 
