i 9 2 Of the SOLIDS 



ence in F, and if FG be drawn at right angles to AB, then 



^ ~ cof <p, and fo z = axJ^ =V AB X AG = AC. 



Therefore, 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, interfering 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 great eft attrac- 

 tion will be defcribed, as already explained, by the revolution of 

 this curve about the axis AB. 



IV. 



To find the area of the curve ACB. 



i. Let ACE, AFG (Fig. 2.) be two radii, indefinitely near to 

 one another, meeting the curve ACB in C and F, and the 

 circle, defcribed with the radius AB, in E and G. Let AC ~z 



as before, the angle BAC — <p f and AB zz a. Then GE =: # <p, 

 and the area AGE = 4. V <p, and fmce AE* : AC" : : Sett. AEG : 

 Sea. ACF, the fedor ACFr=i % % <p. But z 2 = a % cof <p, (§ m.), 

 whence the fedor ACF, or the fluxion of the area ABC— \a*<p eofp, 

 and confequently the area ABC — ~ a 1 fin <p, to which no con- 

 ftant quantity need be added, becaufe it vaniihes when <pz: o, or 



when the area ABC vanifhes. 



The 



