Mifcelianea Cur i of a. 1 7 7 

 • 



ji General Tropofit ion Jhevaing the 

 Dimenfion of the Areas in all 

 thofe kinds of Curves which are 

 defcriPd by the Equable Re- 

 volution of a Circle upon any 

 Bafis, either a Rectilineal or a 

 Circular one. 



By Edm. Halley. 



^rnri I S known that the Primary Cycloid^ 

 JL as alfo the Prolate, and the ContraBed 

 •one (which they call Trochoids) have been 

 largely handled by the Celebrated Dr. Wal- 

 lis and others, and their Properties are now 

 common enough fo that there's fcarce any 

 thing new left to be difcover'd concerning 

 them. But the famous M. De Lattire in a 

 late Treatife, having fliewn fome of the Pro- 

 perties of the Primary Epicycloid, the molt 

 Ingenious Mr. Cafwell did upon that occafion 

 not only demonftrate that the Menfuration 

 of the whole Epicycloidal Space, obtain'd al- 

 fo in the parts of the fame, but alfo gave 

 a perfect Quadrature of the Curvilineal Space 

 UPL. But while I was enquiring after the 

 Demonstration of this Quadrature, which is 

 not very obvious, nor as yet given by the In- 

 veatour, 1 light upon the following general 



H Pro- 



