502 APPENDIX. Cliap. T. 



always bcenunderftood that a circle is generated by keeping one end 

 of a ftraight line fixed, and moving the other round, till it form that 

 one line, under which Euclid fays the circle is comprehended. And, 

 indeed, any the moft vulgar man, without art or fcicnce of any 

 kind, may, by defcribing a circle wi'.h his hand in ithe air or up- 

 on the table, fatisfy himfelf that the Motiotl is. not compounded, 

 a-ny more than the line it defcribes. I know it may be^liud, and I 

 have heard it faid, that the connection of the hand with our body 

 makes the Motion compounded. But, without inquiring whether that 

 he the fad or not^ it is impoffible to deny that we may have an Idea 

 gfa finger, or-of any the leaft part of the hand moving by itfelf, and 

 defcmbing a circle : And, if the circle be one fimple line, as Euclid 

 certainly fuppofes it to be, it is very difficult to conceive how 



the Motion defcribing.it fliould be compoundL^d. From all this, 



I think, I may infer, that it is not only trie common ki\{e of 

 mankind, but the opinion of Euclid, and of all the geometers 

 that have been fince his time, that the circular Motion is in one 

 limple and uncompounded line. And with the geometers agree the 

 antient philofophers, fuch as Ariftotle and Proclus, the former of 

 whom has fiiid that the circular Motion, and the Motion in the 

 ftraight line, are the only fimple Motions *. If, therefore, this pro- 

 pofition is to be geometrically demonftrated, it mud be by a geome- 

 try beyond any that Euclid, or the antient philofophers, knew, fuch 

 as the French call xhcfublime geometry^ or the dodlrine of the infni- 

 ments petits. Now, I have converfed with a man learned in that geo- ' 

 metry, and who, I believe, is the beft mathematician of the age ; ' 

 and he aflures me that the thing is neither capable of demonftration, ' 

 nor true t^ And I will hold it to be fo, till the gentlemen who aifert 

 the contrary produce their demonftration. 



I 



* Ses what I have faid upon this fubjeft, Vol. i. of Metaphyfics, p. 264. where I have 

 quoted the pafTage, both from Arillotle and Proclus. 



t The reader will leadily underftand that the geometer I mean is Dr Horfley. 



