«ct. i.J DISSERTATION SECOND. , 19 



The Cycloid afforded a number of problems, well cal- 

 culated to exercise the proficients in the geometry of in- 

 divisibles, or of infinites. It is the curve described by a 

 point in the circumference of a circle, while the circle it- 

 self rolls in a straight line along a plane. It is not quite 

 certain when this curve, so remarkable for its curious pro- 

 perties, and for the place which it occupies in the history 

 of geometry, first drew the attention of mathematicians. 

 In the year 1639, Galileo informed his friend Torricelli, 

 that, forty years before that time, he had thought of this 

 curve, on account of its shape, and the graceful form it 

 would give to arches in architecture. The same philoso- 

 pher had endeavoured to find the area of the cycloid ; but 

 though he was one of those who first introduced the con- 

 sideration of infinites into geometry, he was not expert 

 enough in the use of that doctrine, to be able to resolve 

 this problem. It is still more extraordinary, that the same 

 problem proved too difficult for Cavalleri, though he cer- 

 tainly was in complete possession of the principles by 

 which it was to be resolved. It is, however, not easv to 

 determine whether it be to Torricelli, the scholar of Caval- 

 leri, and his successor in genius and talents, or to RobervaJ, 

 a French mathematician of the same period, and a man 

 also of great originality and invention, that science is in- 

 debted for the first quadrature of the cycloid, or the proof 

 that its area is three times that of its generating circle. 

 Both these mathematicians laid claim to it. The French 

 and Italians each took the part of their own countryman • 

 and in their zeal have so perplexed the question, that it is 

 hard to say on which side the truth is to be found. Tor- 

 ricelli, however, was a man of a mild, amiable, and can- 

 did disposition ; Roberval of a temper irritable, violent, 

 and envious; so that, in as far as the testimony of the in- 

 dividuals themselves is concerned, there is no doubt which 



