VOL. VIII.] PHILOSOPHICAL TRANSACTIONS. 113 



man, son of Sir Paul Neil. And after him, the same was demonstrated by the 

 Lord Brouncker, and by Sir Christopher Wren, about the months of June and 

 July, 1657 : which was a thing well known here ; and it was published and re- 

 ceived with applause by those gentlemen, who, before the institution of the 

 Royal Society, used to meet on stated days at the mathematical lectures in 

 Gresham College. And the Lord Brouncker communicated the same to me at 

 Oxford, by letter the ensuing August; and at the same time he sent me his owrt 

 demonstration of it. This I communicated exactly by letter to M. Huygens, 

 and afterwards annexed it to my treatise on the cycloid, in 1659, with an impar- 

 tial account of the whole aftair. So that it is surprising how M. Huygens should 

 make Heuraet the first inventor of it. 



In the year l658, Sir Chr. Wren had discovered a right line equal to the 

 cycloidal curve, and its several parts; as was then well known, not in England 

 only, but also in France and Holland; and in particular M. Huygens himself was 

 acquainted with it, even before he knew any thing of Heuraet's discovery, as 

 appears by his letter to me. And though it be allowed that Sir Chr. Wren was 

 the inventor of this, yet he never pretended that he was the first who found 

 out a right line equal to a curve ; for he knew, and he owns as much, that Mr. 

 Neil had discovered it the year before him. Only he assumes this prerogative 

 to himself, that he had rectified the first curve that offered; whereas Mr. Neil 

 applied himself rather to find oat a curve that should admit of rectification. It 

 is true that this curve is of the tribe of the paraboloids; but no one before Mr. 

 Neil took it into consideration. And it is as true that both Mr. Neil's and M. 

 Heuraet's is the very same curve. 



Two others on the same Subject. The^rst of the Right Hon. Lord Plsct. Brouncker, 

 Chancellor to her Majesty, and P. R. S. &c. N° 98, p. 6149. 

 Sir, — Mr. William Neil, in the year 1 65 7 5 found out and demonstrated a 

 straight line equal to a paraboloid ; and communicated the same to others, 

 who used to meet at Gresham College, and it was there received with good 

 approbation; and the same was soon after demonstrated by myself and 

 others; and therefore earlier than that of M. Heuraet, which it seems 



Dr. Seth Ward, he greatly cultivated and improved his genius in mathematics. His success in that 

 study appeared as early as l6o7, at 19 years of age, when he, first of all men, accurately rectified a 

 curve line, as appears by the above letter of Dr. Wallis, and the two next following ones, of Lord 

 Brouncker and Sir Chr. Wren. — Mr. Neil became an early member of the Royal Society, of which he 

 was elected a fellow in Jan. l6()3. His theory of motion was communicated to the Society, April 29, 



1669. But the further expectations, which had been conceived of his genius in mathematical and 

 philosophical subjects, were disappointed by his early deatl), which happened the 524th of August, 



1670, in the 33d year of his age. 



VOL. II. Q • ' 



