330 PHILOSOPHICAL TRANSACTIONS. [aKNO J706. 



this accusation upon him. " First, says he, it appears,* that this method for 

 the transformation of curves, which was invented by Roberval, was known in 

 Italy before the year J 668; for Torricelli, who died in 1647, testifies in his 

 letters, that it was communicated to him by Roberval. Secondly, the adver- 

 sary, however unwilling, is obliged to confess that this method is ihe same as 

 Gregory's. Thirdly, it must therefore iippear very probable that Gregory, when 

 on his travels in Italy, might learn this method from the Italians, which had 

 been so long known in Italy." 



Now, that this method, which appeared in the year 1692, in the name of 

 Roberval, is the same with that which Gregory had published 24 years before, 

 prop. 1 1, Math. Univers. as it is plain to any one that views them both, so I 

 had granted it without any hesitation. Indeed I said, that in the writings of 

 the French, where it is ascribed to Roberval, it was accompanied with a miser- 

 able and shameful demonstration. But that it was the same as Gregory's me- 

 thod I never once questioned, nor made any dispute of; though Galloys made 

 this the chief point of the controversy, and triumphs as if I had yielded him 

 the victory. But I by no means grant him, either that it was known before to 

 the Italians, or that it was communicated by them to Gregory. For how does 

 it appear that it was known to them ? because Roberval had communicated it to 

 Torricelli. How does this appear? from the letter of Torricelli himself. But 

 where is this letter? Galloys has it. When was it written ? about 60 years 

 since. Where has it been hid so long? where all wonderful things are hid, in 

 Roberval's own depository. Whether this epistle be genuine or not, or whether 

 there be any such thing or not, we must not presume to doubt, since there are 

 so many credible witnesses. But by what literary monuments does it appear 

 that Torricelli communicated these inventions to the Italians? About this, 

 there is still a profound silence. Or, if he had imparted these to any, they might 

 by this time have been quite extinct and unknown, since Torricelli himself had 

 been dead 20 years before Gregory went into Italy. Or if they had not been 

 yet out of memory, Galloys should tell us, who among the Italian mathemati- 

 cians imparted these secrets to Gregory, which had been entrusted to him by 

 Torricelli. Perhaps he will say, for he can take the liberty of saying any thing, 

 that they were known to many in Italy. But would the Italians trust these 

 geometrical secrets to Gregory, a mere foreigner, which they had concealed 

 from every body for 20 years ? Would he dare, in the midst of Italy, for his 

 book was printed at Padua, publish things as his own, which he had but just 

 learned of the Italians? or if he had been so devoid of shame, could he have 



* Oeuvres des Ma them, par Mesk de I'Acad. Royal. 



