558 Mathematics. 



unusual lustre of their characters, may have con- 

 tributed, by an influence far from being unnatural, 

 to repress the ambition and discourage the exer- 

 tions of some who came after them. But, al- 

 though the eighteenth century can boast of no 

 discoveries so splendid, nor of any advances so ho- 

 nourable, as belong to the preceding, yet it pro- 

 duced both, in a sufficient degree to secure a re- 

 putable place in the history of this subHme science. 

 Though the Fluxlonai^ Analysis had been in- 

 vented by Newton thirty years before, yet that 

 great mathematician first published his new doc- 

 trine on this subject in 1704. The controversy in 

 which he became involved with Leibnitz, in 

 consequence of this publication, is well known to 

 have been one of the most curious and interesting 

 of the age.' It seems to have been long and ge- 

 nerally agreed, that the credit of this celebrated 

 invention is due to the illustrious British philoso- 

 pher, and, of course, that the claim of his German 

 rival was unfounded."* 



/ Soon after Newton published his doctrine of Fluxions, his book wa» 

 reviewed in the Acta Eruditorum of Leipsic. In the course of this review, 

 an intimation was given that he had borrowed from Leibnitz, and that 

 the honour of the invention properly belonged to the latter. Dr. Keill, 

 Professor of Astronomy in the University of Oxford, undertook the de- 

 fence of his countryman. After a number of controversial papers had 

 been exchanged on the subject, Leibnitz complained to the Royal Society 

 of injustice on the part of Newton and his friends. The Society appointed 

 a committee of its members to investigate the question! in dispute, who, 

 after examining all the letters and other papers relating to it, decided in 

 favour of Newton and Keill. These papers were published in 1712, 

 under the title of Commercium Epistoliciim. 8vo. 



m In the eloquent and comprehensive Eulogimn upon Dr. David Rit- 

 TENHOUSF., the late President of the American Philosophical Society, pro- 

 nounced by Dr. Rush, at the request of the Society, there is the follow- 

 ing passage : " It was durmg the residence of our ingenious philosopher 

 with his father in the country, that he became acquainted with the science of 

 Fluxions, of which sublime invention he believed himself for a while to be 

 the author; nor did he know, for some years afterwards, that a contest had 

 been carried on between Sir Isaac Newton and Leibnitz, for the honour 

 of that great and useful discovery. What a mind was here ! without literary 

 friends or society, and but two or three books, he became, before he had 

 reached his four-and-twentieth year, the rival of the two greatest mathe- 

 maticians in Europe." 



