Mathematics. 363 



Vioned in the last paragraph ; to whose names 

 may be added those of Baron Maseres, of Great- 

 Britain, and of D'Alembert, Vandemonde, and 

 Arbogast, of France. 



The doctrine of Logaritlims has also been, in 

 the course of the last century, in several respects, 

 improved. New methods of calculating loga- 

 rithmic tables have been given by Sharpe, Tay- 

 lor, Jones, Dodson, Reid, our illustrious coun- 

 tryman Dr. RiTTENHOusE,^' and last of all Mr. 

 BoNYCASTLE. Bcsidcs the labours of these great 

 mathematicians the subject of logarithms generally 

 has been more fully and happily illustrated than 

 before, by the several learned works of Leibnitz, 

 WoLFius, Keill, Maclaurin, and Simpson. 



Several of the higher branches o^ Geometry, par- 

 ticularly the doctrines of Curves^ Conic Sectiojis, 

 &c. have been cultivated with great diligence, 

 during the period under review, and carried to 

 higher degrees of precision and refinement than in 

 any preceding age. Among many who are entitled 

 to much honour for their contributions to this class 

 of modern improvements, it will be proper to select 

 Clairaut, L'Hospital, Mairan, AIaclaurin, 

 Emerson, Cramer, Murdoch, Hamilton, Gua- 

 rinus, Euler, Robertson, and Glenie, To at- 

 tempt an enumeration even of the principal im- 

 provements which these, and many other illustri- 

 ous mathematicians, have conferred on this branch 

 of the science, would be to travel far beyond the 

 necessary limits of this chapter. The improved 

 state of Algebra, and of the Fluxionary calculus, 

 and the progress which has been made within a few 

 years past, in the subtleties of Jnalijsis in general, 

 have brought the more sublime parts of geometry- 

 more within the reach of ordinary capacities, and 



^ Sec TrattsactioHS of the American PbilosopL'tcal Society ^ voj. iv. 



