72 Mathematics. [Chap, VI. 



among the earliest cultivators of this department of 

 mathematical science. It was afterwards much im- 

 proved and extended by the successive labours of 

 Simpson, Price, Dodson, Morgan, and ^laseres, of 

 Great Britain ; by Deparcieux, of France ; and by 

 many others, in various parts of Europe. 



About the middle of the century imder review, 

 and for some years afterwards, flourished the cele- 

 brated Euler, a native of Switzerland, and one of 

 the greatest mathematicians, and most excellent 

 men of the age in which he lived. He invented 

 many new formulae for the sines, cosines, &c., and 

 carried to a greater degree of perfection • the In- 

 tegral Calculus ; he also did much to elucidate the 

 theory of the more remarkable Curves ; and contri- 

 buted greatly to simplify and extend the whole 

 system of Analijlical operations. In short, he may 

 be said to have thrown new light upon almost 

 every part of mathematical science*. 



Beside those branches of mathematics which are 



* Leonard Eulei was born at Basil, in 170/, and died in 1/83, 

 in the 76th year of his qgc. The mathematical genins and eru- 

 dition of this man were truly wonderful. No individual of the 

 eighteenth century can be compared to him for the number and 

 value of the discoveries which he made in th's branch of science, 

 and for the improvements of which he was the author. His pub- 

 lications are numerous 5 and there is scarcely a department o,f 

 mathematics on which he has not thrown some new light, or to 

 which he has not made some important additions. On every sub- 

 ject which he undertook to investigate, he displayed a vigour, a 

 peneti'ation, and a comprehensiveness of mind, which entitle him 

 to a place in the first rank of philosophers. Euler was not less 

 distinguished for the excellence of his moral and religious, than 

 for the greatness of his intellectual character. To singular pro- 

 bity, and great social amiableness, he added the piety of an emi- 

 nent christian. He was a warm and active friend to religion, 

 fervent in his devotions, and exemplary in his attention to all pub- 



