Chap. VI.] Mathanatks. 75 



Several of the higher brandies of Geometry, par- 

 ticularly the doctrines of Curves^ Conic SectionSy 

 &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 tliis class 

 of modern improvements, it will be proper to select 

 Chiiraut, rilospital, Maclaurin, Emerson, Cramer, 

 Hamilton, Euler, Ilobertson, and Walker. To at- 

 tempt an enumeration even of the principal im- 

 provements which these, and many other ilhistrious 

 mathematicians, have conferi-ed on this branch of 

 the science, would be to travel far bejond the neces- 

 sary 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 oi Analysis in general, have 

 brought the more sublime parts of geometry more 

 within the reach of ordinary capacities, an.d by 

 their means greatly multiplied the cultivators of 

 this department of mathematical science. 



But, beside this, even those brandies of ma- 

 thematics in which no great discoveries have been 

 made, and upon which no signal light luis been 

 thrown within the last age, have yet recc'i\ ed im- 

 provements of a less interesting and brilliant kind. 

 Former discoveries have been extended ; old doc- 

 trines have been simplified and refined; neater, 

 shorter, and more lucid ways of arriving at the 

 £ame results have been de\ ised ; perspicuous, ele- 

 gant, and comprehensi\e theorems have taken tlie 

 place of those which were more prolix and oh.-currj 



