362 Mathematics. 



and refinement. For these improvements we are 

 indebted to Taylor, Craig, Maclaurin, Em- 

 MERSON, Landen, Simpson, and Waring, of 

 Great-Britain; to Clairaut, Nicole, D'Alem- 

 BERT, Condorcet, De La Croix, and De La 

 Grange," of France; to Manfredi, of Italy; to 

 Pacassi, a nobleman of Germany; and to none, 

 perhaps, more than to the great Euler, whose 

 work on the Integral Calculus, or the inverse me-^ 

 thod of Fluxions, may be considered as holding 

 the first rank on the subject of which it treats. 



The principles of Algebra have received import- 

 ant additions, and been more satisfactorily dis- 

 played during this period, than by the mathema- 

 ticians of former times. Of this department of 

 mathematical science the most distinguished culti- 

 vators were Stirling, Simpson, and Waring, of 

 Great-Britain; the Bernoullis, Cramer, and 

 Euler, of Switzerland; and Clairaut, Bezout^ 

 Lagny, De La Grange, and De La Place, of 

 France. 



It may be asserted that in almost every branch 

 of what is called Modern Analysis, much new light, 

 and many curious refinements have been introduced 

 by the mathematicians of the eighteenth cen- 

 tury. In the doctrines of Series, of Increments, of 

 Differences, of lujinitesimals, &c. great ingenuity 

 has been successfully employed in modern times. 

 And the application of these to astronomy, and 

 other branches of philosophy, may be considered 

 as forming a grand a^ra in the history of science. 

 For many of these improvements the public is in- 

 jdebted to several of. the mathematicians men- 



M. La Grange has lately presented to the world a very important 

 work, entitled, the Theory of the Analyiical Functions, in which he is supposed 

 to have shown, that every thing hitherto called Fluxions, or the Differential 

 Calculus (the phrase chiefly used on the Continent of Europe to express 

 Fluxions), whether according to the ^iiethod of Newton or Leibnitz, 

 may be reduced to the ordinary calculations, of fine '|uantitics. 



