REPORT ON CERTAIN BRANCHES OF ANALYSIS. 287 



on the business of national education in its highest departments. 

 The influence of such men has been felt not merely in the very 

 general diffusion of scientific knowledge in that great nation, 

 but also in the form and character of their elementary books, 

 which are generally remarkable for their precision and clear- 

 ness of statement, for their symmetry of form, and for their 

 adaptation to the most extensive developement of the several 

 sciences upon which they treat. 



The elementary works of M. Lacroix upon almost every de- 

 partment of analytical science have been deservedly celebrated : 

 they possess nearly all the excellences above enumerated as 

 characteristic of French elementary writers, and they are also 

 remarkable for the purity and simplicity of the style in which 

 they are written *. The Cours des Math^matiques Pures of 

 M. Francoeur possesses merits of a similar kind, being too 

 much compressed, however, for the purposes of self-instruction, 

 though well adapted to foi'm a basis for the lectures of a teacher. 

 The works of M. Garnier are chiefly valuable for their careful 

 illustration of, and judicious selection from, the writings of 

 Lagrange, and are well calculated to make the general views 

 and principles of that great analyst and philosopher familiar 

 to the mind of a student, li^he Arithmetic, Algebra-f, and Appli- 

 cation of Algebra to Geometry, of M. Bourdon are works of 

 more than ordinary merit, and present a very clear and fully 

 developed view of the elements of those sciences. Many other 

 works have been published of the same kind and with similar 

 views by Reynaud, Boucharlat and other writers. 



I am too little acquainted with the elementary works which 

 are used in the different Universities of Germany to be able to 

 express any opinion of their character. Those which I have seen 

 have been wanting in that precise and symmetrical form which 

 constitutes the distinguishing merit of the French elementary 

 writers ; but they are generally copious, even to excess, in their 

 examples and illustrations. The immense developement which 

 public instruction, in all its departments, has received in that 

 country would lead us to conclude that they possess elementary 

 mathematical works, which are at least not inferior to those which 



• Before the Revolution, the Cours des Mathematiques Pures et Appliquees 

 of Bezout, in six volumes, was generally used in public education in France : 

 it is a work much superior to any other publication of that period of a simi- 

 lar kind which was to be found in any European language. 



t A part of the Algebra of Bourdon has been translated and highly com- 

 mended by Mr. De Morgan, a gentleman whose philosophical work on Arith- 

 metic and whose various publications on the elementary and higher parts of 

 mathematics, and particularly those which have reference to mathematical 

 education, entitle his opinion to the greatest consideration. 



