^86 THIRD REPORT— 1833. 



works of other authors from which he could venture to exempt 

 his own. 



The elementary works on algebra and on all other branches 

 of analytical and physical science which have been published 

 in France since the period of the Revolution, have been very 

 extensively used, not merely in this country, but in almost 

 every part of the continent of Europe where the French lan- 

 guage is known and understood. The great number of illus- 

 trious men who took part in the lectures at the Normal and 

 Polytechnic Schools at the time of their first institution, and 

 the enlarged views which were consequently taken of the prin- 

 ciples of elementary instruction and of their adaptation to the 

 highest developement of the several sciences to which they 

 lead, combined with the powerful stimulus given to the human 

 mind in all ranks of life, in consequence of the stirring events 

 which were taking place around them, at once placed the scien- 

 tific education of France immensely in advance of that of the 

 rest of Europe. The works of Lagrange, particularly his Calcul 

 des Fonctions and his Theorie des Fonctions Analytiqiies, which 

 formed the substance of lectures given at the Ecole Polytech- 

 nique, exhibited the principles of the differential and integral 

 calculus in a new light, and contributed, in connexion with his 

 numerous other works and memoirs, which are unrivalled for 

 their general elegance and fine philosophical views, to fami- 

 liarize the French student with the most perfect forms and 

 with the most correct and at the same time most general prin- 

 ciples of analytical science. The labours of Monge also, upon 

 the application of algebra to geometry, succeeded in bringing 

 all the relations of space, with which every department of na- 

 tural philosophy is concerned, completely under the dominion 

 of analysis *, and thus enabled their elementary and other 

 MTiters to exhibit the mathematical principles of every branch 

 of natural philosophy under analytical and symmetrical forms. 

 Laplace himself gave lectures on the principles of arithmetic 

 and of algebra, which appear in the Stances de V Ecole Nor- 

 male and in the Journal de V Ecole Polytechniqiie ; and there are 

 very few of the illustrious men of science, of that or of a subse- 

 quent period, who have done so much honour to France, who 

 have not been more or less intimately associated with carrying 



* The developement of the details of this most important branch of analy- 

 tical science, which has been so extensively and successfully cultivated in 

 France, is greatly indebted to Monge's pupils in the Polytechnic School, 

 many of whom have subsequently attained to great scientific eminence : their 

 results are chiefly contained in the three volumes of Correspondance sur 

 I' Ecole Polytechnique. 



