306 Review of the Cambridge Course of Mathematics. 



for communicating every thing capable of delineation or 

 construction, and particularly forms the foundation of the 

 graphic arts. Its second object is, to deduce from the ex- 

 act delineation of objects, every thing which results from 

 their respective forms and positions. In this way, as it of- 

 fers continual examples o! passing from what is known to what 

 is unknown, it becomes an instrument of investigating new 

 truths. The most complete work on this subject, we be- 

 lieve, is, Monge's Geometric Descriptive with M. Hachette's 

 supplement. 



The next volume of M. Lacroix's course, is an elemen- 

 tary treatise on the differential and integral calculus, of 

 which a translation was some years since published in Eng- 

 land. Then comes an elementary treatise, on the calcula- 

 tion of probabilities. The course concludes with a volume 

 consisting of Essays on Instruction in general, and on that 

 of the mathematics in particular; or the method of studying 

 and teaching mathematics. This volume, we hesitate not 

 to say, contains views of study and instruction of the very 

 first importance, founded on a knowledge of the human 

 mind, and on experience gained by directing the studies of 

 a great number of young men, during a long course of 

 years. It also sheds much light on many parts of the oth- 

 er volumes which compose the course, and we shall often 

 have occasion to refer to it in the course of the present ar- 

 ticle. 



The principal remaining work of Lacroix, is his "Traite 

 du Calcul Differejitiel, et du Calcul Integral," 3 Tom. 4to. 

 In this work, he professes to have collected and systematic- 

 ally arranged whatever is most valuable in the treatises of 

 of Euler, Lagrange, Sic, and in the numerous analytical 

 memoirs scattered through the volumes of the different 

 learned societies and academies of Europe. This vast 

 quantity of materials, receiving from the vigorous and sys- 

 tematic mind of Lacroix uniformity of style and develop- 

 ment, is incorporated into one great work, every part of 

 which is impressed with the genius and luminous views of 

 the author, and from which a knowledge of the transcendant 

 analysis, in its present improved slate, can be obtained.* 

 (Edinb. Encyc. vol. IX. 116.) While this treatise was in 

 preparation, the author received a letter from the celebrated 

 Laplace, of which the following is an extract. *'Je vois," 



