Reviezo of the Cambridge Course of Malheraatics. '305 



3. Elements of Algebra, by S. F. Lacroix. Transla- 

 ted from the French, for the use of the students of the 

 University at Cambridge, New England. Cambridge, 

 N.E. HiUiard and Metcalf, 1818. pp.263. 



M. Lacroix, the author of the first and third volumes 

 before us, has long been distinguished as a writer upon the 

 pure mathematics. His mathematical works commence 

 with common arithmetic, and end only with the highest 

 point, to which the science of calculation has been carried^ 

 Most of his treatises have passed through many editions, 

 and are generally used in France, both tor public and pri- 

 vate instruction They are connected with each other by 

 references, a circumstance which adds greatly to the conven- 

 ience and facility of reading them ; and they are probably 

 more complete, and of a higher scientific character, than 

 any other course, which has hitherto been published. His 

 Arithmetic and Elements of Algebra, form the two first 

 volumes of his course, and of these it will be our duty 

 soon to speak particularly. His third volume is upon the 

 Elements of Geometry. This is followed by an elementary 

 treatise on rectilineal and spherical Trigonometry, and on 

 the application of Algebra to Geometry, and by supple-^ 

 menis to the elements of Algebra and Geometry. This 

 last supplement is a treatise upon Descriptive Geometry, a 

 branch of Mathematics which has been recently opened, 

 or rather which has recently been reduced to rigorous prin-; 

 ciples, and been used as an instrument of investigation. It 

 has not been much cultivated out of France.* It was es- 

 tablished as a branch of instruction in the Normal School, 

 created by a law of 30tb October, 1794, and three Profes- 

 sors were appointed for the object, among whom was M. 

 Lacroix. 



Descriptive Geometry has two objects ; the first is, to 

 represent with exactness, upon surfaces which have but 

 two dimensions, objects which have three dimensions, and 

 which are susceptible of a rigorous definition. Under this 

 point of view, it is a language more perfect than any other 



* We observe with pleasure, that Mr. Croyt, Professor of Engineerine; 

 in the Military Academy of the United States, has published the first part 

 of a treatise ou Descripfii'e Geometry, for the ase of the Cadets of that 

 institution. 



