PREFACE. The Treatise on Algebra, by Bourdon, is a work of singular excellence and merit. In France, it is one of the leading text books, and shortly after its publication, had passed through several editions. It has been translated, in part, by Professor De Morgan, of the London University, and it is now used in the University of Cambridge. A translation was made by Lieutenant Ross, and published in 1831, since which time it has been adopted as a text book in the Military Academy, the University of the City of NewYork, Union College, Princeton College, Geneva College, and in Kenyon College, Ohio. The original work is a full and complete treatise on the subject of Algebra, and contains six hundred and seventy pages octavo. The time which is given to the study of Algebra, even in those seminaries where the course of mathematics is the fullest, is too short to accomplish so voluminous a work, and hence it has been found necessary either to modify it, or abandon it altogether. The work which is here presented to the public, is an abridgment of Bourdon, from the translation of Lt. Ross; with such modifications, as experience in teaching it, and a very careful comparison with other standard works, have suggested. It has been the intention to unite in this work, the scientific discussions of the French, with the practical methods of the English school; that theory and practice, science and art, may mutually aid and illustrate each other. Many of the examples have been selected from the Algebra of Bonnycastle. It has been thought best, in the present edition, to transfer the general discussion of the Common Divisor to Chapter VII, and to arrange the subject of Proportions and Progressions directly after Equations of the second degree. It is hoped that these alterations may be regarded as improve ments. Hartford, September 1, 1838. CONTENTS. Preliminary Definitions and Remarks. Algebra-Definitions-Explanation of the Algebraic Signs, Similar Terms-Reduction of Similar Terms, Problems-Theorems-Definition of Question, Addition-Rule, ARTICLES 1-28 28-30 31-33 33-36 |