Elements of Algebra

ADVERTISEMENT BY M. BERNOULLI, THE FRENCH TRANSLATOR. THE Treatise of Algebra, which I have undertaken to translate, was published in German, 1770, by the Royal Academy of Sciences at Petersburg. To praise its merits, would almost be injurious to the celebrated name of its author; it is sufficient to read a few pages, to perceive, from the perspicuity with which every thing is explained, what advantage beginners may derive from it. Other subjects are the purpose of this advertisement. I have departed from the division which is followed in the original, by introducing, in the first volume of the French translation, the first Section of the Second Volume of the original, because it completes the analysis of determinate quantities. The reason for this change is obvious: it not only favors the natural division of Algebra into determinate and indeterminate analysis; but it was necessary to preserve some equality in the size of the two volumes, on account of the additions which are subjoined to the Second Part. The reader will easily perceive that those additions come from the pen of M. De la Grange; indeed, they formed one of the principal reasons that engaged me in this translation. I am happy in being the first to shew more generally to mathematicians, to what a pitch of perfection two of our most illustrious mathematicians have lately carried a branch of analysis but little known, the researches of which are attended with many difficulties, and, on the confession even of these great men, present the most difficult problems that they have ever resolved.