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Entered according to Act of Congress, in the year 1837,

BY JAMES MUNROE AND COMPANY,

in the Clerk's Office of the District Court of the District of Massachusetts.

Cambridge Press:
Metcalf, Torry, and Ballou.

PREFACE.

THE excellent treatises on Algebra, which have been prepared by Professor Smyth and Professor Davies, containing as they do the best improvements of Bourdon and other French writers, would seem to leave nothing to be desired in this department of mathematics. The form, however, adopted in English works of instruction, of dividing the subject as much as possible into separate propositions, is probably the best adapted to the character of the English pupil. This form has, therefore, been adopted in the present treatise, while the investigation of each proposition has been conducted according to the French system of analysis.

Great care has been taken in the choice of examples, and free use has been made of Meier Hirsch's selection of problems. The principal aim has, indeed, been to communicate that mechanical dexterity in the use of symbols, which is so important to the expert algebraist, and without which great progress in the higher branches of the science is almost impossible.

As this work is one of a Course of Mathematics, all subjects have been excluded from it, which do not strictly come within its limits. This will account for the omission of the indeterminate analysis,

which is referred to the Theory of Numbers; for that of the theory of combinations, which is referred to the Doctrine of Chances; and for that of the development of fractions and logarithms into series, which is referred to the Theory of Functions.

The polynomial theorem of Arbogast, in art. 137, which, in beauty and facility of application, rivals the binomial theorem of Newton, will probably be new to most readers, as it is believed never before to have found its way into an elementary treatise. No apology need be made for the length of its demonstration to one, familiar with the original investigations of Arbogast, or who reflects upon its generality and unavoidable intricacy; the learner will, however, find it less complex than it appears to be; and, at any rate, he may easily become familiar with the use of the theorem, even if he find the demonstration too abstruse.

The peculiar class of equations, introduced in article 118, being examples 10, 11, 12 of that article, will probably be as new to most readers, as they were to the author; exhibiting the singular peculiarity of being reduced in degree by the process of elimination. These examples might have been multiplied to any extent, and are by no means accidental in their formation.

BENJAMIN PEIRCE.

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