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progress may, indeed, at first, be a little retarded; but the real knowledge he thence acquires will abundantly compensate his trouble, and enable him to proceed, afterwards, with certainty and success, in matters of greater difficulty, where authors, and their rules, can yield him no assistance, and he has nothing to depend upon but his own observation and judgment.

This second edition has many advantages over the former, as well with respect to a number of new subjects and improvements, interspersed throughout the whole, as in the order and disposition of the elementary parts: in which, particular regard has been had to the capacities of young beginners. The work, as it now stands, will, the author flatters himself, be found equally plain and comprehensive, so as to answer, alike, the purpose of the lower, and of the more experienced class of readers.

P. S. The great reputation of Mr. SIMPson’s TREATIse of ALG EBRA, and the favourable reception it has universally met with since its first publication, and which testifies it to be the best elementary work upon the subject, has induced the proprietor to have this edition carefully revised and corrected throughout by a very eminent mathematician : he therefore trusts it will be found as worthy the approbation of the public as any former edition, or as if revised by the author himself.

3. A method for discovering whether the root of a radical quantity can be extracted - - 284

4. The manner of taking away radical quantities from the denominator of a fraction, and transferring them to the numerator - - - 288

5. A method for determining the roots of certain high Equations, by means of the section of an angle 301

The geometrical construction of a large variety of linear, and plane Problems; with the manner of

resolving the same numerically - - 315 .APPEN"DIX - - - - - - 401

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