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. THE CONTENTS. -o- J1DDITIO.M" - - - - - - 8 SECTION" WI. 4. Of the solution of cubic Equations according to 5. The same method eartended to other, higher Equa- 6. Of the solution of biquadratic Equations according 7. The solution of biquadratics by a new method with- out the trouble of earterminating the second term 150 8. Cases of biquadratic Equations that may be reduced OF FIGURATE JW"U.MBERS - - - 213 1. The Sums of Series, consisting of the reciprocals of jigurate numbers, with others of the like nature 215 metrical progression - - - - 219 3. The combinations of Quantities - - - 225 OF INTEREST.A.N.D.A.N.N'UITIES - - 229 1. Annuities and Pensions in Arrear, computed at sim- 2. The investigation of Theorems for the solution of 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 |