A Treatise of Algebra: Wherein the Principles Are Demonstrated, and Applied in Many Useful and Interesting Inquiries, and in the Resolution of a Great Variety of Problems of Different Kinds. To Which Is Added, the Geometrical Construction of a Great Number of Linear and Plane Problems, With the Method of Resolving the same Numerically. The Second American, from the Eighth London Edition.

Second American Edition, Revised and Corrected. Brown full leather binding with gilt lettering on red leather spine label ("Simpson's Algebra"). 6" x 9." 408 pages, complete. Appendix in back. Pages are clean and intact overall but have some staining, light to moderate foxing, faint offsetting, chip in lower corner of fore-edge on title page, and darkening on first and last few pages and edges of text block. Covers are clean and intact overall but have moderate rubbing, some scratch marks, some bumping and wear to corners and edges, and slight loosening and wear along front and back inner hinges and outer joints. Binding is still strong and holding. A Very Good copy. This is a mathematical textbook that was published in 1821. It is the Second American Edition, from the Eighth London Edition. The emphasis is on algebra, but there are a few sections on geometry as well. The following are the section or chapter titles: "Notation," "Addition," "Subtraction," "Multiplication," "Division," "Involution," "Evolution," "The Reduction of Fractional and Radical Quantities," "Of Equations: The Reduction of single Equations; The Extermination of unknown Quantities, or the reduction of two or more equations to a single one," "Of Arithmetical and Geometrical Proportions," "The Solution of Arithmetical Problems," "The Resolution of Equations of Several Dimensions: Of the origin and composition of Equations; How to know whether some, or all the roots of an Equation be rational, and, if so, what they are; Another way of discovering the same thing, by means of Sir Isaac Newton's method of divisors; with the grounds and explanation of that method; Of the solution of cubic Equations according to Cardan; The same method extended to other, higher Equations; Of the solution of biquadratic Equations according to Des Cartes; The solution of biquadratics by a new method without the trouble of exterminating the second term; Cases of biquadratic Equations that may be reduced to quadratic ones; The resolution of literal Equations, wherein the given, and the unknown quantity are alike affected; The resolution of Equations by the common method of converging series; Another way, more exact; A third method; The method of converging series extended to surd Equations; A method of solving high Equations, when two, or more unknown quantities are concerned in each," "Of Indeterminate Problems," "The Investigation of the Sums of Powers," "Of Figurate Numbers: The Sums of Series, consisting of the reciprocals of figurate numbers, with others of the like nature; The sums of compound Progressions, arising from a series of powers drawn into the terms of a geometrical progression; The combinations of Quantities; A demonstration of Sir Isaac Newton's Binomial theorem," "Of Interest and Annuities: Annuities and Pensions in Arrear, computed at simple interest; The investigation of Theorems for the solution of the various cases in compound interest and annuities," "Of Plane Trigonometry," and "The Application of Algebra to the Solution of Geometrical Problems: An easy way of constructing, or finding the roots of a quadratic equation, geometrically; A demonstration why a problem is impossible when the square root of a negative quantity is concerned; A method for discovering whether the root of a radical quantity can be extracted; The manner of taking away radical quantities from the denominator of a fraction, and transferring them to the numerator; A method for determining the roots of certain high Equations, by means of the section of an angle; The geometrical construction of a large variety of linear, and plane Problems; with the manner of resolving the same numerically.". …