ADVERTISEMENT. As UTILITY is the great object aimed at in this Publication, I have spared no pains to make a careful selection of materials, from the most approved sources, which may tend to elucidate, in a full and clear manner, the Elements of Algebra, both in theory and practice. Those authors of whose labours I have principally availed myself, are Euler, Clairaut, Lacroix, Garnier, Bezout, Lagrange, Newton, Simpson, Emerson, Wood, Bonnycastle, Bridge, and Bland. To Bland's Algebraical Problems, (a work compiled for the use of Students in one of the first Universities in Europe), I am chiefly indebted for the problems in Simple, Pure, and Quadratic Equations. neu Dr. Adrain, ave added, as an Appendix, his method of demonstrating algebraically the propositions in the fifth book of Euclid's Ele ments. New-York, July 1, 1824. Yumis JAMES RYAN, CONTENTS. Page 1. Addition of algebraic quantities, II. Subtraction of algebraic quantities, III. Multiplication of algebraic quantities, Page I. Reduction of simple equations, II. Resolution of simple equations, involving only On Simple Equations, involving two or more un- I. Elimination of unknown quantities from any II. Resolution of simple equations, involving two Examples in which the preceding rules are ap- plied, in the solution of simple equations, involving two unknown quantities, On the Solution of Problems, producing Simple I. Solution of problems producing simple equa- tions, involving only one unknown quantity, II. Solution of problems producing simple equa- |