By permission of the learned Dr. Adrain, I have 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. JAMES RYAN. ! CONTENTS. Page I. Addition of algebraic quantities, II. Subtraction of algebraic quantities, III. Multiplication of algebraic quantities, IV. Method of reducing a fraction whose denomina- tor is a simple or a binomial surd, to another II. Solution of pure equations of the second, and other higher degrees, by evolution, I. Solution of adfected quadratic equations, in- volving only one unknown quantity, On the Solution of Problems producing Quad- I. Solution of problems producing quadratic equa- tions, involving only one unknown quantity, 413 II. Solution of problems producing quadratic equa- |