New Elementary Algebra : Embracing the First Principles of the Science

New Elementary Algebra: Embracing The First Principles Of The Science by Charles Davies is a comprehensive 19th-century algebra textbook that guides learners from basic arithmetic to algebraic reasoning. Davies presents a systematic curriculum beginning with definitions and the signs of operations, then progressing through known and unknown quantities, and the eight fundamental kinds of quantities. The work develops the algebraic language through practical rules for addition, subtraction, multiplication, and division of monomials, polynomials, and fractions, before introducing transformations of fractions and the solution of equations of the first and second degrees. It covers foundational topics such as powers, roots and radicals, factoring, and the binomial theorem, and includes chapters on proportion, logarithms, and the use of formulas. The text emphasizes mental exercises, worked examples, and teacher guidance to connect arithmetic with algebra and foster logical reasoning. This edition reproduces Davies’ classical course, preserving the author’s original method and instructional aims for wide classroom use.