I. Solution of pure equations of the first degree 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 Proportion and Progression. I. Arithmetical proportion and progression, II. Geometrical proportion and progression, AN ELEMENTARY TREATISE ON ALGEBRA. INTRODUCTION. EXPLANATION OF THE ALGEBRAIC METHOD OF NOTATION :DEFINITIONS AND AXIOMS. 1. Algebra is a general method of computation, in which abstract quantities and their several relations are made the subject of calculation, by means of alphabetical letters and other signs. 2. The letters of the alphabet may be employed at pleasure for denoting any quantities, as algebraical symbols or abbreviations; but, in general, quantities whose values are known or determined, are expressed by the first letters, a, b, c, &c.; and unknown or undetermined quantities are denoted by the last or final ones, u, v, w, x, &c. 3. Quantities are equal when they are of the same magnitude. The abbreviation a=b implies that the quantity denoted by a is equal to the quantity denoted by b, and is read a equal to b; a>b or a greater than b, that the quantity a is greater than the quantity b; and ab or a less than b, that the quantity a is less than the quantity b. 4. Addition is the joining of magnitudes into one sum. The sign of addition is an erect cross; thus, a+b implies the sum of a and b, and is called a plus b, if a represent 8 and b, 4; then, a+b represents 12, or a+b=8+4=12. |