THE FIRST PRINCIPLES OF ALGEBRA. PUBLISHED BY COMMAND OF THE LORDS COMMISSIONERS FOR THE USE OF THE BOYS OF THE ROYAL HOSPITAL SCHOOLS, GREENWICH. LONDON: JOHN MURRAY, ALBEMARLE STREET. 1845. ALGEBRA. DEFINITIONS, &c. 1. ALGEBRA is a kind of universal Arithmetic, which is carried on by Rules and Operations similar to those used in common Arithmetic; it is not however confined to numbers, but exhibits in a general and comprehensive manner the relations which exist between the known and unknown quantities in the various investigations to which it is applied, every step of the operations being kept in view; and it affords us Rules by which we can determine, from certain conditions which are supposed to be given, the unknown quantities in terms of the known ones, whatever may be their numeral values. 2. Known or given quantities are represented by the first letters of the alphabet, a, b, c, &c.; unknown ones, by the letters x, y, z, &c. 3. The sign (which is read plus) signifies that the quantity to which it is prefixed is to be added. Thus a+b signifies that the quantity represented by b is to be added to the quantity B |