A SCHOOL ALGEBRA ΤΟ QUADRATIC EQUATIONS, WITH NUMEROUS EXAMPLES. BY CHARLES MANSFORD, B.A., MATHEMATICAL TUTOR IN THE WESTMINSTER TRAINING COLLEGE. ! (SCHOOL BOOK DEPOT, TRAINING COLLEGE, CENTRAL AGENCY:- WESTMINSTER, S. W. HAMILTON, ADAMS, & CO., 32, PATERNOSTER ROW, E.C. LONDON: SIMPKIN, MARSHALL, & Co., STATIONERS' HALL COURT, E.C. JOHN MENZIES & CO. EDINBURGH & GLASGOW:-W. STEWART & CO., 32, NEW BRIDGE MANCHESTER :-JOHN HEYWOOD, DEANSGATE. THE EDUCATIONAL TRADING COMPANIES AND DEPÔTS. PRINTED BY WILKINS AND ELLIS, DERBY. Simple Equations-more difficult Exercises Simple Equations-two unknown quantities Simple Equations-three unknown quantities SIGNS AND SYMBOLS. Symbols. In Arithmetic numbers are denoted by figures, and the same figure or arrangement of figures always represents the same number. In Algebra numbers are represented by the letters of the alphabet, but the letter used may stand for any number we please. There is this difference therefore between the symbols of Arithmetic and those of Algebra, viz.: that in Arithmetic we can always tell by the shape and position of the symbols what numbers are represented, while in Algebra a given symbol may represent any number whatever. In short, the symbols of Arithmetic are particular-and those of Algebra are general. Signs. The signs employed in Algebra are the same as those in Arithmetic. At present it is only needful to notice the meaning of the following: The sign = denotes that the quantities connected by it are equal to one another. The sign (plus) is the sign of addition, and means that the quantity before which it stands is to be added. And the sign (minus) is the sign of subtraction, and means that the quantity before which it stands is to be subtracted. The sign is the sign of multiplication, and denotes that the quantities between which it is placed are to be multiplied together. The sign is the sign of division, and denotes that the quantity standing before it is to be divided by that which follows it. ADDITION (+). 5+5=10 always, but the sum of a+a is not known until we know what number a stands for. If a=3 |