Thompson, Brown & Company, 1877 - Algebra - 291 pages

### Contents

 DEFINITIONS AND NOTATION 7 DEFINITIONS AND NOTATION Continued from Section I 14 SECTION V 25 SECTION VI 31 SECTION VII 37 SECTION VIII 43 SECTION X 54 FRACTIONS 63
 SECTION XV 118 EQUATIONS OF THE FIRST DEGREE CONTAINING BUT ONE UNKNOWN QUANTITY 121 POWERS AND ROOTS 125 SECTION XVII 154 SECTION XVIII 170 Second Method of Completing the Square 182 Problems 193 SECTION XXI 207 SECTION XXII 215

 To subtract Fractions 69 73 103 SECTION XIII 112
 SECTION XXIII 225 SECTION XXIV 236 SECTION XXV 253

### Popular passages

Page 78 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Page 40 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 100 - D. The distance from A to D is 34 miles ; the distance from A to B is to the distance from C to D as 2 to 3 ; and £ of the distance from A to B, added to one half the distance from C to D, is three times the distance from .B to C.
Page 44 - ... the square of the second. In the second case, we have (a — &)2 = a2 — 2 ab + b2. (2) That is, the square of the difference of two quantities is equal to the square of the first, minus twice the product of the two, plus the square of the second.
Page 43 - I. The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 87 - PROPORTION when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 83 - TRANSPOSITION is the changing of terms from one member of an equation to the other, without destroying the equality. The object of transposition is to bring all the unknown terms into one member and all the known into the other, BO that the unknown may become known.
Page 212 - Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d...
Page 209 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
Page 251 - B had during the whole time; and at the same rate as before B would reach Springfield in 5f days. How far from Boston did they meet? Ans. 42 miles. 163. The product of two numbers is 90 ; and the difference of their cubes is to the cube of their difference as 13 : 3. What are the numbers ? 164. A and B start together from the same place and travel in the same direction. A travels the first day 25 kilometers, the second 22, and so on, travelling each day 3 kilometers less than on the preceding day,...