# Eaton's Elementary Algebra: Designed for the Use of High Schools and Academies

Thompson, Brown,, 1872 - Algebra - 252 pages

### Contents

 SECTION 7 DEFINITIONS AND NOTATION Continued from Section I 14 SUBTRACTION 25 MULTIPLICATION 31 DIVISION 37 DEMONSTRATION OF THEOREMS 43 GREATEST COMMON DIVISOR 54 FRACTIONS 63
 SECTION XIV 104 SECTION XV 118 SECTION XVI 125 POWERS AND ROOTS 153 SECTION XIX 178 Second Method of Completing the Square 182 Problems 193 SECTION XXI 207 SECTION XXII 215

 To subtract Fractions 69 Definitions 83 73 103
 SECTION XXIII 225 SECTION XXIV 236

### Popular passages

Page 87 - Batio is the relation of one quantity to another of the same kind ; or it is the quotient which arises from dividing one quantity by another of the same kind. Ratio is indicated by writing the two quantities after one another with two dots between, or by expressing the division in the form of a fraction. Thus, the ratio of a to b is written, a : b, or - ; read, a is to b, or a divided by b.
Page 210 - In a series of equal ratios, 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 = e:f.
Page 247 - 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, while B travels 14£ kilometers each day. In what time will the two...
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 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 45 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 205 - The first term of a ratio is called the antecedent, and the other the consequent; and the two terms together are called a couplet.
Page 205 - PROPORTION when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 87 - Thus, the ratio of a to b is written, a : b, or j ; read, a is to b, or a divided by b. 105. PROPORTION is an equality of ratios. Four quantities are proportional when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 200 - ... from (10) and (12), we obtain (13). Examples under Case III. can generally be reduced best by substituting for one of the unknown quantities the product of the other by some unknown quantity, and then finding the value of this third unknown quantity.