An Introduction to the Elements of Algebra: Designed for the Use of Those who are Acquainted Only with the First Principles of Arithmetic

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Hilliard and Metcalf, 1821 - Algebra - 216 pages
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Page 205 - 300. 74. One hundred stones being placed on the ground, in a straight line, at the distance of a yard from each other, how far will a person travel who shall bring them one by one to a basket, which is placed one yard from the first stone.
Page 16 - is less than 1, for the same reason, that the numerator 2 is less than the denominator 3. 74. If the numerator, on the contrary, be greater than the denominator, the value of the fraction is greater than unity. Thus | is greater than 1, for f is equal to f
Page 209 - 15 and 10. JV. B. This question may be solved likewise by means of one unknown letter. 128. To find three numbers, such that the first, with half the other two, the second with one third of the other two, and the third with one fourth of the other two, may be equal to 34.
Page 19 - an infinite variety of ways. For if we multiply both the numerator and the denominator of a fraction by the same number, which may be assumed at pleasure, this fraction will still preserve the same value. For this reason all the fractions
Page 27 - Hence the following rule : Multiply the numerator of the dividend by the denominator of the divisor, and the denominator of the dividend by the numerator of the divisor ; the
Page 209 - 125. A privateer, running at the rate of 10 miles an hour, discovers a ship 18 miles off making way at the rate of 8 miles an hour ; it is demanded how many miles the ship can run before she will be overtaken ? Ans. 72.
Page 61 - so that the above example will furnish the following theorem; viz. The product of the sum of two numbers, multiplied by their difference, is equal to the difference of the squares of those numbers. This theorem may
Page 210 - 136 There is a certain number, consisting of two digits. The sum of these digits is 5, and if 9 be added to the number itself the digits will be inverted. What is the number ? Ans.
Page 38 - multiplied twice by itself, or, •which is the same thing, when the square of a number has been multiplied once more by that number, -we obtain a product -which is called a cube, or a cubic number. Thus, the cube of a is aaa, since it is the product obtained by multiplying a by itself, or by
Page 42 - To illustrate this still further, we may observe, in the first place, that the powers of 1 remain always the same; because, whatever number of times we multiply 1 by itself, the product is found to be always 1. We shall therefore begin by representing the powers of 2 and of 3. They succeed in the following order

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