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 5 - 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 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 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 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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