Elementary Algebra for the Use of Schools and Colleges

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Macmillan Company, 1900 - Algebra - 672 pages
 

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Page 79 - From the above example it will be seen that in order to divide one multinomial expression by another we proceed as follows: (1) Arrange both dividend and divisor according to ascending or both according to descending powers of some common letter. (2) Divide the first term of the dividend by the first term of the divisor: this will give the first term of the quotient. (3) Multiply
Page 352 - The above proposition has already been proved in Art. 170, Ex. 1. 246. Definitions. Quantities are said to be in continued proportion when the ratios of the first to the second, of the second to the third, of the third to the fourth, etc., are all equal. Thus a,
Page 494 - 338. To find the number of permutations of n different things taken r at a time, where r is any integer not greater than n. Let the different things be represented by the letters a, b, c, •••. It is obvious that there are n permutations of the n things when taken one at a time, so that
Page 561 - [Art. 147.] Hence N— S is divisible by r — 1, and therefore when S is divisible by r — 1, so also is N. As a particular case of the above, any number expressed in the ordinary scale is divisible by 9 when the sum of its digits is divisible by 9.
Page 317 - from the whole expression the square of that part of the root which is already found, and divide the first term of the remainder by twice the first term of the root. have found the first term of the root we can find each of the other terms in succession by the above process. For example, to
Page 316 - 2 X 2 xy, which is twice the product of the first and second terms of the root. Hence, after subtracting from (ii.) the square of the first term of the root, the second term is obtained by dividing the first term of the remainder by twice the first term of the root. the highest power of x is
Page 364 - cubic feet. Find the volume of a cone 9 feet high with a base whose radius is 14 feet. 16. The volume of a sphere varies as the cube of its radius ; if three spheres of radii
Page 317 - 2 , which is twice the product of the first and third terms of the root. Hence, after subtracting from (ii.) the square of that part of the root already found, the next term of the root is obtained by dividing the first term of the remainder by twice the first term of the root. If we now subtract the square of
Page 140 - 6 = 7. Hence we must find two numbers whose product is 12 and whose sum is 7. Pairs of numbers whose product is 12 are 12 and 1, 6 and 2, and 4 and 3 ; and the sum of the last pair is 7. Hence X 2
Page 351 - a is to b as c is to d." The first and fourth, of four quantities in proportion, are sometimes called the extremes, and the second and third of the quantities are called the means. 243. If the four quantities a, b, c, d are proportional, we have by definition a_

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