Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and Horner's Theorems, and Practical Examples

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A.S. Barnes, 1871 - Algebra - 400 pages
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Page 290 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 19 - The number placed over the radical sign is called the index of the root. Thus, 2 is the index of the square root, 3 of the cube root, 4 of the fourth root, &c. 17. The reciprocal of a quantity, is unity divided by that quantity. Thus, — is the reciprocal of a; and, -- - is the reciprocal of a + b.
Page 10 - Logic is a portion of the art of thinking; language is evidently, and by the admission of all philosophers, one of the principal instruments or helps of thought; and any imperfection in the instrument or in the mode of employing it is confessedly liable, still more than in almost any other art, to confuse and impede the process and destroy all ground of confidence in the result.
Page 117 - The first ten numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Roots.
Page 100 - If A and B together can perform a piece of work in 8 days, A and c together in 9 days, and B and c in 10 days, how many days will it take each person to perform the same work alone.
Page 201 - ... divisor, and see how often it is contained in the dividend, and place the quotient for a second figure of the root. Then cube the figures of the root thus found, and if their cube...
Page 35 - We have, then, for the multiplication of polynomials, the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier in succession, aff'ccting the product of any two terms with the sign plus, when tlieir signs are alike, and with the sign minus, when their signs
Page 62 - Subtract the numerator of the subtrahend from the numerator of the minuend, and place the difference over the common denominator. EXAMPLES FOR PRACTICE.
Page 99 - A person has two horses, and a saddle worth 50 ; now, if the saddle be put on the back of the first horse, it will make his value double that of the second ; but if it be put on the back of the second, it will make his value triple that of the first ; what is the value of each horse ? Ans.
Page 182 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the lesser, is equal to 12 ? Ans.

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