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

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### Common terms and phrases

added addition affected algebraic apply approximating arranged becomes binomial called changed co-efficient consequently consider contain continued corresponding decimal deduce denominator denote determine difference Divide dividend division entire equal equation evident exact example exponent expression extract factors figures formula fourth fraction gives greater greatest common divisor hence indicated involving known least less letter limit logarithm manner means method monomial multiplied negative obtain operation perfect performed polynomial positive preceding principles problem progression proposed quotient radical Reduce reference remainder represent result rule satisfy second degree second term similar simplest form square root substituted subtract suppose taken tens term third transformed true units unknown quantity variations whence whole write written

### Popular passages

Page 121 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.

Page 174 - For, we can find the value of one of the unknown quantities in terms of the other and known quantities...

Page 286 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.

Page 39 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.

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 200 - RULE. I. Separate the given number into periods of three figures each, beginning at the right hand ; the left hand period will often contain less than three places of figures.

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 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 41 - Divide the coefficient of the dividend by the coefficient of the divisor.

Page 200 - The cube of a number is equal to the cube of the tens, plus three times the product of the square of the tens by the units, plus three times the product of the tens by the square of the units, plus the cube of the units.