## Elements of Algebra |

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absolute numbers algebraical quantities arithmetical arrangements becomes x binomial Bour calculation coefficient common factor contains continued fraction contrary signs cube root denominator determine divide dividend entire and positive entire function entire numbers entire value enunciation equa equal equation becomes evidently example expression figure formulas given number gives greater greatest common divisor hypothesis indeterminate inequality Let us designate letters logarithms manner method multiplicand multiplied negative nth root number of terms numerical value obtain operations perfect power perfect square performing the division polynomial preceding principle problem progression by difference progression by quotients proposed equation question radical sign reduced remainder resolved result rule satisfy second degree second member second term simple quantity solution square root subtract third tion trinomial twice the product unity unknown quantities verified whence we deduce whole number

### Popular passages

Page 26 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.

Page 53 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive $ '75, and, for every day he was idle, he should forfeit $ '25 ; at the expiration of the time, he received $ 27'50 ; how many days did he work...

Page 106 - It is founded on the following principle. The square root of the product of two or more factors, is equal to the product of the square roots of those factors.

Page 26 - Arrange the dividend and divisor with reference to a certain letter, and then divide the first term on the left of the dividend by the first term on the left of the divisor, the result...

Page 21 - To this result annex all the letters of the dividend, giving to each an exponent equal to the excess of its exponent in the dividend above that in the divisor.

Page 273 - 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 5 - ... the product multiply the number of tens by one more than itself for the hundreds, and place the product of the units at the right of this product, for the tens and units. Thus...

Page 128 - The algebraic sum of the two roots is equal to the coefficient of the second term taken with the contrary sign.

Page 250 - ... to the sum of the extremes multiplied by half the number of terms. Rule. — Add the extremes together, and multiply their sum by half the number of terms ; the product will be the sum of the series.

Page 26 - Though there is some analogy between arithmetical and algebraical division, with respect to the manner in which the operations are disposed and performed, yet there is this essential difference between them, that in arithmetical division the figures of the quotient are obtained by trial, while in algebraical division the quotient obtained by dividing the first term of the partial dividend by the first term of the divisor is always one of the terms of the quotient sought.