## Elements of Algebra |

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according added algebraical already apply arrangements becomes binomial called coefficient combinations common divisor condition consequently consider contains cube deduce denominator designate determine difference divide dividend division enter entire enunciation equal equation evidently example exponent expression extract factor figure formulas fourth fraction francs given gives greater greatest indeterminate indicated interest known less letters logarithms manner means method multiplied necessary negative observe obtain operations particular perform polynomial portion positive preceding principle problem progression proposed equation question quotient radical raise reason reduced remainder remark resolved result root rule satisfy second degree simple quantity solution square square root substituted subtract suppose taken tens third tions units unity unknown quantities verified whence whole number write

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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 271 - 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 127 - The algebraic sum of the two roots is equal to the coefficient of the second term taken with the contrary sign.

Page 248 - ... 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.