## An Introduction to Algebra: Being the First Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges |

### From inside the book

Results 1-5 of 29

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**diminished**, or which is capable of being measured , is called quantity . Thus , a line is a quantity , because it can be made long- er or shorter ; and can be measured , by applying to it another line , as a foot , a yard , or an ell ... Page 13

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**diminish**- ed by 6 i . e . 4 . 29. The sign + is prefixed to quantities which are considered as affirmative or positive ; and the sign - , to those which are supposed to be negative . For the nature of this distinction , see art . 54 ... Page 18

... The quotient of 6 divided by the sum of a and b , is equal to 7 times d ,

... The quotient of 6 divided by the sum of a and b , is equal to 7 times d ,

**diminished**by the quotient of 6 , divided by 36. Ans . 51. It is necessary also , to be able to reverse what NOTATION . 19 is done in the preceding examples , Page 19

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**diminished**by 6 times m , and increased by the quotient of a divided by the sum of a and c ... 3h - c h 2ab + x + y = dx a + b + c - 6 + 6 Ans . c - 6d 3. a + 7 ( h + x ) - 2a + 4 = ( a + h ) x ( b - c ) . Ans . 4 . a - bac : Ans . d ... Page 22

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**diminish**it , must be negative . In a mercantile con- cern , if the stock is supposed to be positive , the profits will be positive ; for they increase the stock ; they are to be added to it . But the losses will be negative ; for they ...### Other editions - View all

### Common terms and phrases

12 rods abscissa added algebraic antecedent applied arithmetic arithmetical progression become binomial calculation called Clearing of fractions co-efficients Completing the square compound quantity consequent cube root cubic equation curve demonstration denominator diminished dividend division divisor dollars equa equal quantities errour Euclid exponents expressed Extracting and transp factors fourth geometrical geometrical progression given quantity greater inches infinite series inverted involution last term less Let x=the letters manner mathematics Mult multiplicand negative quantity notation nth power nth root number of terms ordinate parallelogram perpendicular positive prefixed principle Prob Prod proportion proposition quadratic equation quan quotient radical quantities radical sign ratio reciprocal Reduce the equation remainder rule SECTION sides square root substituted subtracted subtrahend supposed supposition theorem third tion tity Transposing transposition triangle twice uniting terms unknown quantity varies vulgar fraction whole αα

### Popular passages

Page 214 - In an arithmetical progression, the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.

Page 188 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.

Page 265 - The operation consists in repeating the multiplicand as many times as there are units in the multiplier.

Page 227 - 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.

Page 189 - If four quantities are proportional, THE ORDER OF THE MEANS, OR OF THE EXTREMES, OR OF THE TERMS OF BOTH COUPLETS, MAY BE INVERTED, WITHOUT DESTROYING THE PROPORTION.

Page 40 - We have seen that multiplying by a whole number, is taking the multiplicand as many times as there are units in the multiplier.

Page 85 - If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means.

Page 187 - When there is a series of quantities, such that the ratios of the first to the second, of the second to the third, of the third to the fourth, &c., are all equal ; the quantities are said to be in continued proportion.

Page 60 - The Value of a fraction is the quotient of the numerator divided by the denominator.

Page 61 - ... produce the same effect on the value of the fraction, as multiplying the numerator. In all cases...