## 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

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Page 78

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**prob**- lem , the known and unknown quantities are frequently thrown promiscuously together . To find the value of that which is required , it is necessary to bring it to stand by it- self , while all the others are on the opposite side ... Page 88

... , Multiply 4 into 50- ; the product is To this add The sum is From this subtract جو The remainder is 6 the statement of the problem 200 70 270 ! 50 28220 as in こ فرد

... , Multiply 4 into 50- ; the product is To this add The sum is From this subtract جو The remainder is 6 the statement of the problem 200 70 270 ! 50 28220 as in こ فرد

**Prob**. 2. What number is that , to which 86 ALGEBRA. Page 89

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**Prob**. 2. What number is that , to which if its half be added , and from the sum 20 be subtracted , the remainder will be a fourth part of the number itself ? In stating questions of this kind , where fractions are con- cerned , it ... Page 90

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**Prob**. 4. Divide 48 into two such parts , that if the less be divided by 4 and the greater by 6 , the sum of the quotients will be 9 . Here if x be put for the smaller part , the greater will be 48 - x . 48- 1 6x + 192-4x = 216 X By the ... Page 91

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**Prob**. 6. A merchant gains or loses , in a bargain , a certain sum . In a second bargain , he gains 350 dollars , and , in a third , loses 60. In the end , he finds he has gained 200 dol- lars , by the three together . How much did he ...### 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...