## A Treatise on Elementary and Higher Algebra |

### From inside the book

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**inequalities**qn < b , qn + nb shall have place ; in which we may suppose q to be taken so great that n , the difference of the limits qn , qnn , of b , shall be less than any given quantity . = ( 30. ) We are now prepared to show that ... Page 185

Theodore Strong. Now , if we take the integer m , such that the

Theodore Strong. Now , if we take the integer m , such that the

**inequality**m > 1 ÷ p shall have place , then will the**inequality**pm > 1 also have place . If we multiply the two members of ( 3 ) by m , we shall have mA B == mC D + mp ... Page 218

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**inequality**. 5. To find a fourth proportional to 6 , 12 , and 15 ; also , a third proportional to 4 and 6 . 12 From ( 31 ) , we shall have 15 × = 15 × 2 = 30 = the 6 6 fourth proportional ; and from ( 32 ) we shall have 6 × 6 x 1.59 the ... Page 388

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**inequality**, while B and A are those of the second . The first**inequality**is read by saying that A is greater than B , or ( which is often preferable ) by saying that A is not less than B ; also , the second**inequality**is read by ... Page 389

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**inequality**will be changed . 3. Adding the corresponding members of A > B or B < A , and C > D or DC , the sums ...**inequality**which exists in the same sense as the given**inequalities**. 4. Taking the**inequality**x 2 - x 3 > + 1 or 3 ...### Contents

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### Other editions - View all

### Common terms and phrases

a²-b² algebraic arithmetical progression ascending powers becomes binomial called changed divisor changing the sign clear clearly compound quantity conse consequently corresponding cube root cx² denote difference divide dividend and divisor division divisor and dividend equa equal ratios evident EXAMPLES exponent expressed extract the square factors find the greatest find the number Find the product follows fraction given equation gives greater greatest common divisor Hence integer last term least common multiple less logarithm monomials multiplicand multiplier negative roots nth root number of terms numbers or quantities odd number positive integer positive roots preceding prime numbers proportion quently quotient real roots reduced remainder represent result right member rule rule of signs second term square root subtracted successive terms suppose surds third term tion unknown letter Va² whole number xy²

### Popular passages

Page 374 - 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 would it take each person to perform the same work alone ? Ans.

Page 307 - Multiply the complete divisor by the second term of the root, and subtract the product from the remainder.

Page 152 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from, home, it lasted the woman 30 days ; how many days would the man be in drinking it alone ? Ans.

Page 141 - II. Divide the greater number by the less, writing the quotient between the verticals, the product under the dividend, and the remainder below. III. Divide the less number by the remainder, the last divisor by the last remainder, and so on, till nothing remains. The last divisor will be the greatest common divisor sought.

Page 347 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...

Page 161 - ... multiply each numerator by all the denominators, except its own, for a new numerator, and under it write the common denominator.

Page 215 - Or, four terms are in harmonical proportion, when the first is to the fourth as the difference of the first and second is to the difference of the third and fourth.

Page 375 - A, B, C, D, E play together on this condition, that he who loses shall give to all the rest as much as they already have. First A loses, then B, then C, then D, and at last also E. All lose in turn, and yet at the end of the 5th game they all have the same sum, viz. each $32. How much had each when they began to play ? Ans.

Page 209 - The first term, the last term (or the extremes) and the ratio given, to find the sum of the series. RULE. Multiply the last term by the ratio, and from the product subtract the first term ; then divide the remainder by the ratio, less by 1, and the quotient will be the sum of all the terms.

Page 173 - ... proportion, the sum of the extremes is equal to the sum of the means. Thus...