A Treatise on Elementary and Higher Algebra |
From inside the book
Results 1-5 of 35
Page 20
... integer M by the integers a , b , c , etc. , successively , when taken in any order ; then it will be sufficient to ... positive integer , we express the product aaa , etc. , to n factors , which is called the nth power of a , by a ...
... integer M by the integers a , b , c , etc. , successively , when taken in any order ; then it will be sufficient to ... positive integer , we express the product aaa , etc. , to n factors , which is called the nth power of a , by a ...
Page 40
... positive integer n is equal to the number of factors in the product , and we put A1 for the sum of all the 4 quantities , - a , b , c , 40 ELEMENTARY AND HIGHER ALGEBRA .
... positive integer n is equal to the number of factors in the product , and we put A1 for the sum of all the 4 quantities , - a , b , c , 40 ELEMENTARY AND HIGHER ALGEBRA .
Page 64
... integer and a fraction , and indeed of the product of any number of in- tegers by any number of fractions , as is ... positive , the quotient must clearly be positive ; but if the divisor and dividend are both negative , the ...
... integer and a fraction , and indeed of the product of any number of in- tegers by any number of fractions , as is ... positive , the quotient must clearly be positive ; but if the divisor and dividend are both negative , the ...
Page 97
... integer n may be taken so great that 1 x ( x - 1 ) shall become an insensible quantity , which may be rejected ... positive quantity , then the series will indicate that the generating function is infinitely great . If a is ...
... integer n may be taken so great that 1 x ( x - 1 ) shall become an insensible quantity , which may be rejected ... positive quantity , then the series will indicate that the generating function is infinitely great . If a is ...
Page 99
... positive integer , and that for ± we must use + if n is an even number , and that - must be used for when n is an odd number . If a is sensibly less than 1 , then n may be taken so great that ± shall be less than any finite quantity ...
... positive integer , and that for ± we must use + if n is an even number , and that - must be used for when n is an odd number . If a is sensibly less than 1 , then n may be taken so great that ± shall be less than any finite quantity ...
Contents
| 87 | |
| 120 | |
| 129 | |
| 141 | |
| 150 | |
| 157 | |
| 163 | |
| 169 | |
| 175 | |
| 182 | |
| 188 | |
| 196 | |
| 203 | |
| 209 | |
| 215 | |
| 223 | |
| 394 | |
| 415 | |
| 428 | |
| 435 | |
| 441 | |
| 448 | |
| 454 | |
| 462 | |
| 469 | |
| 481 | |
| 494 | |
| 512 | |
| 521 | |
| 535 | |
| 544 | |
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...