Higher Algebra: A Sequel to Elementary Algebra for Schools |
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Page xxi
... . Transformation of equations . 470 471 Equation with roots of sign opposite to those of ƒ ( x ) = 0 Equation with roots multiples of those of ƒ ( x ) = 0 471 472 Equation with roots reciprocals of those of ƒ ( x CONTENTS . xxi.
... . Transformation of equations . 470 471 Equation with roots of sign opposite to those of ƒ ( x ) = 0 Equation with roots multiples of those of ƒ ( x ) = 0 471 472 Equation with roots reciprocals of those of ƒ ( x CONTENTS . xxi.
Page xxiii
... multiple , part , or parts , one quantity is of the other . The ratio of A to B is usually written A : B. The quantities A and B are called the terms of the ratio . The first term is called the antecedent , the second term the ...
... multiple , part , or parts , one quantity is of the other . The ratio of A to B is usually written A : B. The quantities A and B are called the terms of the ratio . The first term is called the antecedent , the second term the ...
Page 16
... multiple of the fourth , according as the multiple of the first is greater than , equal to , or less than the multiple of the second . In algebraical symbols the definition may be thus stated : Four quantities a , b , c , d are in ...
... multiple of the fourth , according as the multiple of the first is greater than , equal to , or less than the multiple of the second . In algebraical symbols the definition may be thus stated : Four quantities a , b , c , d are in ...
Page 17
... multiple , part , or parts , of b that c is of d . But the proofs which have been given for commensurable quantities will still be true for incommensurables , since the ratio of two incom- mensurables can always be made to differ from ...
... multiple , part , or parts , of b that c is of d . But the proofs which have been given for commensurable quantities will still be true for incommensurables , since the ratio of two incom- mensurables can always be made to differ from ...
Page 57
... multiples of powers of 10 ; for instance 25 = 2 × 10 + 5 ; - 47054 × 103 +7 × 102 + 0 × 10 + 5 . X X This method of representing numbers is called the common or denary scale of notation , and ten is said to be the radix of the scale ...
... multiples of powers of 10 ; for instance 25 = 2 × 10 + 5 ; - 47054 × 103 +7 × 102 + 0 × 10 + 5 . X X This method of representing numbers is called the common or denary scale of notation , and ten is said to be the radix of the scale ...
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Other editions - View all
Higher Algebra: A Sequel to Elementary Algebra for Schools H. S. Hall,S. R. Knight No preview available - 2017 |
Higher Algebra: A Sequel to Elementary Algebra for Schools (Classic Reprint) H. S. Hall No preview available - 2017 |
Higher Algebra: A Sequel to Elementary Algebra for Schools H. S. Hall,S. R. Knight No preview available - 2018 |
Common terms and phrases
a+b+c+ a₁ Algebra annuity arithmetic mean arithmetical progression ascending powers ax² b₁ Binomial Theorem C₁ C₂ complete quotient compound interest continued fraction cube root denominator denote digits divisible Elementary Algebra equal equation x² Example expression factors Find the coefficient find the number Find the sum find the value finite geometrical progression given log given series greater greatest term hence infinite series less letters limit logarithms multiplying negative nth term number of solutions number of terms Ny² obtain orders of differences P₁ partial fractions positive integers preceding article proper fraction prove quadratic quadratic equation r+1)th term radix ratio rational integral function recurring series scale of relation series is convergent series is divergent shew solution in positive Solve suppose u₁ U₂ unity vergent whence zero
Popular passages
Page 61 - ... any number divided by 9 will leave the same remainder as the sum of its digits divided by 9.
Page 175 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 117 - The number of combinations of n things г at a time is equal to the number of combinations of n things n—r at a time.
Page 454 - If then we suppose the factors corresponding to the negative and imaginary roots to be already multiplied together, each factor x— a corresponding to a positive root introduces at least one change of sign ; therefore no equation can have more positive roots than it has changes of sign. To prove the second part of Descartes...
Page 11 - In any proportion the product of the extremes is equal to the product of the means. Let the proportion be a : b = с : d.
Page 367 - DEFINITION. If an event can happen in a ways and fail in b ways, and. each of these ways is equally likely, the probability, or the chance, of its happening is , and...
Page 492 - Geese, which were proceeding at the rate of 3 miles in 2 hours, he afterwards met a stage wagon, which was moving at the rate of 9 miles in 4 hours. B overtook the same drove of Geese at the 45th mile stone, and met the same stage wagon exactly forty minutes before he came to the 31st mile stone. Where was B when A reached London 1 Solution.
Page 178 - The integral part of a logarithm is called the characteristic, and the decimal part is called the mantissa.
Page 130 - There are n points in a plane, no three of which are in the same straight line with the exception of p, which are all in the same straight line; find the number of lines which result from joining them.
Page 486 - A railway train after travelling for one hour meets with an accident which delays it one hour, after which it proceeds at three-fifths of its former rate, and arrives at the terminus...