Higher Algebra: A Sequel to Elementary Algebra for Schools |
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Page 15
... b = c + d : c - d . This proposition is usually quoted as Componendo and Divi- dendo . Several other proportions may be proved in a similar way . 24. The results of the preceding article are the algebraical PROPORTION . 15.
... b = c + d : c - d . This proposition is usually quoted as Componendo and Divi- dendo . Several other proportions may be proved in a similar way . 24. The results of the preceding article are the algebraical PROPORTION . 15.
Page 16
... preceding article are the algebraical equivalents of some of the propositions in the fifth book of Euclid , and the student is advised to make himself familiar with them in their verbal form . For example , dividendo may be quoted as ...
... preceding article are the algebraical equivalents of some of the propositions in the fifth book of Euclid , and the student is advised to make himself familiar with them in their verbal form . For example , dividendo may be quoted as ...
Page 51
... preceding articles may be applied to find the sum of the squares , and the sum of the cubes of the terms of the series a , a + d , a + 2d , ........ 70. In referring to the results we have just proved 4-2 THE NATURAL NUMBERS . 51.
... preceding articles may be applied to find the sum of the squares , and the sum of the cubes of the terms of the series a , a + d , a + 2d , ........ 70. In referring to the results we have just proved 4-2 THE NATURAL NUMBERS . 51.
Page 91
... preceding article it follows that the expression ax2 + bx + c will always have the same sign whatever real value x may have , provided that b2-4ac is negative or zero ; and if this condition is satisfied the expression is positive or ...
... preceding article it follows that the expression ax2 + bx + c will always have the same sign whatever real value x may have , provided that b2-4ac is negative or zero ; and if this condition is satisfied the expression is positive or ...
Page 134
... preceding term . 3. The coefficient of the first term is unity ; the coefficient of the second term is the sum of the letters a , b , c , ... ; the coefficient of the third term is the sum of the products of these letters taken two at a ...
... preceding term . 3. The coefficient of the first term is unity ; the coefficient of the second term is the sum of the letters a , b , c , ... ; the coefficient of the third term is the sum of the products of these letters taken two at a ...
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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...