An Elementary Treatise on Algebra, Theoretical and Practical ...W. E. Dean, 1835 - 361 σελίδες |
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Σελίδα 58
... answer for the multiplication of a whole number by a fraction . Now , let us suppose that two fractions are to be multiplied by one another . Let the two equalities be a = b . v , a ' = b ' . v ' ; multiplying one by the other , the two ...
... answer for the multiplication of a whole number by a fraction . Now , let us suppose that two fractions are to be multiplied by one another . Let the two equalities be a = b . v , a ' = b ' . v ' ; multiplying one by the other , the two ...
Σελίδα 100
... answers the condi- tion required , and this value of x is called the root of the equa- tion . 167. Hence the root of an equation is such a number or quantity , as , being substituted for the unknown quantity , will make both sides of ...
... answers the condi- tion required , and this value of x is called the root of the equa- tion . 167. Hence the root of an equation is such a number or quantity , as , being substituted for the unknown quantity , will make both sides of ...
Σελίδα 117
... answer its several con- ditions ; for this purpose , there are four things to be distin- guished : I. The given ... answers given in general terms . A problem solved in this way , furnishes a theorem , which may be applied to the ...
... answer its several con- ditions ; for this purpose , there are four things to be distin- guished : I. The given ... answers given in general terms . A problem solved in this way , furnishes a theorem , which may be applied to the ...
Σελίδα 119
... answer does 179. Thus the capital shall be -206 . not agree with the problem , and still if this value —206 , be substituted for x in the equation found , we obtain 105 × 206 100 + b = 20b , and , performing the operations indicated in ...
... answer does 179. Thus the capital shall be -206 . not agree with the problem , and still if this value —206 , be substituted for x in the equation found , we obtain 105 × 206 100 + b = 20b , and , performing the operations indicated in ...
Σελίδα 127
... answer with respect to the terms of the question , since that a number of soldiers cannot be negative . 181. We shall render this impossibility very plain , by observ- ing that the triple of a number being less than the quadruple of the ...
... answer with respect to the terms of the question , since that a number of soldiers cannot be negative . 181. We shall render this impossibility very plain , by observ- ing that the triple of a number being less than the quadruple of the ...
Άλλες εκδόσεις - Προβολή όλων
An Elementary Treatise on Algebra, Theoretical and Practical: Adapted to the ... James Ryan Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
An Elementary Treatise on Algebra, Theoretical and Practical: Adapted to the ... James Ryan Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
An Elementary Treatise on Algebra, Theoretical and Practical: Adapted to the ... James Ryan Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a²+ab+b² according added adfected algebraic quantities arithmetical becomes binomial changing the signs coefficient completing the square compound quantities consequently cube root DEMONSTRATION denoted difference digits divided dividend division equa equal exponent expressed extracting the root factors find the values formula fourth given equation greater greatest common divisor Hence improper fraction integral least common multiple less letter logarithm lowest terms lues magnitudes manner method miles mixed quantity multiplied number of terms observed positive PROB problem proportion proposed equation quadratic quadratic equation quadratic surds quan quotient radical quantities radical sign ratio Reduce remainder Required the cube Required the square required to find result RULE second equation shillings side simple equations square root substituting subtraction surd third tion tities transposition unity unknown quantity values of x whence whole number
Δημοφιλή αποσπάσματα
Σελίδα 348 - IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents.
Σελίδα 341 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Σελίδα 96 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Σελίδα 146 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Σελίδα 340 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater; that is, ' when the less is contained a certain number of times
Σελίδα 346 - Equal magnitudes have the same ratio to the same magnitude; and the same has the same ratio to equal magnitudes.
Σελίδα 186 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Σελίδα 352 - THEOB.—If four magnitudes be proportionals, they are also proportionals by conversion; that is, the first is to its excess above the second, as the third to its excess above the fourth. Let AB be to BE, as CD to DF: then BA shall be to AE, as DC to CF.
Σελίδα 345 - IF the first be to the second as the third to the fourth, and if the first be a multiple, or part of the second; the third is the same multiple, or the same part of the fourth...
Σελίδα 41 - 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. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.