An Elementary Treatise on Algebra: Theoretical and PracticalCollins and Hannay, 1824 - 516 σελίδες |
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Σελίδα 147
... ratios of vanishing quantities , ratios whose existence is incontestable , and from which we derive much in analysis . 172. In fact , when we compare the functions ax and ax + x2 , we find that their ratio , reduced to its and that it ...
... ratios of vanishing quantities , ratios whose existence is incontestable , and from which we derive much in analysis . 172. In fact , when we compare the functions ax and ax + x2 , we find that their ratio , reduced to its and that it ...
Σελίδα 148
... ratio , of the quanti a + x2 ties ax and ax + x2 can not only attain unity when we make x = 0 , but surpass it when we suppose negative , since it becomes then α a- X 9 a quantity This circum- which is greater than 1 , when x < a ...
... ratio , of the quanti a + x2 ties ax and ax + x2 can not only attain unity when we make x = 0 , but surpass it when we suppose negative , since it becomes then α a- X 9 a quantity This circum- which is greater than 1 , when x < a ...
Σελίδα 218
... ratio p , for which we find y Y — — α α = p ; b ' x b so that it is sufficient to take for x and y the same α multiples of the two terms of the fractions or b ' b simplified , which explains otherwise the indeter- mination of these ...
... ratio p , for which we find y Y — — α α = p ; b ' x b so that it is sufficient to take for x and y the same α multiples of the two terms of the fractions or b ' b simplified , which explains otherwise the indeter- mination of these ...
Σελίδα 221
... ratios - p , q of the three unknown quantities , 30 Z х leaves one of them entirely arbitrary , so that the question is susceptible of an indefinite number of solutions . In order to prove then , that the values of the unknown ...
... ratios - p , q of the three unknown quantities , 30 Z х leaves one of them entirely arbitrary , so that the question is susceptible of an indefinite number of solutions . In order to prove then , that the values of the unknown ...
Σελίδα 299
... ratio of 5 to 4 ; but if each had been 4 yards shorter , the ratio would have been 4 to 3. What are the lengths of the sides ? Ans . 36 , and 28 yards . Prob . 17. A sets out express from C towards D , and three hours afterwards B sets ...
... ratio of 5 to 4 ; but if each had been 4 yards shorter , the ratio would have been 4 to 3. What are the lengths of the sides ? Ans . 36 , and 28 yards . Prob . 17. A sets out express from C towards D , and three hours afterwards B sets ...
Άλλες εκδόσεις - Προβολή όλων
An Elementary Treatise on Algebra: Theoretical and Practical James Ryan,Robert Adrain Πλήρης προβολή - 1824 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a²+ab+b² according added algebraic quantities arithmetical becomes binomial changing the signs coefficients common denominator completing the square compound quantity consequently cube root demonstrated difference divi divided dividend division equa equal exponent expression extracting the root factors find the values formula fourth fraction required greater greatest common divisor greatest common measure Hence improper fraction least common multiple less letter logarithm lowest terms lues magnitudes manner mixed quantity multiplied number of terms numbers or quantities observed operation positive prefixed Prob problem proper sign proportionals proposed equation quadratic quadratic equations quan quotient radical sign ratio Reduce remainder Required the square required to find result RULE shillings side simple equations square root substituting subtracted surd third tion tity transposition unity unknown quantity values of x whence whole number