An Elementary Treatise on Algebra: Theoretical and Practical |
From inside the book
Results 1-5 of 39
Page 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 a and ax + x2 , we find that their ratio , reduced to its a most simple ...
... 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 a and ax + x2 , we find that their ratio , reduced to its a most simple ...
Page 148
... ratio , τα of the quanti-- a + x ' ties ax and ax + x2 can not only attain unity when we make x = 0 , but surpass it when we suppose a negative , since it becomes then α a - x a quantity which is greater than 1 , when x < a . This ...
... ratio , τα of the quanti-- a + x ' ties ax and ax + x2 can not only attain unity when we make x = 0 , but surpass it when we suppose a negative , since it becomes then α a - x a quantity which is greater than 1 , when x < a . This ...
Page 218
... ratio P , for which we find Y 00 -- a b = - a − b = p . 3 = p ; b ' so that it is sufficient to take for x and y the same α α ' multiples of the two terms of the fractions or b simplified , which explains otherwise the indeter ...
... ratio P , for which we find Y 00 -- a b = - a − b = p . 3 = p ; b ' so that it is sufficient to take for x and y the same α α ' multiples of the two terms of the fractions or b simplified , which explains otherwise the indeter ...
Page 221
... ratios - p , -q of the three unknown quantities , XC 2 x 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 , XC 2 x 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 ...
Page 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 ? t Ans . 36 , and 28 yards . Prob . 17. A sets out express from C towards D , and three hours afterwards B ...
... 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 ? t Ans . 36 , and 28 yards . Prob . 17. A sets out express from C towards D , and three hours afterwards B ...
Other editions - View all
Common terms and phrases
a²+ab+b² added adfected algebraic quantities becomes binomial changing the signs coefficient common denominator completing the square compound quantity consequently cube root difference digits divi dividend division enunciation equa equal example exponent expressed extracting the root factors find the values formula fourth gives greater greatest common divisor greatest common measure Hence least common multiple less letter logarithm lowest terms lues magnitudes manner method miles multiplied negative observed operation positive preceding Prob problem proportion proposed equation quadratic equations 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 solution square root substituting subtracted third tion tity transposition travelled unity unknown quantity values of x whence whole number
Popular passages
Page iv - In conformity to the act of Congress of the United States, entitled, " An act for the encouragement of learning, by securing the copies of maps, charts and books, to the authors and proprietors of such copies, during the times therein mentioned ;
Page 498 - 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.
Page 57 - 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.
Page 162 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Page 489 - The first of four magnitudes is said to have the same ratio to the second which the third has to the. fourth, when any equimultiples...
Page 239 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Page 503 - 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.
Page 496 - Equal magnitudes have the same ratio to the same magnitude; and the same has the same ratio to equal magnitudes.
Page 318 - 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.
Page 7 - NB When four magnitudes are proportionals, it is usually expressed by saying, the first is to the second, as the third to the fourth.' VII. When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second...