An Elementary Treatise on Algebra, Theoretical and Practical ... |
Other editions - View all
An Elementary Treatise on Algebra, Theoretical and Practical . . James Ryan No preview available - 2012 |
Common terms and phrases
aČ-bČ aČ+ab+bČ according added adfected algebraic quantities becomes binomial changing the signs coefficient completing the square compound quantities consequently cube root denoted difference digits dividend division enunciation equa equal example exponent expression extracting the root factors find the values formula fourth fraction required greater greatest common divisor greatest common measure Hence improper fraction involving least common multiple less letter logarithm lowest terms lues magnitudes manner method mixed quantity multiplied negative number of terms observed operation prefixed 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 subtraction third tion tities transposition travelled unity unknown quantity values of x whence whole number
Popular passages
Page 380 - 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 373 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Page 146 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Page 384 - 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 378 - Equal magnitudes have the same ratio to the same magnitude; and the same has the same ratio to equal magnitudes.
Page 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.
Page 373 - 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...
Page 388 - When there is a series of quantities, such that the ratios of the first to the second, of the second to the third, of the third to the fourth, &c., are all equal ; the quantities are said to be in continued proportion.
Page 171 - A farmer parting with his stock, sells to one person 9 horses and 7 cows for 300 dollars: and to another, at the same prices, C horses and 13 cows for the same sum.
Page 96 - Any term may be transposed from one side of an equation to the other by changing its sign.