A Theoretical and Practical Treatise on Algebra: In which the Excellencies of the Demonstrative Methods of the French are Combined with the More Practical Operations of the English and Concise Solutions Pointed Out and Particularly Inculcated : Designed for Schools, Colleges and Private StudentsIvison, Phinney & Company, 1861 |
Other editions - View all
Common terms and phrases
3d term algebraic arithmetical arithmetical progression assume binomial square binomial theorem cent Clearing of fractions coefficients Completing the square containing cube root cubic equation decimal degree diff difference Divide the number dividend division dollars equa equal roots equation becomes example Expand exponent expressed extract factors find the values following rule geometrical progression give greater Hence improper fraction infinity last term least common multiple less letter lowest terms method Multiply negative number of terms numbers in geometrical observe operation positive root primitive equation problem Prod proportion quadratic quadratic equations quotient real roots Reduce remainder represent resolved result second term solution specific gravity square root Sturm's Theorem substitute subtract suppose third three numbers Transform the equation transformed equation Transpose trial divisor unity unknown quantity variations of signs whole numbers zero
Popular passages
Page 34 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Page 145 - It is required to divide the number 14 into two such parts that the quotient of the greater divided by the less, may be to the quotient of the less divided by the greater as 16 to 9.
Page 204 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 61 - For, if we have given ab' = a'b, then, dividing by bb', we obtain Corollary. The terms of a proportion may be written In any order which will make the product of the extremes equal to the product of the means.
Page 11 - If the same quantity be both added to and subtracted from another, the value of the latter will not be changed.
Page 188 - From the preceding, it appears, that the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.
Page 44 - Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Page 204 - If four magnitudes constitute a proportion, the first will be to the sum of the first and second as the third is to the sum of the third and fourth.
Page 87 - B, can perform a piece of work together in 16 days. They work together for 4 days, when A being called off, B is left to finish it, which he does in 36 days more. In what time would each do it separately ? Ans. A in 24 days, B in 48 days.
Page 192 - A certain number consists of three digits, which are in arithmetical progression ; and the number divided by the sum of its digits is equal to 26; but if 198 be added to it, the digits will be inverted. What is the number?