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A Treatise on Elementary and Higher Algebra (Classic Reprint)
No preview available - 2018
algebraic arithmetical progression ascending powers becomes becomes x binomial binomial theorem called changing the sign clear clearly coefficients common logarithm conse consequently contains corresponding cube root cubic equation decimal places denominator denote derived function difference divide dividend equa equal ratios equal roots evident EXAMPLES expressed extract the square factors find the number find the roots follows fraction geometrical progression given equation gives greater greatest common divisor Hence imaginary roots incomplete divisor inequality least common multiple less logarithm monomial multiply negative roots number of terms numbers or quantities odd number polynomial positive integer positive roots proportion proposed equation quadratic quently quotient real roots remainder remaining roots represent result right member rule second term solution square root subtract superior limit supposed surds thence theorem third term tion unknown letter variation whole number
Page 374 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 152 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from, home, it lasted the woman 30 days ; how many days would the man be in drinking it alone ? Ans.
Page 141 - II. Divide the greater number by the less, writing the quotient between the verticals, the product under the dividend, and the remainder below. III. Divide the less number by the remainder, the last divisor by the last remainder, and so on, till nothing remains. The last divisor will be the greatest common divisor sought.
Page 347 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 161 - ... multiply each numerator by all the denominators, except its own, for a new numerator, and under it write the common denominator.
Page 215 - Or, four terms are in harmonical proportion, when the first is to the fourth as the difference of the first and second is to the difference of the third and fourth.
Page 375 - A, B, C, D, E play together on this condition, that he who loses shall give to all the rest as much as they already have. First A loses, then B, then C, then D, and at last also E. All lose in turn, and yet at the end of the 5th game they all have the same sum, viz. each $32. How much had each when they began to play ? Ans.
Page 209 - The first term, the last term (or the extremes) and the ratio given, to find the sum of the series. RULE. Multiply the last term by the ratio, and from the product subtract the first term ; then divide the remainder by the ratio, less by 1, and the quotient will be the sum of all the terms.