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Elementary Algebra: Embracing the First Principles of the Science
Uten tilgangsbegrensning - 1856
abº algebraic quantities apples arithmetical arithmetical means arithmetical progression binomial Binomial Formula called cents Charles Clear the equation co-efficient common difference completing the square contrary sign cube denote the number Divide the number dividend division divisor dollars EXAMPLES exponent extracting the square factors find a number Find the square Find the sum Find the values Find two numbers following RULE four fourth power fraction geometrical progression give a sum Give the rule Given Given Given given number greater Hence incomplete equation James John last term least common multiple less Let a denote letter logarithm metical mixed quantity monomial Multiply number added number of terms obtain perfect square polynomial progression proportion quotient ratio Reduce remainder Sabc Saº second degree second term simplest form square root subtract sum equal third three numbers transposing unknown quantity Verification whence yards
Side 160 - 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.
Side 16 - Similarly, any term may be transposed from one member of an equation to the other by changing its sign.
Side 197 - Since the square of a binomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second...
Side 138 - 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. A 14JA days, B 17fa, and C 23JT.
Side 255 - BD we have — = -^, (Art. 169) ; and by clearing the equation of fractions, we have BC = AD; that is, Of four proportional quantities, the product of the two extremes is equal to the product of the two means.
Side 295 - The crew of a ship consisted of her complement of sailors, and a number of soldiers. There were 22 sailors to every three guns, and 10 over ; also, the whole number of hands was five times the number of soldiers and guns together.
Side 167 - These expressions may often be simplified, upon the principle that, the square root of the product of two or more factors is equal to the product of the square...
Side 76 - To reduce fractions having different denominators to equivalent fractions having a common denominator. RULE. Multiply each numerator into all the denominators except its own, for the new numerators, and all the denominators together for a common denominator.
Side 252 - Of four proportional quantities, the first and third are called the antecedents, and the second and fourth the consequents ; and the last is said to be a fourth proportional to the other three taken in order. Thus, in the last proportion, A and C are the antecedents, and B and D the consequents.