Elementary Algebra: Embracing the First Principles of the Science
A. S. Barnes & Company, 1848 - Algebra - 279 pages
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added addition affected algebraic apples arithmetical becomes binomial called cents changing coefficient common difference composed consequent considered contains cube denominator denote difference Divide dividend division divisor dollars double elimination entire equal equation EXAMPLES exponent expression extracting the square factors fifth power figure Find the square Find the values following RULE four fourth power fraction Given gives greater half Hence indicated interest John known last term less letter logarithm means method monomial Multiply negative number of terms obtain operations perfect square periods person polynomial positive pound progression proportion question quotient radical raise ratio receive Reduce remainder represent result second degree second term similar simplest form square root Substituting subtract taken tens term third transposing twice units unknown quantity values of x Verification whence write yards
Page 230 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Page 136 - The result of this operation, 1184, contains twice the product of the tens by the units, plus the square of the units.
Page 231 - Quantities are said to be in proportion by alternation, or alternately, when antecedent is compared- with antecedent and consequent with consequent. Thus, if we have the proportion 3 : 6 : : 8 : 16, the alternate proportion would be 3 : 8 : : 6 : 16. QUEST. — 147. When are three quantities proportional ? What is the middle one called ? — 148. When are quantities said to be in proportion by inversion, or inversely?
Page 155 - Divide the coefficient of the dividend by the coefficient of the divisor.
Page 233 - AC and by clearing the equation of fractions we have BO=AD; that is, Of four proportional quantities, the product of the two extremes is equal to the product of the two means.
Page 234 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 138 - 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 273 - A person has four casks, the second of which being filled from the first, leaves the first four-sevenths full. The third being filled from the second, leaves it one-fourth full, and when the third is emptied into the fourth, it is found to fill only nine-sixteenths of it. But the first will fill the third and' fourth, and leave 15 quarts remaining.
Page 79 - Ibs., his head weighed as much as his tail and half his body, and his body weighed as much as his head and t.ail together : what was the weight of the fish ? Let 2x = the weight of the body, in pounds.
Page 116 - 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.