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Adding Algebra arithmetical called cents changed coefficient common factor complete containing cube root decimal denominator derive difference digits divided dividend division divisor dollars equal equivalent EXAMPLES exceeds exponent expression Extracting the square factors feet figures Find Find the value following rule formula four fourth fraction geometrical given gives greater Hence highest increased indicates inverted last term less letter logarithm mantissa means method miles minutes Multiplying negative Note obtained operation perfect polynomial positive PROBLEMS progression proportion quadratic quotient radical sign ratio Reduce remainder Required result rods rule second term solution Solve the equation Solve the following square root Substituting subtract taken third twice uniting unknown quantity Whence write written
Side 166 - Arts. 200 and 201 we derive the following rule : Extract the required root of the numerical coefficient, and divide the exponent of each letter by the index of the root.
Side 44 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Side 49 - The exponent of b in the second term is 1, and increases by 1 in each succeeding term.
Side 255 - The first and fourth terms of a proportion are called the extremes; and the second and third terms the means. Thus, in the proportion a : b = с : d, a and d are the extremes, and b and с the means.
Side 258 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: b = c: d = e:f.
Side 5 - If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be changed.
Side 44 - The square of the sum of two quantities is equal to the SQuare of the first, plus twice the product of the first by the second, plus the square of the second.
Side 107 - Any term may be transposed from one side of an equation to the other by changing its sign. For, consider the equation x + a = b.
Side 227 - A' courier proceeds from P to Q in 14 hours. A second courier starts at the same time from a place 10 miles behind P, and arrives at Q at the same time as the first courier. The second courier finds that he takes half an hour less than the first to accomplish 20 miles. Find the distance from P to Q.