A Complete Course in Algebra for Academies and High Schools
Leach, Shewell & Sanborn, 1885 - Algebra - 349 pages
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Pages ā faire: 111, 112, 113, 114, 115, 117, 118, 119, 135, 136, 138, 139, 140, 143, 146, 147 et 148.
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abē Adding Algebra arithmetical binomial called cents changed coefficient common factor complete containing cube root denominator derive difference digits Divide dividend division divisor equal equivalent EXAMPLES exponent expression Extracting the square factors figures Find Find the values following equations following rule formula four fourth fraction given gives greater Hence highest increased indicates integral last term less letter logarithm lowest means method miles Multiplying negative Note obtained operation perfect polynomial positive preceding PROBLEMS progression proportion quotient radical sign raised rational Reduce remainder Required result rule second term solution Solve the equation Solve the following square root Substituting Subtracting taken third Transposing twice units unknown quantity Whence write written
Page 211 - In any trinomial square (Art. 108), the middle term is twice the product of the square roots of the first and third terms...
Page 253 - 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.
Page 256 - Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 If any number of quantities are proportional, 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...
Page 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.
Page 253 - 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 164 - 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.
Page 42 - 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.
Page 105 - Any term may be transposed from one side of an equation to the other by changing its sign.
Page 225 - 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.
Page 231 - Equations of this kind may always be solved by finding the value of one of the unknown quantities in terms of the other from the simple equation, and substituting the result in the other equation. 1. Solve the equations j ^ ~ ** = 6^ 0> 1 x + 2y=7.