A Complete Course in Algebra for Academies and High SchoolsLeach, Shewell & Sanborn, 1885 - 349 σελίδες |
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a²b a²b² ab+b² ab² ab³ Adding Algebra arithmetical means arithmetical progression ax² binomial cent coefficient complete divisor Completing the square cube root decimal degree denominator derive the formulæ digits dividend EXAMPLES exponent Extracting the square figures Find the cube Find the values Find two numbers following equations following rule formula geometrical means geometrical progression Hence highest common factor Insert last term logarithm mantissa members the square miles monomial Note number of terms obtained parenthesis perfect square polynomial positive QUADRATIC EQUATIONS quotient r₁ radical sign ratio Reduce the following remainder required root Required the number result rule of Art second term simplest form Solve the equation Solve the following square root Substituting the value third term Transposing trial-divisor twice unknown quantity Whence x²y
Δημοφιλή αποσπάσματα
Σελίδα 213 - In any trinomial square (Art. 108), the middle term is twice the product of the square roots of the first and third terms...
Σελίδα 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.
Σελίδα 258 - 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...
Σελίδα 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.
Σελίδα 255 - 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 107 - Any term may be transposed from one side of an equation to the other by changing its sign.
Σελίδα 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.
Σελίδα 233 - 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.