A Short Course in Higher Algebra: For Academies, High Schools, and Colleges |
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Common terms and phrases
ab² annuity arithmetical means arithmetical progression Binomial Theorem cent compound interest Clearing of fractions coefficient cologarithms common logarithm continued fraction convergent cube root decimal point denominator denote derive the formula digits divided divisor eighth term equal EXAMPLES Expand exponent expression Extracting the square find the logarithm find the number Find the value following equations following rule geometrical means geometrical progression given equation Given log harmonical means Hence increased integral interest being compounded last term mantissa Multiplying Note number corresponding number of combinations number of permutations number of terms obtain partial fractions present value quadratic quadratic equation quantities taken quotient radical sign remainder Required the number result second member second term Solve the equation Solve the following square root Subtracting unknown quantity Whence
Popular passages
Page 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.
Page 213 - In any trinomial square (Art. 108), the middle term is twice the product of the square roots of the first and third terms...
Page 269 - In any proportion the terms are in proportion by Composition; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Page 129 - A person has a hours at his disposal. How far may he ride in a coach which travels b miles an hour, so as to return home in time, walking back at the rate of с miles an hour ? 43.
Page 267 - 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 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 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.
Page 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.
Page 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.
Page 136 - Find the value of one of the unknown quantities, in terms of the other and known quantities...