A Complete Course in Algebra for Academies and High Schools |
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a+b+c a²b a²b² a³b ab+b² ab² ab³ Adding Algebra arithmetical means arithmetical progression ax² binomial cents coefficient cologarithm complete divisor Completing the square cube root decimal derive the formula digits divided divisor EXAMPLES exponent expression Extracting the square Find the H.C.F. Find the value Find two numbers following equations following rule geometrical progression given equations Hence highest common factor last term less lowest common multiple mantissa monomial Note number of terms perfect square polynomial positive proportion QUADRATIC EQUATIONS quotient r₁ radical sign ratio Reduce the following remainder Required the number result rods second term simplest form Solve the equation Solve the following square root Substituting the value Subtracting Transposing trial-divisor twice unknown quantity Wells's Whence x²y
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 257 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
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 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.
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 44 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Page 129 - A banker has two kinds of money. It takes a pieces of the first kind to make a dollar, and b pieces of the second kind. If he is offered a dollar for с pieces, how many of each kind must he give ? 81.
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 31 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
Page 124 - A laborer agreed to serve for 36 days on condition that for every day he worked he should receive $1.25, and for every day he was absent he should forfeit 50 cents.