New Elementary Algebra: Designed for the Use of High Schools and Academies, Book 1 |
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a b c a² b² algebraic algebraic quantities arithmetical arithmetical means cents coefficient common denominator common difference completing the square cube root decimal Define denote Divide dividend entire quantity equa equal Explain the operation Explain the solution expression Extract the square Find the cube Find the logarithm Find the square Find the sum find the values formulas fractional exponent given number Given x² greatest common divisor Hence indicated last term least common multiple letter lowest terms mantissa monomial Multiply NOTE number of terms obtain perfect square places of figures polynomial proportion quadratic equation quadratic form quotient radical ratio Reduce remainder Repeat the Rule Required the square second member second power simplest form solution of Problem square root Theorem tion tity transposing trial divisor units unknown quantity Whence
Popular passages
Page 52 - 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 165 - Find the greatest square in the first- period on the left, and place its root on the right after the manner of a quotient in division. Subtract the square of the root from the first period, and to the remainder bring down the second period for a dividend.
Page 49 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 180 - Find the cube root of the first term, write it as the first term of the root, and subtract its cube from the given polynomial.
Page 158 - ... found by multiplying the coefficient of the preceding term by the exponent of the leading letter of the same term, and dividing the product by the number which marks its place.
Page 249 - Divide the number 24 into two such parts, that their product shall be to the sum of their squares, as 3 to 10.
Page 105 - The root of an equation is found by bringing all the terms containing the unknown quantity into one member, and freeing it from all connection with known quantities. 157. The root of an equation is...
Page 260 - ... two triangles are to each other as the products of their bases by their altitudes.
Page 129 - RULE. Find an expression for the value of the same unknown quantity in each of the equations, and form a new equation, by placing these values equal to each other.
Page 53 - ... 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.