New Elementary Algebra: in which the First Principles of Analysis are Progressively Developed and Simplified for Common Schools and Academies ...
Robert S. Davis & Company, 1863 - 324 pages
a b c a² b² algebraic quantities arithmetical mean binomial factors cents Clearing of fractions coefficient common denominator common difference completing the square cube root Define denote Divide dividend division entire quantity equa equal Explain the operation Explain the solution Extract the square Find the greatest Find the sum find the values formulas fractional exponent geometrical progression Given x² greatest common divisor Hence indicated last term least common multiple letter lowest terms miles monomial Multiply negative exponents NOTE number of terms obtain perfect square polynomial positive proportion quadratic equation quadratic form quan quotient radical sign ratio Reduce remainder Repeat the Rule Required the square second member second power simple equations solution of Problem square root subtraction Theorem tion tity transposing units unknown quantity Whence
Page 56 - 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 305 - ... that is, Any term of a geometric series is equal to the product of the first term, by the ratio raised to a power, whose exponent is one less than the number of terms. EXAMPLES. 1.
Page 294 - ... two triangles are to each other as the products of their bases by their altitudes.
Page 73 - The LEAST COMMON MULTIPLE of two or more quantities is the least quantity that can be divided by each of them without a remainder.
Page 46 - The exponent of a letter in the quotient is equal to its exponent in the dividend, minus its exponent in the divisor. 439. Let it be required to divide a* by a1.
Page 176 - ... 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 281 - Divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5. Ans. 20 and 40.
Page 139 - The method thus exemplified is expressed in the following 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.