New Elementary AlgebraR.S. Davis & Company, 1866 |
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Common terms and phrases
a² b² algebraic quantities arithmetical mean binomial factors cents Clearing of fractions coefficient common denominator common difference complete the square cube root Define degree denote Divide dividend division entire quantity equa 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 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 number Required the square second member second power simple equations solution of Problem square root subtraction Theorem tion tity transposing units unknown quantity Whence
Popular passages
Page 55 - That is, 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 183 - 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 281 - ... if the circumference of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel, in the same distance ; required the circumference of each wheel.
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 18 - If equal quantities be multiplied into the same, or equal quantities, the products will be equal. 4. If equal quantities be divided by the same 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 altered.
Page 281 - Divide the number 24 into two such parts, that their product shall be to the sum of their squares, as 3 to 10.
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 182 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 53 - 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 310 - The mean proportional between two quantities is equal to the square root of their product.