An Elementary Treatise on Algebra, Theoretical and PracticalE.H. Butler & Company, 1857 |
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Common terms and phrases
a²x² arithmetical progression ax² ax³ becomes BINOMIAL THEOREM bx² Clear the equation coefficients completing the square compound interest consequently cube root cubic equation cx² decimals difference Divide dividend division equal EXAMPLES expansion exponent extracting the root factors figure Find a number Find a value find the values Find two numbers gallons geometrical geometrical progression greatest common measure hence imaginary improper fraction infinitum integer last term logarithms method multiplied negative number of solutions number of terms obtained positive preceding PROBLEM proportion proposed equation quadratic QUESTION quotient rational Reduce remainder represent Required the sum required to find result second term simple equation square root substituting subtracting surd third transposing transposition unknown quantity values of x whence whole number
Popular passages
Page 65 - His head weighed as much as his tail and half his body, and his body weighed as much as his head and tail together. What was the weight of the fish ? Let 2x = the weight of the body in pounds.
Page 142 - ... the numerator shows the power to which the quantity is to be raised, and the denominator its root.
Page 82 - ... of the sum of the other three; and it was found that the share of the...
Page 97 - The sum of the first and third of four numbers in geometrical progression is 148, and the sum of the second and fourth is 888.
Page 67 - Ans. 16 and 24. 42. It is required to find a number such, that if it be increased by 7, the square root of the sum shall be equal to the square root of the number itself, and 1 more. Ans. 9.
Page 66 - What part the distance will each have travelled when they meet ? , Ans. One 45 miles, and the other 105. 12. Divide the number 60 into two such parts, that their product may be equal to three times the square of the less ? Ans. The parts are 15 and 45. 13. Divide the number 45 into two parts, such that their product may be equal to the greater minus the square of the less. Ans. The parts are ff and 3ff 6.
Page 141 - The fore-wheel of a carriage makes 6 revolutions more than the hind- wheel in going 120 yards; but 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.
Page 84 - If four quantities are in arithmetical proportion, the sum of the extremes is equal to the sum of the means. Thus...
Page 94 - Prob. 2. What number is that, to which if 1, 5 and 13, be severally added, the first sum shall be to the second, as the second to the third 1 Prob.
Page 136 - It is required to find three numbers in geometrical progression, such that their sum shall be 14, and the sum of their squares 84.