An Elementary Treatise on Algebra, Theoretical and Practical: With Attempts to Simplify Some of the More Difficult Parts of the Science, Particularly the Demonstration of the Binomial Theorem in Its Most General Form, [etc.]
Hogan and Thompson, 1839
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according added addition amount arithmetical assumed becomes binomial called changed chapter Clear coefficients column common completing the square compound consequently consist containing denominator determine difference Divide division divisor equal equation evidently EXAMPLES expansion expression extracting the root factors figure find the values four fourth fraction gallons Given gives greater greatest hence imaginary impossible increased infinite integer interest known last term least less letters logarithms manner means method multiplied negative obtained operation performed positive possible preceding present PROBLEM progression proportion proposed quadratic QUESTION quotient rational Reduce remainder represent Required the sum required to find respectively result rule side similar simple solutions square root substituting subtracting successively Suppose surd taken THEOREM third transposing transposition unknown quantity values of x whence whole
Side 83 - В can perform a piece of work in 8 days, A and С together in 9 days, and В and С together in 10 days ; in how many days can each alone perform the same work ? Let...
Side 116 - The plate of a looking-glass is 18 inches by 12, and it is to be surrounded by a plain frame of uniform width/ having a surface equal to that of the glass.
Side 99 - 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.
Side 99 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?
Side 75 - There is a number consisting of two digits, which is equal to four times the sum of those digits; and if 18 be added to it, the digits will be inverted. What is the number?
Side 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.
Side 52 - An equation of the third, fourth, &c. degree, is one in which the highest power of the unknown quantity is the third, fourth, &c.
Side 114 - It is required to find two numbers, such, that their sum, product, and difference of their squares, shall be all equal.