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according added addition arithmetical assumed becomes binomial called coefficients column common completing the square compound consequently consist containing denominator determine difference Divide division divisor equal equation evidently EXAMPLES expansion exponent expression extracting the root factors figure find the values four fourth fraction gallons Given gives greater hence increased integral interest known last term least less logarithms manner means method multiplied negative obtained operation performed positive possible preceding PROBLEM progression proportion proposed quadratic quantity QUESTION quotient rational Reduce remainder represented Required the sum required to find respectively result side signs simple solutions square root substituted subtracting successively Suppose surd taken term THEOREM third tion transposition unknown quantity values of x whence whole
Page 74 - If four quantities be in arithmetical •proportion, the sum of the extremes is equal to the sum of the means.
Page 85 - 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 85 - 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?
Page 72 - ... of the sum of the shares of the other three, the share of the second ^ of the sum of the other three, and the share of the third...
Page 39 - MULTIPLY THE QUANTITY INTO ITSELF, TILL IT is TAKEN AS A FACTOR, AS MANY TIMES AS THERE ARE UNITS IN THE INDEX OF THE POWER TO WHICH THE QUANTITY IS TO BE RAISED.
Page 57 - Required his income. dollars. 41. There are two numbers in proportion of 2 to 3, and if 4 be added to each of them, the sums will be in proportion of 5 to 7 ? 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.