Algebra: An Elementary Text Book for the Higher Classes of Secondary Schools and for Colleges, Part 2

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A. and C. Black, 1889 - Algebra
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Page 33 - There are n points in a plane, no three of which are in the same straight line, with the exception of p, which are all in the same straight line ; find the number of lines which result from joining them.
Page 575 - MORGAN -AN ESSAY ON PROBABILITIES, And on their Application to Life Contingencies and Insurance Offices.
Page 538 - If on taking any very large number N out of a series of cases in which an event A is in question, A happens on pN occasions, the probability of the event A is said to be p.
Page 71 - The limit can be found by dividing numerator and denominator by the highest power of x that occurs in either.
Page vii - Every mathematical book that is worth reading must be read "backwards and forwards," if I may use the expression. I would modify Lagrange's advice a little and say, "Go on, but often return to strengthen your faith." When you come on a hard or dreary passage, pass it over; and come back to it after you have seen its importance or found the need for it further on.
Page 48 - ... power of their arithmetical mean, according as m does not or does lie between 0 and 1.
Page 563 - A and B each take twelve counters and play with three dice on this condition, that if eleven is thrown, A gives a counter to B, and if fourteen is thrown, B gives a counter to A; and he wins the game who first obtains all the counters. Show that A's chance is to B's as 244 14o625 is to 282429536481.
Page 12 - A man has 7 relatives, 4 of them are ladies and 3 gentlemen, his wife has 7 relatives and 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man's relatives and 3 of wife's relatives ? Solution.
Page 94 - ... is the tangent of the inclination to the axis of x of the...
Page 506 - If the equation rj? + y3 = ?i had an integral solution, show that one of the three x, y, z must be of the form 7m, and one of the form 3m. (36.) The area of a right-angled triangle with commensurable sides cannot be a square number. (37.) The sum of two integral fourth powers cannot be an integral square.

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