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By Todhunter, I. (Isaac)

ISBN-10: 1178318060

ISBN-13: 9781178318067

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Extra info for A History of the mathematical theory of probability from the time of Pascal to that of Laplace

Sample text

The chapter closes with an extract from the Arithmetic of Buckley and an explanation of it; to this we have already referred in Art. 38. 49. rder, in any Nwmber oj things proposed. Here he gives some examples of what are now usually called permutations; . thus if there are four letters a, b, c, d, the numbel' of permutations when they are taken all together is 4 x 3 x 2 x 1. Wallis accordingly exhibits the 24 permutations of these four letters. He forms the product of the first twenty-four natural numbers, which is the numbel' of· the permutations of twenty-four things taken all together.

In his tenth proposition he investigates in how many throws a player may undertake to throw a six with a single die. In his eleventh proposition he investigates in how many throws a player may undertake to throw twelve with a pair of dice. In his twelfth proposition he investigates how many dice a player must have in order to undertake that in one throw tlVO sixes at least may appear. The thirteenth proposition consists of the following problem. A and B. They aie shewn to be as 13 is to 11. BUYGEN8.

Numhers of the first order; he caJls the numbers 1. 2. 3, 4, ••• which form the second row, numbers of the second order; and so on. The numbers of the third order 1, 3, 6. 10,... dy received the name of triangular numbers; and the numbers of the fourth order 1, 4, 10. 20, ... the name of pyramidal numbers. Pascal says that the numbers of the :fifth order 1. 5, 15, 35, ... had not yet received an express name, and he proposes to call them triangulo- triangulairea. b order is n(1&+I) ... nd that immediately to the left of it.

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A History of the mathematical theory of probability from the time of Pascal to that of Laplace by Todhunter, I. (Isaac)

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