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.

### 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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