By Todhunter, I. (Isaac)
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Extra info for A History of the mathematical theory of probability from the time of Pascal to that of Laplace
With respect to Sir William Petty, to whom MontucIa refers, we may remark that his writings do not seem to have been very important in connenon with our present subject. A rithmetique Politique of the original French Encyclopedie; the article is reproduced in the Encyclopedie Methodique. Gouraud speaks of Petty thus in a note on his page 16, Apr~ Graunt, Ie chevalier W. Petty, daus dift'erauts essais d'economie politique, ou il y avait, il est vrai, plus d'imagination que de jugement, s'6tait, de 1682 a 1687, occupe de semblables recherches.
11 haS been reprinted in facsimile by Friedlander at Berlin in 1861. a. grant 27. At the time when the Theory of Probability started from the hands of Pascal and Fermat, they were the most distinguished mathematicians of Europe. Descartes died in 1650, and Newton and Leibnitz were as yet unknown; Newton was born in 1642, and Leibnitz in 1646. Huygens was born in 1629, and had already given specimens of his powers and tokens of his futUre eminence; but at this epoch he could not have been placed on the level of Pascal and Fermat.
A is entitled to 28 2'"+~ • 8 F . -2- , that IS to 2'" (2'" + ~); so that he may be considered to have recovered his own stake and to have won the fraction ~ of his adversary's stake. In the third example we have M +N= 2'"-1, M-N= 2l:=.! =.! 2A(n-l) In-l)n-l = r Thus we shall find that A may be considered to have recovered his own stake, and to have won the fraction 2~-J. of his adversary's stake. Hence; comparing the second and third examples, we see that if the player who wins the first point also wins the second point, his advantage when he has gained the second point is double what it was when he had gained the first point, whatever may be the number of points in the game.