Todhunter, I. (Isaac)'s A History of the mathematical theory of probability from the PDF

By Todhunter, I. (Isaac)

ISBN-10: 1178318060

ISBN-13: 9781178318067

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

Example text

Cerning Divi80rs and Aliquot Parts. It contains solutions of two problems which Fermat had proposed as a challenge to Wallis and the English mathematicians. The problems relate to what is now called. the Theory of Numbers. 3-2 36 PRESTET. 62. llis in any manner that materially bears upon our subject. ; and the Theory of Numbers more cultivated than the Theory of Probability. The judgment of Montmort seems correct that nothing of any importance in the Theory of Combinations previous to his own work had been added to the results of Pascal.

Time, con4natio, and so on. (2) The mathematical treatment of the subject of combinations is far inferior to that given by Pascal; probably Leibnitz had not seen the work. of Pascal. Leibnitz seems to intimate that his predecessors had confined themselves to the combinations of things two at a time, and that he. had himself extended the subject so far as to shew how to obtain n'Om his table the combinations of things taken together more than two at a time; generaJiorem modum 'I'W8 detea:imUB, specialis est vulgatus.

We have thus 2 + 3 + 6 elections. LSIBNITZ. t 11 elections can. be made. In his following sections Schooten proceeds to apply these results to questions relating to the number of divisors in a number. Thus, for example, supposing a. b, c, d, to be different prime factors~ numbers of the following forms all have 16 divisors, abed. aBbe, a81J8, a'b, alii. Hence the question may be asked, what is the least number which has 16 divisors 1 Th~s question must be answered by trial; we must take the smallest prime numbers 2, 8, ...

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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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