PDF⋙ History of the Mathematical Theory of Probability by I. Todhunter
History of the Mathematical Theory of Probability by I. Todhunter
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Excerpt from A History of the Mathematical Theory of ProbabilityDe Moivre's Doctrine of Chances formed a treatise on the subject, full, clear and accurate; and it maintained its place as a standard work, at least in England, almost down to our own day.
The tenth Chapter gives an account of some miscellaneous investigations between the years 1700 and 1750. These investigations are due to Nicolas Bernoulli, Arbuthnot, Browne, Mairan, Nicole, Buffon, Ham, Thomas Simpson and John Bernoulli.
The eleventh Chapter relates to Daniel Bernoulli, containing an account of a series of memoirs published chiefly in the volumes of the Academy of Petersburg; the memoirs are remarkable for boldness and originality, the first of them contains the celebrated theory of Moral Expectation.
The twelfth Chapter relates to Euler; it gives an account of his memoirs, which relate principally to certain games of chance.
The thirteenth Chapter relates to D'Alembert; it gives a full account of the objections which ho urged against some of the fundamental principles of the subject, and of his controversy with Daniel Bernoulli on the mathematical investigation of the gain to human life which would arise from the extirpation of one of the most fatal diseases to which the human race is liable.
The fourteenth Chapter relates to Bayes; it explains the method by which he demonstrated his famous theorem, which may be said to have been the origin of that part of the subject which relates to the probabilities of causes as inferred from observed effects.
The fifteenth Chapter is devoted to Lagrange; he contributed to the subject a valuable memoir on the theory of the errors of observations, and demonstrations of the results enunciated by De Moivre respecting the Duration of Play.
The sixteenth Chapter contains notices of miscellaneous investigations between the years 1750 and 1780. This Chapter brings before us Kaostner, Clark, Mallet, John Bernoulli…
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