Category: Mathematics
This philosophical essay is the development of a lecture on probabilities which I delivered in 1795 to the normal schools whither I had been called, by a decree of the national convention, as professor of mathematics with Lagrange. I have recently published upon the same subje...
This philosophical essay is the development of a lecture on probabilities which I delivered in 1795 to the normal schools whither I had been called, by a decree of the national...
9. CHAPTER II.All events, even those which on account of their insignificance do not seem to follow the great laws of nature, are a result of it just as necessarily as the revolutions of the...
10. CHAPTER III._First Principle._—The first of these principles is the definition itself of probability, which, as has been seen, is the ratio of the number of favorable cases to that of all t...
11. CHAPTER IV.The probability of events serves to determine the hope or the fear of persons interested in their existence. The word _hope_ has various acceptations; it expresses generally the...
12. CHAPTER V.The application of the principle which we have just expounded to the various questions of probability requires methods whose investigation has given birth to several methods of...
13. CHAPTER VI.The combinations which games present were the object of the first investigations of probabilities. In an infinite variety of these combinations many of them lend themselves read...
14. CHAPTER VII.Inequalities of this kind have upon the results of the calculation of probabilities a sensible influence which deserves particular attention. Let us take the game of heads and t...
15. CHAPTER VIII.Amid the variable and unknown causes which we comprehend under the name of _chance_, and which render uncertain and irregular the march of events, we see appearing, in the measu...
16. CHAPTER IX.The phenomena of nature are most often enveloped by so many strange circumstances, and so great a number of disturbing causes mix their influence, that it is very difficult to r...
17. CHAPTER X.We have just seen the advantages of the analysis of probabilities in the investigation of the laws of natural phenomena whose causes are unknown or so complicated that their res...
18. CHAPTER XI.The majority of our opinions being founded on the probability of proofs it is indeed important to submit it to calculus. Things it is true often become impossible by the difficu...
19. CHAPTER XII.The probability of the decisions of an assembly depends upon the plurality of votes, the intelligence and the impartiality of the members who compose it. So many passions and pa...
20. CHAPTER XIII.Analysis confirms what simple common sense teaches us, namely, the correctness of judgments is as much more probable as the judges are more numerous and more enlightened. It is...
21. CHAPTER XIV.The manner of preparing tables of mortality is very simple. One takes in the civil registers a great number of individuals whose birth and death are indicated. One determines ho...
22. CHAPTER XV.Let us recall here what has been said in speaking of hope. It has been seen that in order to obtain the advantage which results from several simple events, of which the ones pro...
23. CHAPTER XVI.The mind has its illusions as the sense of sight; and in the same manner that the sense of feeling corrects the latter, reflection and calculation correct the former. Probabilit...
24. CHAPTER XVII.Induction, analogy, hypotheses founded upon facts and rectified continually by new observations, a happy tact given by nature and strengthened by numerous comparisons of its ind...
25. CHAPTER XVIII.Long ago were determined, in the simplest games, the ratios of the chances which are favorable or unfavorable to the players; the stakes and the bets were regulated according to...