A History of the Mathematical Theory of Probability from the Time of Pascal to That of Laplace
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1865 edition. Excerpt: ...they were approximately correct. rn+l Moreover the error arising in taking I sdx and S to be equal in J n value becomes very small if we suppose S to be, not the value of s when x = n or n + 1 but, the intermediate value when x = n +; and nothing in Daniel Bernoulli's investigation forbids this supposition. 517. We have put the objection in the preceding Article as D'Alembert ought to have put it in fairness. He himself however really assumes n--0, so that his attack does not strictly fall on the whole of Daniel Bernoulli's table but on its first line; see Art. 403. This does not affect the principle on which D'Alembert's objection rests, but taken in conjunction with the remarks in the preceding Article, it will be found to diminish the practical value of the objection considerably. See D'Alembert's pages 312--314. 518. Another objection which D'Alembert takes is also sound; see his page 315. It amounts to saying that instead of using the Differential Calculus Daniel Bernoulli ought to have used the Calculus of Finite Differences. We have seen in Art. 417 that Daniel Bernoulli proposed to solve various problems in the Theory of Probability by the use of the Differential Calculus. The reply to be made to D'Alembert's objection is that Daniel Bernoulli's investigation accomplishes what was proposed, namely an approximate solution of the problem; we shall however see hereafter in examining a memoir by Trembley that, assuming the hypotheses of Daniel Bernoulli, a solution by common algebra might be effected. 519. D'Alembert thinks that Daniel Bernoulli might have solved the problem more simply and not less accurately. For Daniel Bernoulli made two assumptions; see Art. 401. D'Alembert says that only one is required; namely to assume some function of...
- Paperback | 176 pages
- 189 x 246 x 10mm | 327g
- 26 Jun 2012
- Miami Fl, United States
- Illustrations, black and white