- Bernoulli , Jakob . 1899 . Wahrscheinlichkeitsrechnung 75 – 75 . Leipzig pt 4 Originally in Latin.
- T/Avoth 318. Compare, however, Maimonides's later statement about ‘mathematical astronomy’: ‘our sages confirmed [that it was] the true wisdom in the sight of the people. But the theories of the astrologists are devoid of any value’ Letter to the Jews of Marseilles Letters Stitskin L.D. New York 1977 118 129 in (122)
- Hasofer , A.M. 1967 . Random Mechanisms in Talmudic Literature . Biometrika , 54 : 316 – 321 . enlarged version as ‘Some Aspects of Talmudic Probabilistic Thought’, in Proceedings of the Association of Orthodox Jewish Scientists (irregular edition) (Jerusalem and New York, 1977), ii, 63–80; N. L. Rabinovitch, Probability and Statistical Inference in Ancient and Medieval Jewish Literature (Toronto, 1973).
- 1962 . Encyclopaedia Hebraica Vol. XIV , 920 – 921 . Tel Aviv as quoted by Rabinovitch (note 4), xi. Rabinovitch did not mention, either here or in several other cases, that his sources were in Hebrew.
- Rabinovitch , N.L. 1974 . Early Antecedents of Error Theory . Archive for the History of Exact Sciences , 13 : 348 – 358 . [hereafter AHES]
- Ineichen , Robert . 1996 . Würfel und Wahrscheinlichkeit Heidelberg
- Sheynin , Oscar . 1974 . On the Prehistory of the Theory of Probability . AHES , 12 : 97 – 141 . idem, ‘The Notion of Randomness from Aristotle to Poincaré, Mathématiques, Informatique et Sciences Humaines, 29e année, no. 114 (1991), 41–55.
- Sheynin , Oscar . 1991 . Poincaré's Work on Probability . AHES , 42 : 137 – 171 . (§ 9)
- Poincaré , Henri . 1912 . Calcul des Probabilités , 2nd edn 5 – 5 . Paris The Introduction of 23 pp. lacking in the 1st edn of 1896, was reprinted from an article of the author's written in 1907. A reprint of the 2nd edition: Sceaux (1987).
- Kepler , Johannes . 1952 . “ Epitome of Copernican Astronomy ” . In Great Books of the Western World Vol. 54 , 845 – 1004 . Chicago in XVI (932). The Epitome was originally published in Latin in 1618–21.
- Rabinovitch . 1973 . Probability and Statistical Inference in Ancient and Medieval Jewish Literature 77 – 77 . Toronto with a reference to Milhamot haShem III-4.
- Poincaré . 1912 . Calcul des Probabilités , 2nd edn 1 – 1 . Paris
- For example Uspensky Vladimir Semenov Alexei Algorithms: Main Ideas and Applications Dordrecht 1993 § 2.6
- Poisson , Siméon Dénis . 1837 . Recherches sur la probabilité des jugements 47 – 47 . Paris
- Rabinovitch . 1973 . Probability and Statistical Inference in Ancient and Medieval Jewish Literature 44 – 44 . Toronto refers to Makhshirin 23–11 and Baba Batra 61. In the former, the statement is rather that the majority is equivalent to the whole.
- Ketubot 110 and Makhshirin 29; see also Rabinovitch Probability and Statistical Inference in Ancient and Medieval Jewish Literature Toronto 1973 45 45
- Poisson . 1837 . Recherches sur la probabilité des jugements 140 – 141 . Paris
- Sheynin , Oscar . 1991 . On the Prehistory of the Theory of Probability . AHES , 12 § 7.1
- Moreau Maupertuis , Pierre Louis . 1745 . Venus physique , in his Oeuvres, 4 vols (Lyon, 1756), II, 1–133 (109, 120–1).
- Moreau Maupertuis , Pierre Louis . 1751 . Système de la nature ibid., 135–84 (146)
- Rabinovitch . 1973 . Probability and Statistical Inference in Ancient and Medieval Jewish Literature 74 – 74 . Toronto with reference to Sefer haMitzvot, negative commandment 290. At the same time, however, Maimonides maintained that ‘the events befalling men are the result not of accident, but of God's justice’; see his ‘Letter to the Jews of Marseilles’ (note 2), 124.
- Rabinovitch . 1973 . Probability and Statistical Inference in Ancient and Medieval Jewish Literature 164 – 164 . Toronto with reference to Mishna Torah, Edut XXI-1. Large possible gains were thus preferred even without their being objectively more advantageous. The same subjective feeling exists in our time.
- Sheynin , Oscar . 1977 . Early History of the Theory of Probability . AHES , 17 : 201 – 259 . (206–9)
- de Moivre , Abraham . 1756 . The Doctrine of Chances 329 – 329 . London repr. (New York, 1967); 1st edn (1718).
- Laplace , Pierre Simon . 1995 . Philosophical Essay on Probabilities 9 – 9 . New York originally in French (1814). For earlier examples of this kind, see my paper ‘Newton and the Classical Theory of Probability’, AHES, 7 (1971), 217–43 (229).
- Kepler , Johannes . 1977 . A Thorough Description of an Extraordinary New Star . Vistas in Astronomy , 20 : 333 – 339 . (337); originally in German (1604).
- Also see Rabinovitch Probability and Statistical Inference in Ancient and Medieval Jewish Literature Toronto 1973 87 87 90 and 84 respectively
- Lots are known to have been widespread in antiquity. When carried out in the approved manner, they were thought to reveal knowledge from God; otherwise, the outcome of a lot was regarded as pure chance. See, for example Hasofer Random Mechanisms in Talmudic Literature Biometrika 1977 54 64 64
- T/Taanit 42; see also Rabinovitch Probability and Statistical Inference in Ancient and Medieval Jewish Literature Toronto 1973 355 355
- Celsus , Aulus Cornelius . 1935 . De medicina Vol. 1 , 19 – 19 . London of the English translation
- Rabinovitch . 1973 . Probability and Statistical Inference in Ancient and Medieval Jewish Literature 91 – 91 . Toronto with reference to Responsa
- Horayot 11; see also Rabinovitch Probability and Statistical Inference in Ancient and Medieval Jewish Literature Toronto 1973 38 38
- Rabinovitch . 1973 . Probability and Statistical Inference in Ancient and Medieval Jewish Literature 59 – 59 . Toronto introduced reasonable assumptions and attempted to solve this problem by means of Bayes' theorem, i.e. to choose the more probable (and, at the same time, the likely enough) hypothesis out of the two possible ones. But he was unable to come up with a definite answer.
- Bernoulli . 1899 . Wahrscheinlichkeitsrechnung 75 – 75 . Leipzig pt 4 He followed the teaching of probabilism, which allowed one to base conclusions on any probable opinion of any Father of the Catholic Church. Accordingly, he admitted even such ‘non-additive’ (subjective) probabilities whose sum was larger than unity. Today's epistemic (subjective) probabilities retain this property; see Glenn Shafer, ‘Non-additive Probabilities in the Work of [Jakob] Bernoulli and Lambert’, AHES, 19 (1978), 309–70.
- 1963 . Guide for the Perplexed II – 23 . Chicago see also Rabinovitch (note 4), 138
- Rabinovitch . 1973 . Probability and Statistical Inference in Ancient and Medieval Jewish Literature 41 – 41 . Toronto with reference to Mishna Torah, Forbidden Foods XV.
- Leibniz , Gottfried Wilhelm . 1765 . Neue Abhandlungen über den menschlichen Verstand Vol. 2 , 511 – 511 . Frankfurt/Main 1961
- The German edition of the Talmud Vol. 3 , 707 – 707 .
- Freudenthal , Hans and Steiner , H.-G. 1966 . “ Aus der Geschichte der Wahrscheinlichkeitstheorie und der mathematischen Statistik ” . In Grundzüge der Mathematik Edited by: Behnke , H. Vol. 5 , Göttingen iv, 149–95 (153–4)
- Bernoulli . 1899 . Wahrscheinlichkeitsrechnung 80 – 80 . Leipzig pt 4
- Rabinovitch . 1973 . Probability and Statistical Inference in Ancient and Medieval Jewish Literature 111 – 111 . Toronto with the same reference as in note 23.
- Verschollenheit . 1987 . Jüdisches Lexikon Vol. iv , 1199 – 1199 . Frankfurt/Main 4 vols pt 2
- Makkot 315–16; see also Rabinovitch Probability and Statistical Inference in Ancient and Medieval Jewish Literature Toronto 1973 120 120
- Newton , Isaac . 1960 . Mathematical Principles of Natural Philosophy Edited by: Cajori , Florian . 547 – 547 . Berkeley This is from the 3rd edn (1729).
- Lampel , Zwi L. , ed. 1975 . Introduction to the Talmud 123 – 123 . New York
- Newton . 1960 . Mathematical Principles of Natural Philosophy Edited by: Cajori , Florian . 398 – 398 . Berkeley
- Sheynin , Oscar . 1996 . The History of the Theory of Errors 17 – 18 . Egelsbach (estimation of bounds), 20–1 (treatment of observations).
- Price , D.J. 1955 . Medieval Land Surveying and Topographical Maps . Geographical Journal , 121 : 1 – 10 .
- See Early Antecedents of Error Theory Archive for the History of Exact Sciences 1974 13 348 358 [hereafter AHES]
- Sheynin . 1996 . The History of the Theory of Errors 22 – 23 . Egelsbach 26–7
- Sheynin . 1974 . On the Prehistory of the Theory of Probability . AHES , 12 : 117 – 119 .
- Sheynin . 1974 . On the Prehistory of the Theory of Probability . AHES , 12 : 108 – 108 .
- Sheynin . 1974 . On the Prehistory of the Theory of Probability . AHES , 12 : 112 – 112 . note 68
Annals of Science
Volume 55, 1998 - Issue 2