Abstract
IN a historical note by Karl Pearson in 19241, evidence was presented which shows that Abraham De Moivre (1667–1754) invented the normal curve and the normal probability integral about 1721. The name of Gauss is usually attached to the normal curve, although it is not uncommon to find it more correctly attributed to Laplace. But as Pearson shows, De Moivre ante-dated both Laplace and Gauss in this by many years. “The matter is,” Pearson says, “a very singular one historically. De Moivre published in 1730 his Miscellanea AnalyticaMany copies of this work have attached to them a Supplementum with separate pagination, ending in a table of 14 figure logarithms of factorials from 10! to 900! by differences of 10. But only a very few copies have a second supplement, also with separate pagination (pp. 1–7) and dated Nov. 12, 1733.” The title of the second supplement is “Approximatio ad Summam Terminorum Binomii (a + b)n in Seriem expansi”, and it contains not only the first use of the normal curve, but also the first use of the approximation for large factorials commonly but improperly known as Stirling's. It is also clear that herein occurred the first correct use of the law of large numbers, usually attributed to Jacques Bernoulli (1654–1705) and often called Bernoulli's theorem. Further pertinent comments have also been made by Karl Pearson2.
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References
Biometrika, 16, 402–404; 1924.
Biometrika, 17, 201–210; 1925.
Isis, 8, No. 4, 671–683, October 1926.
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DEMING, W. De Moivre's “Miscellanea Analytica”, and the Origin of the Normal Curve. Nature 132, 713 (1933). https://doi.org/10.1038/132713a0
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DOI: https://doi.org/10.1038/132713a0
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