On the mathematical treatment of observations by L. Euler
Identifieur interne : 000570 ( Istex/Corpus ); précédent : 000569; suivant : 000571On the mathematical treatment of observations by L. Euler
Auteurs : B. SheyninSource :
- Archive for History of Exact Sciences [ 0003-9519 ] ; 1972-01-01.
Abstract
Abstract: Euler's memoirs pertaining to the mathematical treatment of observations in the theory of errors are described. Section 1 is devoted to the treatment of direct observations. Euler's commentaries on memoris of La Grange and D. Bernoulli are expounded, and, in particular, one of Euler's remarks is related heuristically to the method of least squares. Section 2 is devoted to the treatment of indirect observations. Euler's use of several methods of calculation which preceded the method of least squares is described. A special section, the third one, is devoted to a short description of Euler's work in demographical statistics. The question why Euler's achievements in the theory of probability were insignificant is raised. Being an outstanding astronomer, Euler mainly treated astronomy in regard to general theory, but he also repeatedly took up the mathematical treatment of observations and (as also was the case with map projections) numerical calculations in general. In this paper I shall restrict myself to such calculations as are related to the theory of errors and probability.
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DOI: 10.1007/BF00348539
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<front><div type="abstract" xml:lang="en">Abstract: Euler's memoirs pertaining to the mathematical treatment of observations in the theory of errors are described. Section 1 is devoted to the treatment of direct observations. Euler's commentaries on memoris of La Grange and D. Bernoulli are expounded, and, in particular, one of Euler's remarks is related heuristically to the method of least squares. Section 2 is devoted to the treatment of indirect observations. Euler's use of several methods of calculation which preceded the method of least squares is described. A special section, the third one, is devoted to a short description of Euler's work in demographical statistics. The question why Euler's achievements in the theory of probability were insignificant is raised. Being an outstanding astronomer, Euler mainly treated astronomy in regard to general theory, but he also repeatedly took up the mathematical treatment of observations and (as also was the case with map projections) numerical calculations in general. In this paper I shall restrict myself to such calculations as are related to the theory of errors and probability.</div>
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<abstract lang="en">Abstract: Euler's memoirs pertaining to the mathematical treatment of observations in the theory of errors are described. Section 1 is devoted to the treatment of direct observations. Euler's commentaries on memoris of La Grange and D. Bernoulli are expounded, and, in particular, one of Euler's remarks is related heuristically to the method of least squares. Section 2 is devoted to the treatment of indirect observations. Euler's use of several methods of calculation which preceded the method of least squares is described. A special section, the third one, is devoted to a short description of Euler's work in demographical statistics. The question why Euler's achievements in the theory of probability were insignificant is raised. Being an outstanding astronomer, Euler mainly treated astronomy in regard to general theory, but he also repeatedly took up the mathematical treatment of observations and (as also was the case with map projections) numerical calculations in general. In this paper I shall restrict myself to such calculations as are related to the theory of errors and probability.</abstract>
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