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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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. 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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. 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Section 1 is devoted to the treatment of direct observations. <Emphasis Type="SmallCaps">Euler</Emphasis>'s commentaries on memoris of <Emphasis Type="SmallCaps">La Grange</Emphasis> and <Emphasis Type="SmallCaps">D. Bernoulli</Emphasis> are expounded, and, in particular, one of <Emphasis Type="SmallCaps">Euler</Emphasis>'s remarks is related heuristically to the method of least squares.</Para><Para>Section 2 is devoted to the treatment of indirect observations. <Emphasis Type="SmallCaps">Euler</Emphasis>'s use of several methods of calculation which preceded the method of least squares is described.</Para><Para>A special section, the third one, is devoted to a short description of <Emphasis Type="SmallCaps">Euler</Emphasis>'s work in demographical statistics. The question why <Emphasis Type="SmallCaps">Euler</Emphasis>'s achievements in the theory of probability were insignificant is raised.</Para><Para>Being an outstanding astronomer, <Emphasis Type="SmallCaps">Euler</Emphasis> 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.</Para></Abstract><ArticleNote Type="CommunicatedBy"><SimplePara><Emphasis Type="Italic">Communicated by</Emphasis><Emphasis Type="SmallCaps">A. Youschkevitsch</Emphasis></SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>On the mathematical treatment of observations by L. 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Naehr. und Samml</title><imprint><biblScope unit="volume">1748</biblScope><biblScope unit="page" from="52" to="83"></biblScope><date type="published" when="1750"></date></imprint></monogr></biblStruct><biblStruct xml:id="b1"><analytic><title level="a" type="main">Methode tier kleinsten Quadrate in moderner Darstellung. Berlin, t961. See § 14.5. (Originally published in Russian in t958.) 3~ EULER, L., Eldments de la trigonomdtrie sphdroidique tir~s de la mdthode des plus grands et plus petits</title><author><persName><forename type="first">Cauci-Iy</forename></persName></author><author><persName><forename type="first">A</forename><forename type="middle">L</forename></persName></author></analytic><monogr><title level="j">J. W</title><imprint><biblScope unit="volume">12</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="36" to="46"></biblScope><date type="published" when="1755"></date></imprint></monogr><note>Mdmoire. sur l'dvaluation d'inconnues, determindes par un grand hombre d'dquations, t863. Oeuvres completes. 3s. LINNII¢. ENESTR6M. 2t5). Opera omnia set. 1, t. 27. Turici, 1954</note></biblStruct><biblStruct xml:id="b2"><monogr><title></title><author><persName><forename type="first">Maire</forename></persName></author><author><persName><forename type="first">[</forename><forename type="middle">C ]</forename><surname>Boscovich</surname></persName></author><imprint><biblScope unit="page">305</biblScope></imprint></monogr></biblStruct><biblStruct xml:id="b3"><monogr><title level="m" type="main">See § § 483 and 545-546 of voL 1. 4o GNEDENKO, B . W . , tYber die Arbeiten L. 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The quotation is from p. 196</note></biblStruct><biblStruct xml:id="b4"><analytic><title level="a" type="main">Euler' s Verdienste um das Versicherungswesen</title><author><persName><forename type="first">Do</forename><surname>Pasquier</surname></persName></author><author><persName><forename type="first">L</forename><forename type="middle">G</forename></persName></author><author><persName><forename type="first">L</forename></persName></author></analytic><monogr><title level="j">Vierteljahresschr . Natur/orsch. Ges. 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Mathematiker-Vereinigung Bd</title><imprint><biblScope unit="volume">25</biblScope><biblScope unit="issue">79</biblScope><biblScope unit="page" from="251" to="264"></biblScope><date type="published" when="1916"></date></imprint></monogr></biblStruct><biblStruct xml:id="b6"><analytic><title level="a" type="main">Recueil des articles et matdriaux en commdmoration du 150-anniversaire du jour de sa mort</title><author><persName><forename type="first">Pajevsky</forename></persName></author><author><persName><forename type="first">V</forename><forename type="middle">V</forename></persName></author><author><persName><forename type="first">Les</forename><surname>Travaux Ddmographiques De</surname></persName></author><author><persName><forename type="first">L</forename><surname>Euler</surname></persName></author></analytic><monogr><title level="j">Moscou-Leningrad</title><imprint><biblScope unit="page" from="103" to="10"></biblScope><date type="published" when="1935"></date></imprint></monogr><note>(. 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