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Fitting equations to data before Legendre

The following list is based on that provided by Mansfield Merriman and augmented by Leon Harter. See the Nineteenth Century for further details.
  1. [1722] Roger Cotes "�stimatio errorum in mixta mathesi, per variationes partium trianguli plani et sph�rici," Opera miscellanea (appended to Harmonia mensurarum; pp. 1-22. The last paragraph gives a rule for combining observations.

  2. [1749] Leonhard Euler. Pi�ce qui a remporte le prix de l'Academie royale des sciences en 1748, sur les inegalities du mouvement de Saturne et de Jupiter. Paris. p. 123. This is E120.

  3. [1750] Tobie Mayer. "Abhandlung �ber die Umw�lzung des Mondes um seine Axe," Kosmographische Nachrichten u. Sammlungen for 1748, pp. 52-183.

  4. [1754] Abraham G. K�stner. "Om geometriska aberrationer," Svenska Vetensk. Akad. Handl. for 1753, p. 126. German translation in Schwedische Akad. Abhandl. for 1753, p. 131-140. 

  5. [1755] Roger Boscovich SJ utilized the method of least absolute deviations to fit equations. See the De litteraria expeditione per Pontificam ditionem ad dimentiendos duos meridiani gradus, or the French translation by Hugon Voyage astronomique et geographique, dans l'�tat de l'eglise,....

  6. [1756] Thomas Simpson. See "A letter to the Right Honorable George Earl of Macclesfield,  President of the Royal Society, on the Advantage of taking the Mean of a number of Observations, in practical Astronomy," Phil. Trans. Lond. for 1755, Vol. XLIX, Pt. I, pp. 82-93.

  7. [1757] Thomas Simpson "An Attempt to show the advantage arising by taking the mean of a number of observations, in practical astronomy," Miscellaneous Tracts, pp. 64-75.

  8. [1760] Roger Boscovich SJ. "De recentissimis graduum dimensionibus, et figura, ac magnitudine terr� inde derivanda." Philosophia recentior � Benedicto Stay .... (Romae, 3 vols., 8vo), Vol. I, Vol. II, pp. 406-426.

  9. [1760] Johann Heinrich Lambert. Photometria sive de mensura et gradibus luminis...

  10. [1763] James Short. Second paper concerning the parallax of the sun determined from the observations of the late transit of Venus, in which this subject is treated more at length, and the quantity of the parallax more fully ascertained. Phil. Trans. 53, pp. 300-345.

  11. [1765] Johann Heinrich Lambert. "Theorie der Zuverl�ssigkeit der Beobachtungen und Versuche." Beytr�ge zum Gebrauche der Mathematik .... (Berlin, 1765-70, 3 vols., 8vo; second ed., 1792), Vol. I, pp. 424-488. See also the "Anmerkungen und Zus�tze zur practischen Geometrie" in the same volume.
     
  12. [1774] Pierre S. Laplace. "Determiner le milieu que l'on doit prendre entre trois observations donnees d'un meme ph�nom�me," Mem. Acad. Paris, par divers savans [etrangers], Vol. IV, pp. 634-644. This is Part V of "M�moire sur la probabilit� des causes par les �v�nemens."

  13. [1774] Joseph Louis Lagrange. "Memoire sur l'utilit� de la methode de prendre le milieu les resultats de plusieurs observations; dans lequel on examine les avantages de cette methode par le calcul des probabilit�s; & o� l'on r�soud differens probl�mes relatifs � cette matiere," Miscellanea Taurinensia (M�m. Soc. Turin) for 1770-1773, Vol. V, pp. 167-232 of the mathematics part.

  14. [1778] Daniel Bernoulli  "Dijudicatio maxime probabilis plurium observationum discrepantium atque verisimillima inductio inde formanda," Acta Acad. Petrop. for 1777, Pt. I, pp. 3-23 of the memoirs.

  15. [1778] Leonhard Euler. "Observationes in pr�cedentem dissertationem Illustr. Bernoulli," Acta Acad. Petrop. for 1777, Part I, pp. 24-33 of the memoirs.

  16. [1781] Pierre S. Laplace. "Memoire sur les Probabilit�s," Hist. Acad. Paris for 1778, pp. 227-332 of the math. part.

  17. [1785] Jean III Bernoulli. "Milieu." Article.in the Encyclop�die M�thodique (Paris), Vol. II, pp. 404-409. Second edition, 1789, entitled Dictionaire Encycl. des Math�matiques.

  18. [1786] Pierre S. Laplace. "Memoire sur la figure de la terre," M�m. Acad. Sci. Paris 1783, pp. 17-46. In Oeuvres Compl�tes de Laplace Vol. 11, pp. 3-32.

  19. [1788] Leonhard Euler. "Eclaircissemens sur Ie memoire de Mr De La Grange insc�s� dans le Ve volume de M�langes de Turin, concernant la methode de prendre le milieu entre les r�sultats de plusieurs observations, &c.," Nova Acta Acad. Petrop. for 1785, Vol. III, pp. 289-297 of the memoirs.

  20. [1789] Adrien-Marie Legendre. "M�moire sur les Op�rations trigonometriques, dont les r�sultats d�pendent de la figure de la terre," Hist. Acad. Paris for 1787, pp. 352-383 of the memoirs.

  21. [1792] Pierre S. Laplace. "Sur les degr�s mesures des meridiens, et sur les longueurs observ�es du pendule." This refers to the memoir "Sur quelques points du syst�me du monde," Hist. Acad. Sci. Institut de France for 1789, pp. 1-87. See in particular pp.18-43. Also in Oeuvres Compl�tes de Laplace Vol. 11, pp.477-558.

  22. [1799] Pierre S. Laplace. Trait� de M�canique C�leste, Vol. 2. Reprinted as Vol. 2 of Oeuvres Compl�tes de Laplace. See especially pp. 134-165.

  23. [1799] Chr�tien Kramp. "Table premi�re. Int�grales de e-ttdt, depuis une valeur quelconque de t jusqu'� t infinie." and "Table seconde. Logarithmes des integrales  e-ttdt, Analyse des refractions astronomiques et terrestres (Strasbourg), pp. 195-206.

  24. [1804] Jean Trembley. "Observations sur la m�thode de prendre les milieux entre les observations," M�moires Acad. Berlin for 1801, pp. 29-58 of the mathematical part.

  25. [1804] Gaspard de Prony. Recherches physico-math�matiques sur la th�orie des eaux courantes. (Paris)