In 1809 Gauss published his monograph " " Theoria motus corporum coelestium in sectionibus conicis solem ambientium " " where among other things he introduces several important statistical concepts, such as the method of least squares, the method of maximum likelihood, and the " normal distribution ".
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Meanwhile, the famous mathematician Carl Friedrich Gauss was entrusted from 1821 to 1825 with the triangulation of the kingdom of Hanover, for which he developed the method of least squares to find the best fit solution for problems of large systems of simultaneous equations given more real-world measurements than unknowns.
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Finally in 1812, Pierre-Simon Laplace published his " Th�orie analytique des probabilit�s " in which he consolidated and laid down many fundamental results in probability and statistics such as the moment generating function, method of least squares, inductive probability, and hypothesis testing, thus completing the final phase in the development of classical probability.
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Upon these follow special methods of induction applicable to quantity : the method of curves, the method of means, the method of least squares and the method of residues, and special methods depending on resemblance ( to which the transition is made through the law of continuity ), such as the method of gradation and the method of natural classification.
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These included attempts at the automation of observations ( appealing to the presumed objectivity of machines ), training observers to try to avoid certain known errors ( such as those caused by lack of sleep ), developing machines that could allow multiple observers to make observations at the same time, the taking of redundant data and using techniques such as the method of least squares to derive possible values from them, and trying to quantify the biases of individual workers so that they could be subtracted from the data.
