The Theory of Errors and Method of Least Squares PDF ePub eBook

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The Theory of Errors and Method of Least Squares free pdf Excerpt from The Theory of Errors and Method of Least Squares The basis adopted in this book for the theory of accidental errors is that laid down by Gauss in the Theoria Motus Corporum CaUstium (republished as vol. vii of the Werke) which may be described for the most part in his own words, as follows: "The hypothesis is in fact wont to be considered as an axiom that, if any quantity has been determined by several direct observations, made under similar circumstances and with equal care, the arithmetical mean between all the observed values presents the most probable value, if not with absolute rigor, at least very nearly so, so that it is always safest to adhere to it." (Art.177.) Then introducing the notion of a law of facility of error to give precise meaning to the phrase "most probable value," we cannot do better than to adopt that law of facility in accordance with which the arithmetical mean is the most probable value. After deriving this law and showing that it leads to the principle of least squares, he says: "This principle, which in all applications of mathematics to natural philosophy admits of very frequent use, ought everywhere to hold good as an axiom by the same right as that by which the arithmetical mean between several observed values of the same quantity is adopted as the most probable value." (Art. 179) About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully- any imperfections that remain are intentionally left to preserve the state of such historical works.

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Details Book

Author : William Woolsey Johnson
Publisher : Forgotten Books
Data Published : 27 September 2015
ISBN : 1332339131
EAN : 9781332339136
Format Book : PDF, Epub, DOCx, TXT
Number of Pages : 210 pages
Age + : 15 years
Language : English
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