Analytical Theory of Probability

Japanese: 《確率の解析的理論》 - かくりつのかいせきててきりろん

…Then came the period when the basic content of mathematical theory was formed by P. Laplace of France and CF Gauss of Germany, and a wealth of applications were found. Laplace wrote “The Analytical Theory of Probability” in 1812, in which he analytically discussed probability distribution and limit theorems. Gauss created and developed the least squares method to deal with measurement errors and accurately determine true values in surveying and astronomical observations, but these were from the late 18th century to the 19th century. …

From [Mathematics]

… PS Laplace always held high positions from the end of the monarchy through the revolutionary, Napoleonic and Restoration periods, and was a mathematician who reached the pinnacle of 18th-century analysis, although he lacked political integrity. He left behind the five-volume Celestial Mechanics (1799-1825) and the Analytical Theory of Probability (1812). The former includes potential theory and is a summary of the theory of the solar system based on Newton, Euler and others, while the latter is a large work that includes the theory of the Laplace transform and the theory of generating functions. …

From Laplace

…Laplace’s nebular theory can also be found there. His major works include the five-volume Celestial Mechanics (1799-1825) and the Analytical Theory of Probability (1812). The former describes the new methods of analysis he introduced and develops a new field of solar astronomy on a grand scale. …

*Some of the terminology explanations that refer to "Analytical Theory of Probability" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

…次いで訪れたのは，フランスのP.ラプラスやドイツのC.F.ガウスらによって数学的理論の基礎的内容が形成され豊かな応用が見いだされた時代である。ラプラスは1812年に《確率の解析的理論》を著し確率分布や極限定理などを解析的に論じた。ガウスは測量や天文観測の際，測定誤差を処理して真の値を正確に知るために最小二乗法を創始し発展させたが，これらは18世紀後半から19世紀にかけてであった。…

【数学】より

…　P.S.ラプラスは，王政末期から革命時代，ナポレオン時代，さらに王政復古の時代にかけていつも高い地位にあり，政治的節操には欠けるところがあったが，18世紀解析学の頂点をきわめた数学者である。彼は5巻の《天体力学》(1799‐1825)と《確率の解析的理論》(1812)を残した。前者はポテンシャル論を含み，ニュートン，オイラーらにもとづく太陽系の理論をまとめたもの，後者はラプラス変換論や生成関数論を含む大著である。…