J.H. Lambert's work on probability

Abstract

Johann Heinrich Lambert (1728–1777) worked in different spheres of mathematics and its applications, including optics, map projections, and geodesy, and also in astronomy. In the theory of probability proper he is the author of a small article and of a few posthumously published notes, and his work in this sphere seems rather slight, but his philosophical reasonings in regard to probability are very interesting. Lambert published also works on the then most important applications of probability: demographical statistics and the theory of errors. His contribution to demographical statistics, while essentially a commentary on the contributions of D. Bernoulli, nevertheless presents a methodical elaboration of the mathematical foundation of this discipline. As to the theory of errors, Lambert should be credited as the main predecessor of Gauss. This paper is presented in three sections: § 1—theory of probability; § 2—demographical statistics; and § 3—theory of errors. There is no complete edition of Lambert's works [10], and his numerous articles, scattered in various periodicals, are not readily available. For this reason I do not claim to give a complete description, but the main deductions stated above and elaborated in the paper itself seem to be established beyond reasonable doubt.