Ars conjectandi, opus posthumum : Accedit tractatus de seriebus infinitis, et epistola gallicè scripta de ludo pilae reticularis
Jacobi Bernoulli(1654-1705)
 Jacob or Jacques Bernoulli was the oldest and most distinguished member of a famous family which made great contributions to mathematics and physics in the seventeenth and eighteenth centuries. He was both a Cartesian and Newtonian and did much to further spread the ideas of Newton in Europe. It was in this work that he gave the first proof of Newton’s binomial theorem. He also studied Leibniz’s differential and integral calculus, in which he first used the word ‘integralis’ in a treatise on the isochrone in 1620. However, his greatest achievement was the establishment of the fundamental principles of the calculus of probabilities.
 This book is Bernoulli’s revolutionary contribution to the theory of probability and that the first work to deal entirely with that theory merely referred to in the works of Tartaglia, Pascal, Huygens and Newton. The work consists of four parts. In the first part Bernoulli restated the problems proposed by Huygens with his own annotations. The second part is an exhaustive discussion of combinations and permutations as they apply to probability estimates. The third explains the use of his doctrines in games of chance. The fourth and most important part, unfortunately unfinished, is concerned with the applications of this theory to economic and moral problems—the estimates which laid the basis for the modern practice in all fields where probability is concerned. He proposed the ‘law of large numbers’ which demonstrates that the multiplication of occurrence of the phenomenon improves the estimation of probability of that, a very fundamental principle of the modern probability theory. In this work Bernoulli also introduced a series of fractions, designated by Euler as ‘Bernoulli’s numbers’, and which proved to be of major importance in several areas of calculus. The book was not yet completed upon the author’s death and was edited and published posthumously by his nephew Nicholas.