Béguelin was a Swiss lawyer and writer. His place of birth is Courtelary, Switzerland, Canton Berne. He studied law and mathematics at the University of Basel (1729) and while there followed the lessons of Johann Bernoulli.
Béguelin was successively attached to the ambassador from Prussia at Dresden, Bavaria; made professor at Joachmstal, a small city northwest of Berlin; and named by Frederick the Great (ruled 1740-86) sous-gouverneur of Prince Frederick William II, himself the nephew and successor to Frederick. This last position carried with it responsibility for the education of the young prince. In 1764 he lost this governorship as a result of court intrigue. Only twenty years later did he return to the good graces of Frederick and receive a pension. When Frederick William II took the throne in 1786 upon the death of Frederick the Great, he named his old master director of the Academy of Berlin, gave him a grant of land and promoted him to nobility.
He published memoirs on jurisprudence, mathematics and philosophy which were published in the records of the Academy of Berlin. In fact, he was a member of the Academy of Sciences at Berlin from 1747 and director of the philosophy section from 1786 to 1789.
Volume 21 for the year 1765 of the Mémoires de l'Académie de Berlin contained four papers regarding sequences in the outcome of drawings of the Genoise Lottery. One paper was by Leonhard Euler, Sur la probabilité des sequences dans la loterie genoise. Another was by Jean Bernoulli, Sur les suites ou séquences dans la loterie de Genes. Béguelin wrote two memoirs which treated the results of Euler and Bernoulli simultaneously. These are the Sur les suites ou séquences dans la lotterie de genes, First Memoir and the Second Memoir.
Volume 23 for the year 1768 of the Mémoires de l'Académie de Berlin contained the remaining memoir by Béguelin. It is Sur l'usage du principe de la raison suffisante dans le calcul des probabilités. This last memoir is curious for several reasons. Béguelin took upon himself the challenge of D'Alembert to put probability on a firm foundation. He offered six solutions to the Petersburg problem.
Primary source: Grand dictionnaire universel du XIXe siècle, français, historique, géographique, mythologique, bibliographique, littéraire, artistique, scientifique, etc. ... Par Pierre Larousse. Paris, Administration du Grand dictionnaire universel, 1866-.