‎"[LEIBNITZ, GOTTFRIED WILHELM].‎
‎Epistola ad Christ. Wolfium circa scientiam infiniti. - [LEIBNIZ INTRODUCES THE PROBABILISTIC ARGUMENT]‎

‎Leipzig, Grosse & Gleditsch, 1713. 4to. Contemporary full vellum. Faint handwritten title on spine. Two small stamps to title page and pasted library label to pasted down front free end-paper. In: ""Actrum Eruditorum, Supplementa. Tomus V"". As usual with various browning to leaves and plates. Pp 264-70 + 1 engraved plate. [Entire volume: (2), 541,(27) pp. + 4 engraved plates].‎

Reference : 44014

‎First printing of Leibniz exceedingly important letter to Christian Wolff in which he introduced the ""probabilistic argument"", that influenced Johann and Daniel Bernoulli. Leibniz corresponded with several other mathematicians about divergent series, the present letter being the most important and having the longest lasting impact. Leibniz had been asked if he thought whether or not a sum existed for Grandi series. ""He reasoned that the sum of n terms of this series would either be 1 or 0 depending on whether n is odd or even, so that the values 0 and 1 occur with equal frequency"" therefore, according to the laws of probability, the most probable sum should be the arithmetic mean ."" (Tucciarone. The Development of the Theory of Summable Divergent Series. P. 1). The letter was rediscovered in 1880 by German mathematician Georg Frobenius in his paper ""Ueber die Leibnitzsche Reihe"" (On Leibniz's series). Frobenius' short paper, begins by quoting from Leibniz's treatment of 1 - 1 + 1 - 1 + ... He states that Leibniz was actually stating a generalization of Abel's Theorem. The result, now known as Frobenius' theorem, and the paper is today regarded as being the first article in the modern history of divergent series.‎