The first true statement in an analytical form is
Daniel bernoulli (1738): Specimen theoriae novae de mensura sortis.
Commentarii Academiae Scientiarum Imperialis Petropolitanae. Bd. V pp.
175-192. 1730-31 (1738) III.I -St. 22 reprinted in Die Werke von Daniel
Bernoulli. Bd. 2 , Analysis, Wahrscheinlichkeitsrechnung, D. Speiser
(ed.), Basel : Birkhäuser, 1982.

English translation as "Exposition of a New Theory on the Measurement of
Risk" Econometrica, Vol. 22, No. 1. (Jan., 1954), pp. 23-36.

http://www.econ.ucsb.edu/~tedb/Courses/GraduateTheoryUCSB/Bernoulli.pdf

(This is the so-called St. Petersburg paradox).

Its first use, to my knowledge, in economic theory is in Hermann Heinrich
Gossen: Entwick(e)lung der Gesetze des menschlichen Verkehrs, und der
daraus fliessenden Regeln für menschliches Handeln. Braunschweig,
1854. [published by the author]. There is a so-called 3rd edition with a
foreword by F.A. Hayek [Berlin: R.L. Prager 1927].

English translation by Rudolph Blitz, with a brilliant introductory essay
by Nicholas Georgescu-Roegen: Laws of human relations and the rule of
human action derived therefrom, MIT Press, 1983.

Nicholas Theocarakis