1738 in science
- Pierre Louis Maupertuis publishes Sur la figure de la terre, which confirms Newton's view that the earth is an oblate spheroid slightly flattened at the poles.
- Publication of Hortus Cliffortianus, a detailed description by Linnaeus of George Clifford's gardens at Hartekamp, Netherlands, including the raising of exotic plants such as bananas in a greenhouse.
- Abraham de Moivre publishes the second English edition of his The Doctrine of Chances containing a study of the coefficients in the binomial expansion of (a + b)n.
- February – Great Plague of 1738, an outbreak of bubonic plague, begins to spread from Banat across central Europe.
- Establishment of The Mineral Water Hospital in Bath, England.
- William Champion of Bristol patents a process to distill zinc from calamine using charcoal in a smelter.
- June 24 – Lewis Paul and John Wyatt obtain a British patent for roller cotton-spinning machinery.
- Jacques de Vaucanson presents the world's first automaton, The Flute Player (1737) to the French Academy of Sciences.
- Black Forest clockmaker Franz Ketterer produces one of the earliest cuckoo clocks.
- June 21 – Charles Townshend, 2nd Viscount Townshend, English agriculturalist (born 1674)
- September 23 – Herman Boerhaave, Dutch physician (born 1668)
- "XVIII Century". Banat's Historical Chronology for the last Millennium. Genealogy RO Group. Retrieved 2011-06-22.