1742 in science
- January 14 – Death of Edmond Halley; James Bradley succeeds him as Astronomer Royal in Great Britain.
- June – Christian Goldbach produces Goldbach's conjecture.
- Colin Maclaurin publishes his Treatise on Fluxions in Great Britain, the first systematic exposition of Newton's methods.
Physiology and medicine
- Surgeon Joseph Hurlock publishes his A Practical Treatise upon Dentition, or The breeding of teeth in children in London, the first treatise in English on dentition.
- Benjamin Robins publishes his New Principles of Gunnery, containing the determination of the force of gun-powder and an investigation of the difference in the resisting power of the air to swift and slow motions in London, containing a description of his ballistic pendulum and the results of his scientific experiments into improvements in ballistics.
- The first large (12 ft focal length) reflecting telescope is made, in Gregorian form, by James Short, for use by Charles Spencer, 3rd Duke of Marlborough, in London.
- March 15 (bapt.) – John Stackhouse, English botanist (died 1819).
- May 18 – Lionel Lukin, English inventor (died 1834).
- December 3 – James Rennell, English geographer, historian and oceanographer (died 1830).
- December 9 – Carl Wilhelm Scheele, Swedish chemist (died 1786).
- December 26 – Ignaz von Born, Hungarian metallurgist (died 1791).
- January 14 – Edmond Halley, English astronomer, geophysicist, mathematician, meteorologist, and physicist (born 1656).
- February 28 – Willem 's Gravesande, Dutch polymath (born 1688).
- May 13 – Nicolas Andry, French physician (born 1658).
- September 22 – Frederic Louis Norden, Danish explorer (born 1708).
- Crilly, Tony (2007). 50 Mathematical Ideas you really need to know. London: Quercus. p. 37. ISBN 978-1-84724-008-8.
- Celsius, Anders (1742). "Observationer om twänne beständiga grader på en thermometer" (Observations about two stable degrees on a thermometer). Kungliga Svenska Vetenskapsakademiens Handlingar (Proceedings of the Royal Swedish Academy of Sciences) 3:171-180 and .
- Jervis-Smith, Frederick John (1911). "Chronograph". In Chisholm, Hugh. Encyclopædia Britannica. 6 (11th ed.). Cambridge University Press. p. 302.
- Routh, Edward John (1905). The Elementary Part of A Treatise on the Dynamics of a System of Rigid Bodies. London: Macmillan.
- Ferguson, Niall (2011). Civilization: The West and the Rest. London: Allen Lane. ISBN 978-1-84614-273-4.
- Museum of the History of Science, Oxford, inventory 98721 (exhibit label noted 2012).