1714 in science

• March – Roger Cotes publishes Logometrica in the Philosophical Transactions of the Royal Society. He provides the first proof of what becomes known as Euler's formula and constructs the logarithmic spiral.
• May – Brook Taylor publishes a paper, written in 1708, in the Philosophical Transactions of the Royal Society which describes his solution to the center of oscillation problem.Vol. 28: p. 40.
• Gottfried Leibniz discusses the harmonic triangle.{{cite book|first=Tony|last=Crilly|title=50 Mathematical Ideas you really need to know|location=London|publisher=Quercus|year=2007|isbn=978-1-84724-008-8|page=53}}

• April 14 – Anne, Queen of Great Britain, performs the last touching for the "King's evil".{{cite journal|last=Werrett|first=Simon|title=Healing the Nation's Wounds: Royal Ritual and Experimental Philosophy in Restoration England|journal=History of Science|volume=38|year=2000|pages=377–99|bibcode=2000HisSc..38..377W}}
• Dominique Anel uses the first fine-pointed syringe in surgery, later known as "Anel's syringe".
• Herman Boerhaave introduces a modern system of clinical teaching at the University of Leiden.
• The anatomical engravings of Bartolomeo Eustachi (died 1574) are published for the first time as Tabulae anatomicae by Giovanni Maria Lancisi.{{cite book|first1=B. G.|last1=Firkin|first2=J. A.|last2=Whitworth|title=Dictionary of Medical Eponyms|edition=2nd|page=225|location=New York|publisher=Parthenon Publishing Group|year=1996|isbn=1-85070-477-5}}

• Henry Mill obtains a British patent for a machine resembling a typewriter.

• July – The Parliament of Great Britain offers the Longitude prize to anyone who can solve the problem of accurately determining a ship's longitude.

• January 21 – Anna Morandi, Bolognese anatomist (died 1774){{cite book|first=Rebecca|last=Messbarge|title=The Lady Anatomist: The Life and Work of Anna Morandi Manzolini|location=Chicago|publisher=The University of Chicago Press|year=2019|page=3|isbn=978-0-22652-083-4}}
• January 6 – Percivall Pott, English surgeon (died 1788)
• June 17 – César-François Cassini de Thury, French astronomer (died 1784)
• September 6 – Robert Whytt, Scottish physician (died 1766)
• October 16 – Giovanni Arduino, Italian geologist (died 1795)
• October 25 – James Burnett, Lord Monboddo, Scottish philosopher and evolutionary thinker (died 1799)
• December 19 – John Winthrop, American astronomer (died 1779)
• December 31 – Arima Yoriyuki, Japanese mathematician (died 1783)
• Alexander Wilson, Scottish surgeon, type founder, astronomer, meteorologist and mathematician (died 1786)

• October 5 – Kaibara Ekiken, Japanese philosopher and botanist (born 1630)
• November 1 – John Radcliffe, English physician and benefactor (born 1650)
• November 5 – Bernardino Ramazzini, Italian physician (born 1633)

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Category:18th century in science

Category:1710s in science