1714 in science

Mathematics

• March – Roger Cotes publishes Logometrica in the Philosophical Transactions of the Royal Society. He provides the first proof of what is now 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.
• Gottfried Leibniz discusses the harmonic triangle.

  Medicine

• April 14 – Anne, Queen of Great Britain, performs the last touching for the "King's evil".
• 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 are published for the first time as Tabulae anatomicae by Giovanni Maria Lancisi.

  Technology

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

  Events

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

  Births

• January 21 – Anna Morandi, Bolognese anatomist
• January 6 – Percivall Pott, English surgeon
• June 17 – César-François Cassini de Thury, French astronomer
• September 6 – Robert Whytt, Scottish physician
• October 16 – Giovanni Arduino, Italian geologist
• October 25 – James Burnett, Lord Monboddo, Scottish philosopher and evolutionary thinker
• December 19 – John Winthrop, American astronomer
• December 31 – Arima Yoriyuki, Japanese mathematician
• Alexander Wilson, Scottish surgeon, type founder, astronomer, meteorologist and mathematician

  Deaths

• October 5 – Kaibara Ekiken, Japanese philosopher and botanist
• November 1 – John Radcliffe, English physician and benefactor
• November 5 – Bernardino Ramazzini, Italian physician