Samuel Scott
William Hogarth
Giovanni Battista TiepoloFrom WikipediaJanuary–June
- January 26 – Stanislaus I of Poland abdicates his throne.
- February 12 – Francis I, Holy Roman Emperor weds Maria Theresa of Austria, ruler of the Habsburg Empire.
- April 14 – The Porteous Riots erupt in Edinburgh after the execution of smuggler Andrew Wilson, when town guard captain John Porteous orders his men to fire at the crowd. Porteous is arrested later.
- May 8 – Frederick, Prince of Wales marries Augusta of Saxe-Gotha.
- May 26 – Battle of Ackia: British and Chickasaw Native Americans defeat French troops.
- June 8 – Leonhard Euler writes to James Stirling, describing the Euler-Maclaurin summation formula. He also solves the mathematical problem known as the seven bridges of Königsberg.
July–December
- July – Russo-Turkish War, 1735-1739: Russian forces under Peter Lacy storm the Ottoman fortress of Azov.
- September 7 – An Edinburgh crowd drags John Porteous out of his cell in Tolbooth Prison and lynches him.
- December 7 – Ben Franklin builds the first volunteer fire company in Philadelphia, Pennsylvania.
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