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1725 was a common year starting on Monday of the Gregorian calendar and a common year starting on Friday of the Julian calendar, the 1725th year of the Common Era (CE) and Anno Domini (AD) designations, the 725th year of the 2nd millennium, the 25th year of the 18th century, and the 6th year of the 1720s decade. As of the start of 1725, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.
- The Terengganu Sultanate is established at Terengganu Darul Iman (now known as Terengganu Darul Iman, Malaysia).
- February 8 – Catherine I becomes Empress of Russia, on the death of her husband, Peter the Great.
- February 20 – The first reported case of white men scalping Native Americans takes place in New Hampshire colony.
- March 2 – In London, a night watchman finds a severed head by the Thames; it is later recognized to be that of the husband of Catherine Hayes. She and an accomplice are later executed.
- March 30 – The second performance of Johann Sebastian Bach's St John Passion, BWV 245 (including 5 movements from his Weimarer Passion), takes place at St. Thomas Church, Leipzig.
- April 30 – Emperor Charles VI of Austria and King Philip V of Spain sign the Treaty of Vienna.
- May 12 – The Black Watch is raised as a military company, as part of the pacification of the Scottish Highlands under General George Wade.
- May 21 – The Order of Alexander Nevsky is instituted in Russia by Empress Catherine I.
- May 24 – Jonathan Wild, fraudulent Thief-Taker General, is hanged at Tyburn in London, for actually aiding criminals.
- June 24 – The Grand Lodge of Ireland in Dublin holds its first recorded meeting, making it the second most senior Grand Lodge in world Freemasonry, and the oldest in continuous existence.
- January 25 – Antoine Court de Gébelin, French pastor (d. 1784)
- February 4 – Dru Drury, English entomologist (d. 1804)
- February 5 – James Otis, American lawyer, patriot (d. 1783)
- February 15 – Abraham Clark, American signer of the Declaration of Independence (d. 1794)
- February 25 – Karl Wilhelm Ramler, German poet (d. 1798)
- February 26 – Nicolas-Joseph Cugnot, French steam vehicle pioneer (d. 1804)
- March 6 – Henry Benedict Stuart, Italian-born cardinal, Jacobite claimant to the British throne (d. 1807)
- March 17 – Lachlan McIntosh, Scottish-born American military and political leader (d. 1806)
- March 20 – Abd-al-Hamid I, Ottoman Sultan (d. 1789)
- March 24
- March 28 – Andrew Kippis, English non-conformist clergyman, biographer (d. 1795)
- April 2 – Giacomo Casanova, Italian adventurer, writer (d. 1798)
- April 6 – Pasquale Paoli, Corsican patriot, military leader (d. 1807)
- April 23 – Gerard Majella, Italian Catholic lay brother and saint (d. 1755)
- April 25 – Augustus Keppel, 1st Viscount Keppel, British admiral (d. 1786)
- May 12 – Louis Philip I, Duke of Orléans, French soldier, writer (d. 1785)
- May 25 – Samuel Ward, American politician (d. 1776)
- June 29 – Maria Teresa Cybo-Malaspina, Duchess of Massa, Italian aristocrat (d. 1790)
- July 1
- July 24 – John Newton, English cleric and hymnist (d. 1807)
- August 21 – Jean-Baptiste Greuze, French painter (d. 1805)
- August 29 – Charles Townshend, English politician (d. 1767)
- September 5 – Jean-Étienne Montucla, French mathematician (d. 1799)
- September 12 – Guillaume Le Gentil, French astronomer (d. 1792)
- September 16 – Nicolas Desmarest, French geologist (d. 1815)
- September 24 – Arthur Guinness, Irish brewer (d. 1803)
- September 29 – Robert Clive, British general, statesman (d. 1774)
- October 12 – Etienne Louis Geoffroy, French pharmacist, entomologist (d. 1810)
- October 21 – Franz Moritz Graf von Lacy, Austrian field marshal (d. 1801)
- December 11 – George Mason, American founding father (d. 1792)
- December 18 – Johann Salomo Semler, German historian, Bible commentator (d. 1791)
- date unknown – Magdalena Dávalos y Maldonado, Ecuadorian scholar, socialite (d. 1806)
- May 24 – Jonathan Wild, English criminal (b. 1682)
- May 31 – Erik Carlsson Sjöblad, Swedish governor, admiral, and baron (b. 1647)
- June 29
- July 11 – Salomon Franck, German lawyer, scientist, poet (b. 1659)
- September 16 – Antoine V de Gramont, French military leader (b. 1672)
- October 10
- October 11 – Hans Herr, Swiss-born Mennonite bishop (b. 1639)
- October 16 – Ralph Thoresby, British historian (b. 1658)
- October 24 – Alessandro Scarlatti, Italian composer (b. 1660)
- November 20 – William, Landgrave of Hesse-Rotenburg (from 1683) (b. 1648)
- December 7 – Florent Carton Dancourt, French dramatist, actor (b. 1661)
- December 10 – Nicolaas Hartsoeker, Dutch mathematician and physicist (b. 1656)
- date unknown