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|( 1780s: ) 1784|
- January 6 – Treaty of Constantinople: The Ottoman Empire agrees to Russia's annexation of the Crimea.
- January 14 – The Congress of the United States ratifies the Treaty of Paris with Great Britain to end the American Revolutionary War, with the signature of President of Congress Thomas Mifflin.*
- February 28 – John Wesley ordains ministers for the Methodist Church in the United States.
- May 20 – A treaty is signed in Paris between the Kingdom of Great Britain and the Dutch Republic, formally ending the Fourth Anglo-Dutch War.
- July 9 – The Bank of New York opens as the first in New York state and continues to operate under that name for almost 223 years until being acquired by Mellon Financial and becoming BNY Mellon.
- July 29 – The United States and the Kingdom of France sign a convention for establishing diplomatic relations and "determining the functions and prerogatives of their respective consuls, vice consuls, agents, and commissaries".
- August 13 – The East India Company Act, sponsored by British Prime Minister William Pitt is given royal assent.
- August 15 – Cardinal de Rohan is called before the French court to account for his actions, in the Affair of the Diamond Necklace.
- August 16 – Britain creates the colony of New Brunswick.
- September 22 – Russia establishes a colony at Kodiak, Alaska.
- October 31–December 14 – The Revolt of Horea, Cloșca and Crișan in Transylvania causes Joseph II, Holy Roman Emperor to suspend the Hungarian Constitution.
- November 26 – The Roman Catholic Apostolic Prefecture of the United States is established.
- November 30 – Richard Henry Lee of Virginia is selected as the new President of the Confederation Congress.
- December – Immanuel Kant's essay "Answering the Question: What Is Enlightenment?" is published.
- December 25 – The Methodist Episcopal Church in the United States is officially formed at the "Christmas Conference", led by Thomas Coke and Francis Asbury.
- The India Act requires that the governor general be chosen from outside the British East India Company, and makes company directors subject to parliamentary supervision.
- Britain receives its first bales of imported American cotton.
- King Carlos III of the Spanish Empire authorizes land grants in Alta California.
- Princess Yekaterina Vorontsova-Dashkova is named first president of the newly created Russian Academy.
- The Japanese famine continues as 300,000 die of starvation.
- Antoine Lavoisier pioneers quantitative chemistry.
- Cholesterol is isolated.
- January 28 – George Hamilton-Gordon, 4th Earl of Aberdeen, Prime Minister of the United Kingdom (d. 1860)
- February 5 – Nancy Hanks, mother of Abraham Lincoln (d. 1818)
- February 29 – Leo von Klenze, German neoclassicist architect, painter and writer (d. 1864)
- March 12 – William Buckland, English geologist, paleontologist (d. 1856)
- March 22 – Samuel Hunter Christie, English physicist, mathematician (d. 1865)
- March 23 – Tom Molineaux, African-American boxer (d. 1818)
- March 27 – Jonathan Jennings, American politician and the first governor of Indiana (d. 1834)
- April 5 – Louis Spohr, German violinist, composer (d. 1859)
- April 13 – Friedrich Graf von Wrangel, Prussian field marshal (d. 1877)
- April 24 – Peter Vivian Daniel, Associate Justice of the Supreme Court of the United States (d. 1860)
- June 24 – Juan Antonio Lavalleja, Uruguayan military, political figure (d. 1853)
- July 21 – Charles Baudin, French admiral (d. 1854)
- July 22 – Friedrich Bessel, German mathematician, astronomer (d. 1846)
- July 27 – Denis Davydov, Russian general, poet (d. 1839)
- August 18 – Robert Taylor, British Radical writer, freethought advocate (d. 1844)
- September 4 – William Pope Duval, first civilian governor of the Florida Territory (d. 1854)
- October 13 – King Ferdinand VII of Spain (d. 1833)
- October 15 – Thomas Robert Bugeaud, Marshal of France and duke of Isly (d. 1849)
- October 19
- October 20 – Henry Temple, 3rd Viscount Palmerston, Prime Minister of the United Kingdom (d. 1865)
- October – Sarah Biffen, armless English painter (d. 1850)
- November 24 – Zachary Taylor, 12th President of the United States (d. 1850)
- November 27 – August, Prince of Hohenlohe-Öhringen (d. 1853)
- February 4 – Princess Friederike Luise of Prussia, Prussian princess (b. 1714)
- February 27 – Count of St. Germain, French philosopher, adventurer (b. 1710)
- March 26 – Thomas Bond, American physician and surgeon (b. 1712)
- March 27 – Ralph Bigland, British officer of arms (b. 1712)
- March 31 – Thomas Adam, Clergyman, religious writer (b. 1701)
- April 26 – Nano Nagle, Irish convent founder (b. 1718)
- April 29 – Agustín de Jáuregui, Spanish colonial governor (b. 1711)
- May 3 – Anthony Benezet, French-born American abolitionist and educator (b. 1713)
- May 10 – Antoine Court de Gébelin, French pastor (b. 1725)
- May 12 – Abraham Trembley, Swiss naturalist (b. 1710)
- June 8 – Lukrecija Bogašinović Budmani, Croatian poet (b. 1710)
- June 13 – Henry Middleton, American president of the Continental Congress (b. 1717)
- June 14 – Andrzej Mokronowski, Polish general (b. 1713)
- June 26 – Caesar Rodney, American lawyer, signer of the United States Declaration of Independence (b. 1728)
- July 1 – Wilhelm Friedemann Bach, German composer (b. 1710)
- July 31 – Denis Diderot, French philosopher, encyclopedist (b. 1713)
- August 4 – Giovanni Battista Martini, Italian musician (b. 1706)
- August 10 – Allan Ramsay, Scottish portrait-painter (b. 1713)
- August 14 – Nathaniel Hone, Irish-born painter (b. 1718)
- August 28 – Junípero Serra, Spanish Franciscan missionary (b. 1713)
- September 1 – Jean-François Séguier, French astronomer and botanist (b. 1703)
- September 4 – César-François Cassini de Thury, French astronomer (b. 1714)
- September 8 – Ann Lee, American religious leader (b. 1736)
- September 15 – Nicolas Bernard Lépicié, French painter (b. 1735)
- November 1 – Jean-Jacques Lefranc, Marquis de Pompignan, French polymath, author and poet (b. 1709)
- November 9 – George Baylor, officer in the American Continental Army (b. 1752)
- December 5 – Phillis Wheatley, first published African-American author (b. 1753)
- December 13 – Samuel Johnson, English writer, lexicographer (b. 1709)
- December 25 – Yosa Buson, Japanese poet, painter (b. 1716)
- December 26 – Seth Warner, American revolutionary leader (b. 1743)
- date unknown – Lê Quý Đôn, Vietnamese philosopher, poet, encyclopedist, and government official (b. 1726)
- date unknown – Raja Haji Fisabilillah, Buginese monarch of riau lingga, warrior, emperor, and government official
|Title||Born||Place of birth||Died||Summary||Description|
|George Hamilton-Gordon||28 January 1784||Scotland|
|14 December 1860||Politician||UK PM|
|Henry John Temple||20 October 1784||Westminster|
|18 October 1865||Politician||A British politician who served twice as Prime Minister in the mid-19th century.|
|Zachary Taylor||24 November 1784||Virginia|
|9 July 1850||Soldier|
|President of the United States. Poisoned.|