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1759 (MDCCLIX) was a common year starting on Monday of the Gregorian calendar and a common year starting on Friday of the Julian calendar, the 1759th year of the Common Era (CE) and Anno Domini (AD) designations, the 759th year of the 2nd millennium, the 59th year of the 18th century, and the 10th and last year of the 1750s decade. As of the start of 1759, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923. In Great Britain, this year was known as the Annus Mirabilis, because of British victories in the Seven Years' War.
- January 6 – George Washington marries Martha Dandridge Custis.
- January 11 – In Philadelphia, the first American life insurance company is incorporated.
- January 13 – Távora affair: The Távora family is executed, following accusations of the attempted regicide of Joseph I of Portugal.
- January 15 –
- February 16 – The Comte de Lally (Thomas Lally) ends the French Army's his two-month siege of the British Indian fort at Madras and retreats. 
- February 17 – "The greatest fleet that had ever put out for America"  departs from Portsmouth with 250 ships (including 49 Royal Navy warships under the command of Vice Admiral Charles Saunders, on a mission to capture French-controlled Quebec.  The ships bring 14,000 sailors, marines and British Army troops under the command of Major General James Wolfe, along with another 7,000 men in merchant service.
- March 4–November 20 – Étienne de Silhouette serves as Controller-General of France.
- April 14 – Seven Years' War – Battle of Bergen: A French army defeats Ferdinand, Duke of Brunswick.
- May 1 – Josiah Wedgwood founds the Wedgwood Pottery Company in England.
- June 4 – After arriving at Canada, the Royal Navy fleet sails out of British-controlled Halifax toward the St. Lawrence River to prepare the invasion of French Quebec. 
- June 15 – The first vascular surgery in history is performed by a Dr. Hallowell (whose first name has been lost to history) at Newcastle upon Tyne, who uses suture repair rather than a tying off with a ligature to repair an aneurysm on a patient's brachial artery. The case is reported
in 1761 by Dr. Richard Lambert in the paper "A new technique of treating an aneurysm", published in the journal Medical Observations and Inquiries.  The new procedure of reconstructing a damaged artery replaces the practice of ligation that had risked the amputation of a limb or to organ failure. 
- June 26 – After the fleet finishes navigation of the St. Lawrence and arriving Île d'Orléans, British troops go ashore at France's North American territory and begin the siege of Quebec City 
- July 19 – The Great Stockholm Fire 1759 breaks out at Södermalm in Stockholm, Sweden.
- July 25 – Seven Years' War (French and Indian War): In Canada, British forces capture Fort Niagara from the French, who subsequently abandon Fort Rouillé.
- July 26–27 – Seven Years' War (French and Indian War) – Battle of Ticonderoga: At the southern end of Lake Champlain, French forces withdraw from Fort Carillon, which is taken by the British under General Amherst, and renamed Fort Ticonderoga.
- August 1 – Battle of Minden: Anglo–Hanoverian forces under Ferdinand of Brunswick defeat the French army of the Duc de Broglie, but due to the disobedience of the English cavalry commander Lord George Sackville, the French are able to withdraw unmolested.
- August 10 – Ferdinand VI of Spain dies, and is succeeded by his half–brother Charles III. Charles resigns the thrones of Naples and Sicily to his third son, Ferdinand IV.
- August 12 – Battle of Kunersdorf: Frederick the Great is rebuffed in bloody assaults, on the combined Austro–Russian army of Pyotr Saltykov and Ernst von Laudon. This is one of Frederick's greatest defeats.
- August 18 – Battle of Lagos: The British fleet of Edward Boscawen defeats a French force under Commodore Jean-François de La Clue-Sabran, off the Portuguese coast.
- September 10 – Battle of Pondicherry: An inconclusive naval battle is fought off the coast of India, between the French Admiral d'Aché and the British under George Pocock. The French forces are badly damaged and sail home, never to return.
- September 13 – Seven Years' War (French and Indian War) – Battle of the Plains of Abraham: Quebec falls to British forces, following General Wolfe's victory just outside the city. Both the French Commander (the Marquis de Montcalm) and the British General James Wolfe are fatally wounded. 
- September 14 – Carrington Bowles publishes A Journey Through Europe, a board game designed by John Jefferys, the earliest board game whose designer's name is known.
- October 16 – Smeaton's Tower, John Smeaton’s Eddystone Lighthouse off the coast of South West England, is first illuminated.
- October 30 – Near East earthquakes of 1759: The first event in an earthquake doublet occurs to the north of the Sea of Galilee, with a surface wave magnitude of 6.6 and a maximum Mercalli intensity of VIII–IX (Severe–Violent). About 2,000 are killed in Safed.
- November 20 – Battle of Quiberon Bay: The British fleet of Sir Edward Hawke defeats a French fleet under Marshal de Conflans, near the coast of Brittany. This is the decisive naval engagement of the Seven Years' War – after this, the French are no longer able to field a significant fleet.
- November 21 – Battle of Maxen: The Austrian army of Marshal von Daun cuts off and forces the surrender of a Prussian force, under Friedrich von Finck.
- November 25 – Near East earthquakes of 1759: The second and stronger event in an earthquake doublet occurs to the east of Beirut, with a surface wave magnitude of 7.4 and a maximum Mercalli intensity of IX (Violent), destroying all the villages in the Beqaa Valley.
- November 29 – Alamgir II, the Mughal Emperor of India, is assassinated in a conspiracy orchestrated by his Prime Minister, Imad-ul-Mulk. The Shah Alam II, a grandson of the 17th century Emperor Aurangzeb, is made the new Mughal Emperor. 
- December 6 – The Germantown Union School (now called Germantown Academy), America's oldest nonsectarian day school, is founded.
- December 31 – The Guinness Brewery is leased by Arthur Guinness in St. James's Gate, Dublin, Ireland, for the brewing of Guinness.
- Adam Smith publishes his Theory of Moral Sentiments, embodying some of his Glasgow lectures.
- The town of Egedesminde (modern Aasiaat) is founded in Greenland.
- English clockmaker John Harrison produces his "No. 1 sea watch" (H4), the first successful marine chronometer.
- Kew Gardens established in England by Princess Augusta of Saxe-Gotha, the mother of George III.
- Churton Town, the Orange County, North Carolina county seat laid out in 1754, is renamed Childsburgh, in honor of North Carolina attorney general Thomas Child. It is later renamed Hillsborough in 1766.
- Fire destroys 250 houses in Stockholm.
- Madame du Coudray publishes Abrégé de l'art des accouchements (The Art of Obstetrics), and the French government authorizes her to carry her instruction "throughout the realm" and promises financial support.
- January 25 – Robert Burns, Scottish poet (d. 1796)
- January 29 – Louis Augustin Guillaume Bosc, French botanist (d. 1828)
- February 15 – Friedrich August Wolf, German philologist, archaeologist (d. 1824)
- February 22 – Claude Lecourbe, French general (d. 1815)
- April 22 – James Freeman, first clergyman in America to call himself a Unitarian (d. 1835)
- April 27 – Mary Wollstonecraft, English feminist author (d. 1797)
- May 15 – Maria Theresia von Paradis, Austrian musician, composer (d. 1824)
- May 20 – William Thornton, American architect (d. 1828)
- May 21 – Joseph Fouché, French statesman (d. 1820)
- May 28 – William Pitt the Younger, statesman and Prime Minister of the United Kingdom (d. 1806)
- June 21 – Alexander J. Dallas, American statesman and financier (d. 1817)
- July 2 – Nathan Read, American engineer and politician (d. 1849)
- July 31 – Ignaz Anton von Indermauer, Austrian nobleman and government official (d. 1796)
- August 24 – William Wilberforce, British abolitionist (d. 1833)
- September 10 – Lemuel Cook, American Revolutionary War veteran (d. 1866)
- September 19 – William Kirby, English entomologist (d. 1850)
- October 25
- October 26 – Georges Danton, French Revolutionary leader (d. 1794)
- November 5 – Simon Snyder, American politician (d. 1819)
- November 10 – Friedrich Schiller, German writer (d. 1805)
- November 27 – Franz Krommer, Czech composer (d. 1831)
- November 23 – Felipe Enrique Neri, legislator and colonizer of Texas (d. 1820)
- December 2 – James Edward Smith, English botanist (d. 1828)
- Date unknown – Maria Petraccini, Italian anatomist, physician (d. 1791)
- January 12 – Anne, Princess Royal and Princess of Orange, regent of Friesland (b. 1709)
- February 27 – Jacob Theodor Klein, German scholar (b. 1685)
- March 11 – John Forbes, British general (b. 1707)
- April 6 – Johann Gottfried Zinn, German anatomist, botanist (b. 1727)
- April 14 – George Frideric Handel, German composer (b. 1685)
- May 12 – Lambert-Sigisbert Adam, French sculptor (b. 1700)
- June 3 – Didier Diderot, French craftsman (b. 1685)
- June 20 – Margareta Capsia, Finnish artist (b. 1682)
- July 6 – William Pepperrell, English colonial soldier (b. 1696)
- July 27 – Pierre Louis Moreau de Maupertuis, French mathematician (b. 1698)
- August 6 – Eugene Aram, English philologist (b. 1704)
- August 8 – Carl Heinrich Graun, German composer (b. 1704)
- August 10 – King Ferdinand VI of Spain (b. 1713)
- August 24 – Ewald Christian von Kleist, German poet (b. 1715)
- September 10 – Ferdinand Konščak, Croatian explorer (b. 1703)
- September 13 – James Wolfe, British general (b. 1727)
- September 14 – Louis-Joseph de Montcalm, French general (b. 1712)
- November 14 – Grégoire Orlyk, Ukrainian-born French Lieutenant General (b. 1702)
- November 29 – Nicolaus I Bernoulli, Swiss mathematician (b. 1687)
- October 27 – Konstancja Czartoryska, Polish noblewoman politician (b. 1700)
- date unknown
- Newman, Frank G. (January 1965). "The Acquisition of a Life Insurance Company". The Business Lawyer. American Bar Association. 20 (2): 411–416. Retrieved 2016-04-04.
The first life insurance company in America was organized in 1759 under the corporate title 'The Corporation for Relief of Poor and Distressed Presbyterian Ministers, and of the Poor and Distressed Widows and Children of Presbyterian Ministers'.
- S. B. Bhattacherje, Encyclopaedia of Indian Events & Dates (Sterling Publishers, 2009) p94
- George M. Wrong, The Conquest of New France: A Chronicle of the Colonial Wars (Yale University Press, 1921) p214
- "Quebec, Capture of", in Encyclopedia of Naval History, ed. by Anthony Bruce and William Cogar (Routledge, 2014) p297
- Richard Middleton and Anne Lombard, Colonial America: A History to 1763 (John Wiley & Sons, 2011)
- "History of Microsurery", by Yoshikazu Ikuta, in Telemicrosurgery: Robot Assisted Microsurgery (Springer, 2012) p5
- Steven G. Friedman, MD, A History of Vascular Surgery (John Wiley & Sons, 2008) p ix
- "Eddystone Lighthouse". Trinity House. Archived from the original on September 9, 2006. Retrieved 2006-09-06.
- Royal Observatory Greenwich souvenir guide. 2012. pp. 34–35. ISBN 978-1-906367-51-0.
the first precision watch and considered by many today as the most important timekeeper ever.
- "Royal Botanic Gardens, Kew". World Heritage. UNESCO. Archived from the original on August 17, 2010. Retrieved 2010-07-04.