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April 16 - The London premiere of Alcina by George Frideric Handel, his first Italian opera for the Royal Opera House at Covent Garden.

July 11 - Mathematical calculations suggest it was on this day that Pluto moved closer to the Sun than Neptune for the last time before 1979.

August 4 - Freedom of the press: New York Weekly Journal writer John Peter Zenger is acquitted of seditious libel against the royal governor of New York, on the basis that what he published was true.

October - War of the Polish Succession concludes a preliminary peace, ratified in 1738

Russo-Turkish War, 1735-1739: Russian forces fail to occupy the Crimea due to rasputitsa.

French make peace with the Austro-Hungarian Empire (until 1740)

Ship building industry begins in Mumbai

Carolus Linnaeus publishes his Systema Naturae

End of the reign of Emperor Nakamikado of Japan

Emperor Sakuramachi ascends to the throne of Japan

Euler-Maclaurin formula developed

George Hadley correctly explains global circulation for the first time

King's Highway (Charleston to Boston) is completed

Etienne Fourmont writes Réflexions critiques sur les histoires des anciens peuples

The Qianlong Emperor succeeds Yongzheng and begins a 60-year-long reign of the Qing Dynasty.

Construction begins on the Chemin du roy between Quebec and Montreal

William Hogarth Publishes "A Rakes Progress"

Edmund Curll tries to publish "Mr Pope's Literary Correspondence" The stock of which is subsequently seized

Augusta, Georgia is founded

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January 1 - Paul Revere, American silversmith and patriot (d. 1818)

January 8 - John Carroll (priest) first Roman Catholic Archbishop in the U.S. (d. 1815)

February 28 - Alexandre-Théophile Vandermonde French musician and chemist (d. 1796)

April 13 - Isaac Low, New York delegate to the Continental Congress (d. 1791)

May 1 - Lorenzo Hervás y Panduro Spanish Jesuit philologist (d. 1809)

September 5 - Johann Christian Bach, German composer (d. 1782)

September 28 - Augustus FitzRoy, 3rd Duke of Grafton, Prime Minister of the United Kingdom (d. 1811)

October 1 - Augustus Henry Fitzroy, 3rd Duke of Grafton (d. 1811)

October 9 - Karl Wilhelm Ferdinand, Duke of Brunswick (d. 1806)

October 21 - Richard Gough, English antiquary (d. 1809)

October 30 - John Adams, 2nd President of the United States (d. 1826)

November 10 - Granville Sharp, English abolitionist (d. 1813)

December 29 - Thomas Banks, English sculptor and artist (d. 1805)

December 31 - Jean de Crévecoeur, French-American writer (d. 1813)

John Julius Angerstein, English merchant and insurer (d. 1822)

Charles Joseph, Prince de Ligne, (d. 1814)

Étienne Clavière, French financier and politician (d. 1793)

James Keir, Scottish geologist, chemist, and industrialist (d. 1820)

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January 12 - John Eccles, British composer (b. 1668)

January 18 - Maria Clementina Sobieski, Polish princess (b. 1702)

February 27 - John Arbuthnot, British physician and author (b. 1667)

April 5 - William Derham, English minister and writer (b. 1657)

April 5 - Samuel Wesley, English poet and religious leader (b. 1662)

June 10 - Thomas Hearne, British antiquarian (b. 1678)

September 27 - Peter Artedi, Swedish naturalist (drowned) (b. 1705)

October 8 - Yongzheng Emperor of China (b. 1678)

December 14 - Thomas Tanner, English bishop and antiquarian (b. 1674)

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Chinese Calendar: Yongzheng-13 雍正十三年