March 5 – The 1730 papal conclave to elect a new Pope for the Roman Catholic church begins with 30 Cardinals, 12 days after the death of Pope Benedict XIII. By the time his successor is elected on July 12, there are 56 Cardinals.
March 16 – The establishment by Thomas Cresap of Wright's Ferry under the authority of the Province of Pennsylvania<ref name=Egle>William H. Egle, History of the Commonwealth of Pennsylvania, Civil, Political and Military from Its Earliest Settlement to the Present Time, Including Historical Descriptions of Each County in the State, Their Towns, and Industrial Resources (E.M. Gardner Co., 1883) p322</ref> becomes the basis for Cresap's War, a nine-year-long conflict also known as the Maryland-Pennsylvania boundary dispute; the conflict mainly centers in Lancaster County, Pennsylvania and York County, Pennsylvania on either bank of the Susquehanna River.
June 27 – French explorer Alphonse de Pontevez, commanding the frigate Le Lys, claims an Indian Oceanatoll for France and names it after himself as the Alphonse Atoll. The next day, he claims and names the St. François Atoll.
August 4 – Maria Madlener becomes the last person to be executed after the Galgeninsel witch trials in Bavaria, and is beheaded by sword.
August 5 – Prince Frederick of Prussia, the eldest son of King Frederick William and a high-ranking officer, attempts to flee to England after deserting the Prussian Army and is captured along with his fellow officer Hans Hermann von Katte. Katte is executed, and Crown Prince Frederick is imprisoned at Küstrin (modern-day Kostrzyn nad Odrą in Poland) for a year before being forgiven by his father. Prince Frederick later succeeds his father as King and will be remembered as Frederick the Great.<ref name=Durant>Will Durant and Ariel Durant, The Story of Civilization, Volume IX: The Age of Voltaire (Simon & Schuster, 1965)</ref>
August 25 – French Protestant Marie Durand is imprisoned in the Tower of Constance at Aigues-Mortes for her defiance of the Roman Catholic government, and is kept captive for the next 38 years. During her incarceration, she continues to resist converting to Catholicism as a condition of release. She is finally set free on April 14, 1768 and lives 8 more years.
September 1 – A volcano erupts on Lanzarote, the easternmost of the Canary Islands and threatens the Spanish inhabitants. On Gran Canaria, the regent of the islands reports to Madrid that the flames are visible even from Template:Convert away.<ref name=Scarth>Alwyn Scarth, Volcanoes: An Introduction (Taylor & Francis, 2004)</ref>
December 27 – The Dutch East India Company ends an almost 11-year effort of trying to maintain a colony around Delagoa Bay in southern Africa in modern-day Mozambique. The entire population of the settlement, Fort Lydzammheid (near modern-day Maputo) is evacuated by the ships Snuffelaar, Zeepost and Feyenoord and the group returns to Cape Town.<ref>Template:Cite book</ref>
