Pedro Álvares Cabral, a Portuguese nobleman, military commander, navigator and explorer, sailed far into the western Atlantic Ocean, perhaps intentionally, and made landfall (April 1500) on what he initially assumed to be a large island. As the new land was within the Portuguese sphere according to the 1494 Treaty of Tordesillas, Cabral claimed it for the Portuguese Crown. He explored the coast, realizing that the large land mass was probably a continent, and dispatched a ship to notify King Manuel I of the new territory. The continent was South America, and the land he had claimed for Portugal later came to be known as Brazil. The fleet reprovisioned and then turned eastward to resume the journey to India.

The Castilian navigator and cartographer, Juan de la Cosa, creates a world map that includes the earliest known representation of the New World and the first depiction of the equator and the Tropic of Cancer on a nautical chart. Juan de la Cosa's map is a manuscript nautical chart of the world drawn on two joined sheets of parchment sewn onto a canvas backing. It measures 96 cm high by 183 cm wide. A legend written in Spanish at the western edge of the map translates as "Juan de la Cosa made this (map) in the port of Santa Maria in the year 1500". The overall style is similar to other contemporary charts of the Mediterranean, especially maps produced in Majorca, an important center of map making at the time.

Chinese legendary adventurer Wan Hu attempts to leave the Earth by sitting on a chair with 47 rockets tied to it, holding a kite in each of his hands, and flying into the sky after his servants were ordered to light the fuses to the rockets. But the rockets exploded and Wan Hu was gone when the air cleared. While most authorities consider the story apocryphal, some Chinese scholars believe that foreigners from several different countries in the west were unlikely to fabricate such a story out of thin air. The tale may be based on the stories told by European missionaries who arrived in China since the late Ming dynasty, and then passed on by word of mouth. Alternatively, these European and American scholars may have indirectly relied on records in an ancient Chinese document that has been subsequently lost.

Leonardo da Vinci, finding many fossils in canal building sites, proposes that fossil shells of marine animals are found on mountains because Earth undergoes transformations that cause areas once submerged to become exposed.

Leonardo da Vinci as comparative anatomist: human leg vs. canine leg.

Amerigo Vespucci maps the two stars Alpha Centauri and Beta Centauri, as well as the stars of the constellation Crux, which are below the horizon in Europe.

Christopher Columbus leaves Cadiz, Spain for his fourth and final voyage to the New World.

Portuguese explorers, led by Pedro Álvares Cabral, sail into Guanabara Bay, Brazil, mistaking it for the mouth of a river, which they name Rio de Janeiro.

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Christopher Columbus uses his knowledge of a lunar eclipse this night (February 29) to convince Jamaican tribesmen to provide him with supplies. Three days before the eclipse, Columbus requested a meeting with the Arawak chief and informed him that his Christian god was very angry with his people for no longer supplying him and his men with food. Therefore, he was about to provide a clear sign of his displeasure: Three nights hence, he would all but obliterate the rising full moon, making it appear "inflamed with wrath," which would signify the evils that would soon be inflicted upon all of them. On the appointed evening, as the sun set in the west and the moon started emerging from beyond the eastern horizon, it was plainly obvious to all that something was terribly wrong. By the time the moon appeared in full view, a small but noticeable dark scallop had been removed from its lower edge. And, just over an hour later, as evening twilight ended and full darkness descended, the moon indeed exhibited an eerily inflamed and "bloody" appearance: In place of the normally brilliant late winter full moon there now hung a dim red ball in the eastern sky. According to Columbus' son, Ferdinand, the Arawaks were terrified at this sight and "with great howling and lamentation came running from every direction to the ships laden with provisions and beseeching the admiral to intercede with his god on their behalf." They promised that they would happily cooperate with Columbus and his men if only he would restore the moon back to its normal self.

Leonardo da Vinci produces his Codex on the Flight of Birds, a relatively short codex. It comprises 18 folios and measures 21 × 15 centimetres. Now held at the Royal Library of Turin, the codex begins with an examination of the flight behavior of birds and proposes mechanisms for flight by machines. Leonardo constructed a number of these machines, and attempted to launch them from a hill near Florence. However, his efforts failed. In the codex, Leonardo notes for the first time that the center of gravity of a flying bird does not coincide with its center of pressure.

Bermuda is discovered by Spanish explorer Juan de Bermúdez. Bermúdez made 11 registered trips to the New World from 1495 to 1519.

Christopher Columbus dies.

First publication of the Waldseemüller map or Universalis Cosmographia ("Universal Cosmography") is a printed wall map of the world by German cartographer Martin Waldseemüller. It is known as the first map to use the name "America". The name America is placed on South America on the main map. As explained in Cosmographiae Introductio, the name was bestowed in honor of the Italian Amerigo Vespucci. The map is drafted on a modification of Ptolemy's second projection, expanded to accommodate the Americas and the high latitudes. A single copy of the map survives, presently housed at the Library of Congress in Washington, D.C.

(no entry for this year)

The Constantinople earthquake occurs in the Sea of Marmara on 10 September 1509 at about 22:00. The earthquake had an estimated magnitude of 7.2 ± 0.3 on the surface-wave magnitude scale. A tsunami and 45 days of aftershocks followed the earthquake. The death toll of this earthquake is poorly known; estimates range between 1,000 and 13,000.

Luca Pacioli's De divina proportione, concerning the golden ratio, is published in Venice, with illustrations by Leonardo da Vinci. Its subject was mathematical proportions (the title refers to the golden ratio) and their applications to geometry, to visual art through perspective, and to architecture. The clarity of the written material and Leonardo's excellent diagrams helped the book to achieve an impact beyond mathematical circles, popularizing contemporary geometric concepts and images.