1584 in science
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- Completion of Tycho Brahe's subterranean observatory at Stjerneborg.
- Giordano Bruno, in England, publishes his "Italian Dialogues", including the cosmological tracts La Cena de le Ceneri ("The Ash Wednesday Supper"), De la Causa, Principio et Uno ("On Cause, Principle and Unity") and De l'Infinito Universo et Mondi ("On the Infinite Universe and Worlds").
- Lucas Janszoon Waghenaer publishes the first atlas of nautical charts, Spieghel der zeevaerdt (Mariner's Mirror).
- The Italian Jesuit Matteo Ricci, in Zhaoqing, produces the first Chinese world map, on wood, Yudi Shanhai Quantu (舆地山海全图).
- Abraham Ortelius publishes Itinerarium per nonnullas Galliæ Belgicæ partes in Anvers.
- June 4 – Walter Ralegh sends Philip Amadas and Arthur Barlowe to explore the Outer Banks of Virginia (now North Carolina), with a view to establishing an English colony; they locate Roanoke Island.
- Jean Errard publishes Premier livre des instruments mathématiques at Nancy.
- Fabrizio Mordente publishes Il Signor del Compasso Fabritio Mordente. Con altri istromenti mathematici, suo fratello Gasparo da ritrovati at Anvers and introduces the parallel rulers.
- Zhu Zaiyu calculates equal temperament.
- Jacques Guillemeau publishes his ophthalmology textbook Traite des maladies de l'oeil.
- Thomas Muffet publishes De jure et praestantia chemicorum medicamentorum.
- Nikola Vitov Gučetić publishes Sopra le Metheore d' Aristotile giving explanations for the causes of winds and of the movement of air in caves.
- March 22? – Grégoire de Saint-Vincent, Flemish mathematician (died 1667)
- William Baffin, English explorer (died 1622)
- Giovanni Baptista Ferrari, Italian botanist and linguist (died 1655)
- Walter Rumsey, Welsh judge and amateur scientist (died 1660)
- June 13 – János Zsámboky, Hungarian physician and scholar (born 1531)
- July 12 – Steven Borough, English explorer (born 1525)
- Elman, Benjamin A. (April 2005). "Sino-Jesuit Accommodations During the Seventeenth Century". On their own terms: science in China, 1550–1900. Cambridge, MA: Harvard University Press. p. 127. ISBN 978-0-674-01685-9.
- Grun, Bernard (1991). The Timetables of History (3rd ed.). New York: Simon & Schuster. p. 259. ISBN 0-671-74919-6.