1533 in science

Astronomy

• Petrus Apianus publishes at Ingolstadt Apiani horoscopion, Buch Instrument and Folium populi.

Botany

• Rembert Dodoens publishes his Herbarium.

Exploration

• October 30 – The Concepción and San Lázaro, on the instruction of Hernán Cortés, leave Manzanillo to explore the Pacific Ocean.
• Fortún Ximénez is the first European known to land in Baja California.

History of science

• Georgius Agricola publishes De Mensuis et Ponderibus on the weights and measures of Classical antiquity.

Mathematics

• First printed edition of Euclid's Elements in the original Greek published in Basel, edited by Simon Grynaeus including integral diagrams and the first printing of Proclus' commentary on the first book.
• Gemma Frisius publishes De Locorum describendorum ratione in Antwerp, containing the first known statement of the principles of triangulation and a means for determining longitude.

Technology

• Antonio da Sangallo the Younger constructs the Fortezza da Basso in Florence, considered as a model in bastion fortress design.

Births

• May 20 – Hieronymus Fabricius, Italian anatomist
• August 2 – Theodor Zwinger the elder, Swiss philosopher, physician and encyclopedist
• November 23 – Prospero Alpini, Venetian-born physician and botanist Approx. date
• * Jacques Le Moyne de Morgues, French scientific illustrator
• * Friedrich Risner, German mathematician
• * Lucas Janszoon Waghenaer, Dutch nautical chartmaker

Deaths

• May 31 – Ambrosius Ehinger, Bavarian explorer of South America
• August 16 – Diogo Ribeiro, Portuguese-Spanish cartographer and explorer
• Johannes Ruysch, cartographer