The year 1685 in science and technology involved some significant events.

Mathematics

• Adam Adamandy Kochański publishes an approximation for squaring the circle.^[1]

Physiology and medicine

• Charles Allen publishes the first book in English on dentistry, The Operator for the Teeth.^[2]
• Govert Bidloo publishes an atlas of human anatomy, Ontleding des menschelyken lichaams, with plates by Gerard de Lairesse.

Technology

• Menno van Coehoorn publishes his principal treatise on fortification, Nieuwe Vestingbouw op een natte of lage horisont, in Leeuwarden.

Births

• August 18 – Brook Taylor, English mathematician (died 1731)
• November 17 – Pierre Gaultier de Varennes et de la Vérendrye, French Canadian explorer (died 1749)

Deaths

• February 2 – Pierre Bourdelot, French physician, anatomist, freethinker, abbé and libertine (born 1610)
• November 23 – Bernard de Gomme, military engineer in England (born 1620)
• December 12 – John Pell, English mathematician (born 1610)