1691 in science

• Italian Jesuit scholar Filippo Bonanni publishes the results of his microscopic observations of invertebrates in Observationes circa Viventia, quae in Rebus non-Viventibus.

• Gottfried Leibniz discovers the technique of separation of variables for ordinary differential equations.
• Michel Rolle invents Rolle's theorem.

• Anton Nuck's Adenographia curiosa et uteri foeminei anatome nova is published at Leiden, including a description of the canal of Nuck{{cite web|first=Ole Daniel|last=Enersen|title=Nuck's canal|url=http://www.whonamedit.com/synd.cfm/2644.html|work=Whonamedit?|accessdate=2012-10-15}} and a demonstration that the embryo is derived from the ovary and not the sperm.{{cite book|last=Speert|first=Harold|title=Obstetric and Gynecologic Milestones|publisher=Macmillan|location=New York|year=1958|pages=95–101}}

• Edmond Halley devises a diving bell.{{cite journal|author1=Edmonds, Carl|author2=Lowry, C.|author3=Pennefather, John|title=History of diving|journal=South Pacific Underwater Medicine Society Journal|volume=5|issue=2|url=http://archive.rubicon-foundation.org/5894|accessdate=2011-06-17|archive-date=2010-10-14|archive-url=https://web.archive.org/web/20101014013941/http://archive.rubicon-foundation.org/5894|url-status=dead}}
• In music, the "equal temperament scale" used in modern music is developed by organist Andreas Werckmeister.

• November 18 – Mårten Triewald, Swedish mechanical engineer (died 1747)

• January 17 – Richard Lower, English physician who performed the first direct blood transfusion (born 1631)
• December 31 – Robert Boyle, Anglo-Irish chemist (born 1627){{cite web |title=Robert Boyle {{!}} Biography, Contributions, Works, & Facts |url=https://www.britannica.com/biography/Robert-Boyle |website=Encyclopedia Britannica |access-date=4 December 2020 |language=en}}

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Category:17th century in science

Category:1690s in science