1671 in science

The year 1671 in science and technology involved some significant events.

Astronomy

Completion of Paris Observatory, the world's first such national institution.{{cite web|url=http://www.paris-walking-tours.com/observatoryofparis.html|publisher=Paris Walking Tours|title=Observatory of Paris|accessdate=2011-05-10}}
February 27 – The Ortenau meteorite lands in Germany.
October 25 – Italian-born French astronomer Giovanni Domenico Cassini discovers Iapetus, the second known moon of the planet Saturn.

James Gregory develops a series expansion for the inverse tangent function and discovers Taylor's theorem.
{{nihongo|Sawaguchi Kazuyuki|沢口一之}} publishes Kokin-Sanpo-Ki (古今算法之記), in which he gives the first comprehensive applied account of Chinese algebra in Japan.

Publication of Les secrets de la medecine des Chinois, the first Western book on traditional Eastern medicine, in Grenoble.
Publication of Jane Sharp's The Midwives Book: or the Whole Art of Midwifry Discovered, the first on the subject to be written by an Englishwoman.{{cite journal|last=Bosanquet|first=Anna|date=2009|title=Inspiration from the past (1) Jane Sharp|url=http://www2.warwick.ac.uk/fac/arts/history/students/eportfolios/bosanquet/publications_presentations/sharp_practising_midwife_article.pdf|journal=The Practising Midwife|volume=12|issue=8|pages=33–35|pmid=19813367}}

Jacques Rohault publishes Traité de physique in Paris, disseminating Cartesian physics.

March 31 – The English Royal Navy launches HMS Royal James at Portsmouth Royal Dockyard, its first warship to have a frame reinforced by iron bars rather than an all wooden ship, an innovation by naval architect Anthony Deane.