Etymology
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tangent (adj.)

1590s, "meeting at a point without intersecting," from Latin tangentem (nominative tangens), present participle of tangere "to touch," from PIE root *tag- "to touch, handle." First used by Danish mathematician Thomas Fincke in "Geomietria Rotundi" (1583). Extended sense of "slightly connected with a subject" is first recorded 1825. Related: Tangence; tangency.

tangent (n.)

1590s as a geometric function, from tangent (adj.). From 1650s as "a tangent line." Figurative use of off on a tangent is from 1771.

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Definitions of tangent

tangent (n.)
a straight line or plane that touches a curve or curved surface at a point but does not intersect it at that point;
tangent (n.)
ratio of the opposite to the adjacent side of a right-angled triangle;
Synonyms: tan
From wordnet.princeton.edu