'Tangent' is Latin for 'touching' — a line that touches a curve at one point. Coined in 1583.
A straight line that touches a curve at a single point without crossing it; a completely different line of thought or action (as in 'go off on a tangent').
From Latin 'tangēns' (touching), the present participle of 'tangere' (to touch, to handle, to reach), from PIE *tag- (to touch, to handle). The PIE root *tag- runs through a dense cluster of English words: 'taste' (to touch with the tongue), 'tax' (to assess by touching/handling goods), 'tactile' (of touch), 'contact' (touching together), 'intact' (untouched), and 'contaminate' (to touch together, defile). The mathematical term was coined by the Danish mathematician Thomas Fincke in his 'Geometria Rotundi' (1583): a tangent is a
The trigonometric tangent function (tan) gets its name from the same geometric concept: in a unit circle, the tangent of an angle equals the length of the line segment that is tangent to the circle at the point (1,0) and extends to the terminal side of the angle. The abbreviation 'tan' that millions of students use in mathematics is literally an abbreviation of the Latin word for 'touching.'