Yours, Etc.: Origins and Uses of 8 Sign-Offs
1590s, "meeting at a point without intersecting," from Latin tangentem (nominative tangens), present participle of tangere "to touch," from PIE root *tag- "to touch, to handle" (cf. Latin tactus "touch," Greek tetagon "having seized," Old English þaccian "stroke, strike gently"). First used by Danish mathematician Thomas Fincke in "Geomietria Rotundi" (1583). Extended sense of "slightly connected with a subject" is first recorded 1825. The noun also is attested from 1590s.