On a sudden digression or change of course, as in The professor's hard to follow; he's always off on a tangent. This phrase often occurs in the idioms
fly off or go off on a tangent, as in The witness was convincing until he went off on a tangent. This expression alludes to the geometric tangent—a line or curve that touches but does not intersect with another line or curve.
[ Second half of 1700s