trace

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A visible mark, such as a footprint, made or left by the passage of a person, animal, or thing.
• noun Evidence or an indication of the former presence or existence of something; a vestige.
• noun An extremely small amount or barely perceivable indication.
• noun A constituent, such as a chemical compound or element, present in quantities less than a standard limit.
• noun A path or trail that has been beaten out by the passage of animals or people.
• noun An act of researching or ascertaining the origin or location of something.
• noun A line drawn by a recording instrument, such as a cardiograph.
• noun The point at which a line, or the curve in which a surface, intersects a coordinate plane.
• noun The sum of the elements of the principal diagonal of a matrix.
• noun An engram.
• intransitive verb To go along or follow (a path, for example).
• intransitive verb To follow the course or trail of.
• intransitive verb To ascertain the successive stages in the development or progress of.
• intransitive verb To discover or determine by searching or researching evidence.
• intransitive verb To locate or ascertain the origin of.
• intransitive verb To draw (a line or figure); sketch; delineate.
• intransitive verb To form (letters) with special concentration or care.
• intransitive verb To copy by following lines seen through a sheet of transparent paper.
• intransitive verb To follow closely (a prescribed pattern).
• intransitive verb To imprint (a design) by pressure with an instrument on a superimposed pattern.
• intransitive verb To make a design or series of markings on (a surface) by such pressure on a pattern.
• intransitive verb To record (a variable), as on a graph.
• intransitive verb To make one's way along a trail or course.
• intransitive verb To have origins; be traceable.
• adjective Occurring in extremely small amounts or in quantities less than a standard limit.
• noun One of two side straps or chains connecting a harnessed draft animal to a vehicle or whiffletree.
• noun A bar or rod, hinged at either end to another part, that transfers movement from one part of a machine to another.
• idiom (kick over the traces) To act in a way that contravenes social expectations or propriety.

from The Century Dictionary.

• To mark out upon the ground the lines of a field-work.
• noun The original position or place of a figure after that figure has been supposed to move: thus a circle is the closed line which will slide in its trace
• noun The intersection of a surface by a given line or surface: as, the trace of a liue is a point; the trace of a surface is a line.
• noun In angling, a short line or a length of gut by which the hook is attached to the reel-line; a snell; a snood; a leader.
• noun One of the two straps, ropes, or chains by which a carriage, wagon, or other vehicle is drawn by a harnessed horse or other draft-animal. See cut under harness.
• To hitch up; put in the traces.
• Nautical, a form of trice.
• To draw; delineate; mark out, as on a map, chart, or plan; map out; design; sketch.
• To write, especially by a careful or laborious formation of the letters; form in writing.
• Specifically To copy, as a drawing or engraving, by following the lines and marking them on a superimposed sheet, through which they appear.
• To cover with traced lines, as with writing or tracery.
• To follow the track, trail, or path of; pursue: a general term, the verbs track and trail being more specific, as in hunting.
• To follow the course of by observation of the remains or vestiges; ascertain the position, course, contour, etc., of by noting and following the traces that exist.