An Etymological Dictionary of Astronomy and Astrophysics

1a) A surviving mark, sign, or evidence of the former existence, influence, or action of some agent or event; vestige.

1b) A barely discernible indication or evidence of some quantity, quality, characteristic, expression, etc.

1c) An extremely small amount of some chemical component (Dictionary.com).

1d) Math.: → trace of a matrix.

2a) To follow the footprints, track, or traces of.

2b) To follow, make out, or determine the course or line of, especially by going backward from the latest evidence, nearest existence, etc. (Dictionary.com).

Etymology (EN): M.E. tracen, from M.Fr. tracier, from V.L. *tractiare “delineate, score, trace,” from L. tractus “track, course,” literally “a drawing out,” from p.p. stem of trahere “to pull, draw.”

Etymology (PE): Gilaki mâle “mark, trace, fingerprint; scar,” pâ mâle “footprint,” gaz mâle “bite mark;” Aftari mâl “trace, mark,” pae mâl “footprint,” ponjé mâl “mark of hand with fingers;” Tabari mâl “mark, trace,” ling mâl “footprint,” probably related to mâlidan “to touch, rub; besmear;”
Mid.Pers. mâlih- “to be touched;” (Gurâni) mâl, mâlâ- Xunsâri mâl-/mâlâ “to smear, stroke.”