To Carpent and other such things

Today as we were discussing hyperbolas in my calculus class we touched on the concept of the suffix -ix as used in latin, meaning "to do", such as the determinix of a parabola (the imaginary line which is the same distance at every point from the parabola as the parabola is from its focal point) which acts to determine the direction in which a parabola faces. This led to the discussion of the english equivalent, "er". For instance, a brick layer is one who lays bricks, this led me to wonder however, what does one carpent, for obviously a carpenter is one who is "to do" carpentry, which would be the act of carpenting. As of yet, it would seem my query will remain unanswered as to what has happened to the lost word "carpent"