apotome

Apotome is a historical term from ancient Greek geometry used to denote a line segment that results when a prescribed portion is cut away from a longer segment. The word comes from Greek apo- meaning away from and temnein meaning to cut. In surviving mathematical treatises, apotomes appear as objects involved in constructions and in discussions of proportional relationships, serving as a tool for reasoning about how segments relate to one another.

The concept is closely tied to the broader Greek interest in dividing and combining segments to study ratios and mean proportionals. Different authors and manuscripts sometimes describe apotomes in slightly different ways, but the common thread is the idea of a portion removed from a given straight line to yield a new segment with particular geometric or proportional properties.

Apotome is easy to confuse with apothem, a term used in modern polygonal geometry. The apothem is the perpendicular distance from the center of a regular polygon to the midpoint of a side, not a subdivided line segment. The two terms are unrelated in their practical meanings, though their similarity in spelling has led to occasional mix-ups in historical discussions.

Today, apotome is primarily of historical interest. It appears in the context of ancient Greek geometry and in some later translations or commentaries, where it is referenced as a technical object within segment division and proportion problems. In contemporary mathematics, the concept is generally described without retaining the specific named object, using generic language about segments, subtraction, and ratios.