Apotomē is an archaic mathematical

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 term which, according to Webster's 1828 Dictionary, is the difference

Subtraction

In arithmetic, subtraction is one of the four basic binary operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with...

 of two quantities that are commensurable

Commensurability (mathematics)

In mathematics, two non-zero real numbers a and b are said to be commensurable if a/b is a rational number.-History of the concept:...

 only in power

Exponentiation

Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent n...

. According to Bailey's 1761 Dictionary it is "an irrational remainder or residual when from a rational line a part is cut off which is only commensurate in power to the whole line". It appears not to be in modern usage.

This concept of the Apotome appears in book X of Euclid's Elements

Euclid's Elements

Euclid's Elements is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria c. 300 BC. It is a collection of definitions, postulates , propositions , and mathematical proofs of the propositions...

.