A number of points on a line segment. The term was first used by Desargues (Cremona 1960, p. x). If the points , , , ... lie on a line segment
with the coordinates of the points such that , they are said to form a range, denoted . Let denote the signed distance . Then the range satisfies the relation

(1)

The range
satisfies

(2)

and

(3)

the latter of which holds even when is not on the line (Lachlan 1893).

Graustein (1930) and Woods (1961) use the term "range" to refer to the totality of points on a straight line, making it the dual
of a pencil.