# cline

## English

### Etymology 1

Ancient Greek κλίνειν (klínein, to lean, incline). Doublet of climate.

#### Noun

cline (plural clines)

1. (systematics) A gradation in a character or phenotype within a species or other group.
• 2005, Ronnie Cann, Ruth Kempson and Lutz Marten, The Dynamics of Language, an Introduction, p. 412
This account effectively reconstructs the well-known grammaticalisation cline from anaphora to agreement, …

### Etymology 2

From c(ircle) + line; compare circline.

#### Noun

cline (plural clines)

1. (geometry, inversive geometry) A generalized circle.
• 2001, Michael Henle, Modern Geometries: Non-Euclidean, Projective, and Discrete[1], page 77:
Let C1 and C2 be two nonintersecting clines. Prove that there is a unique pair of points that are simultaneously symmetric to both C1 and C2.
• 2009, Michael P. Hitchman, Geometry with an Introduction to Cosmic Topology[2], page 64:
To visualize Möbius transformations, it is helpful to focus on fixed points and, in the case of two fixed points, on two families of clines with respect to these points.
• 2011, Dominique Michelucci, What is a Line?, Pascal Schreck, Julien Narboux, Jürgen Richter-Gebert (editors), Automated Deduction in Geometry, 8th International Workshop, ADG 2010, Revised Selected Papers, LNAI 6877, page 139,
Let Ω be a fixed, arbitrary, point. Then circles (in the classical sense) through Ω can be considered as lines. For convenience, such circles are called clines in this section. Two distinct clines cut in one point (ignoring Ω and the two cyclic points); it can happen that Ω is a double intersection point; in this case, one may say that the two clines are parallel, and that they meet at a point at infinity, which is Ω.