# cline

## Contents

## English[edit]

### Etymology 1[edit]

From Ancient Greek *κλίνειν* (klínein, “to lean, incline”) (from which also *climate*), from Proto-Indo-European **ḱley-* (English *lean*).

#### Pronunciation[edit]

#### Noun[edit]

**cline** (*plural* **clines**)

- (systematics) A gradation in a character or phenotype within a species or other group.
- Any graduated continuum.
**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, …

##### Derived terms[edit]

##### Related terms[edit]

### Etymology 2[edit]

From *c(ircle)* + *line*; compare *circline*.

#### Pronunciation[edit]

#### Noun[edit]

**cline** (*plural* **clines**)

- (geometry, inversive geometry) A generalized circle.
**2001**, Michael Henle, Modern Geometries: Non-Euclidean, Projective, and Discrete^{[1]}, page 77:- Let
*C*and_{1}*C*be two nonintersecting_{2}**clines**. Prove that there is a unique pair of points that are simultaneously symmetric to both*C*and_{1}*C*._{2}

- Let
**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.

- To visualize Möbius transformations, it is helpful to focus on fixed points and, in the case of two fixed points, on two families of
**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*.

- Let

##### Synonyms[edit]

- (generalized circle): circline, generalized circle

### Further reading[edit]

- cline at
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