Definition: Collinear Points

The concept of collinearity is the same in projective geometry as already defined for the Euclidean geometry. Here, we recall this definition and reformulate it for the purposes of the projective geometry1:

Different points which are incident to a straight line are said to be collinear. We also say that a line $l$ joins the points $A_1,A_2,\ldots$ and write $$l=A_1A_2\ldots.$$

We agree that the order of points in this notation does not play any role, e.g. $AB$ and $BA$ for two points $A$ and $B$ denote the same line.


The following figure shows an example of four collinear points on a straight line $l=ABCD.$

Chapters: 1 2
Definitions: 3 4

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  1. getting rid of collinear segments and rays, which are not terms of projective geometry