Proposition XI.2 — If two straight lines cut one another, they are in one plane…

Proof

Two intersecting lines pick out three non-collinear points (one at the intersection, one on each line); through these three points passes exactly one plane (the analogue in 3D of Postulate 1).

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Full neighborhood

Depends on (2)

XI.1Proposition XI.1A part of a straight line cannot be in the plane of reference and a part in a plane more elevated.
I.7Definition I.7A plane surface is a surface which lies evenly with the straight lines on itself.

Required by (dependents) (3)

XI.5Proposition XI.5If a straight line be set up at right angles to three straight lines which meet one another, at their common point of…
XI.6Proposition XI.6If two straight lines be at right angles to the same plane, the straight lines will be parallel.
XI.7Proposition XI.7If two straight lines be parallel, and points be taken at random on each of them, the straight line joining the points…

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