Definition:Parallel

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Definition

Lines

In the words of Euclid:

Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in either direction, do not meet one another in either direction.

(The Elements: Book $\text{I}$: Definition $23$)


Planes

Two planes are parallel if, when produced indefinitely, do not intersect at any place.


In the words of Euclid:

Parallel planes are those which do not meet.

(The Elements: Book $\text{XI}$: Definition $8$)