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Each of the points at either end of a line segment is called an endpoint of that line segment.

Similarly, the point at which an infinite half-line terminates is called the endpoint of that line.

In the words of Euclid:

The extremities of a line are points.

(The Elements: Book $\text{I}$: Definition $3$)

Also known as

The term endpoint can also be seen rendered as end point.

The more archaic term extremity can also be found, in particular in T.L. Heath's translation of Euclid: The Thirteen Books of The Elements.