The existence and uniqueness of a straight line through two points was just postulated in one of the five axioms of Euclid's Elements written more than 2,000 years ago. By means of modern analytic geometry, we are able to actually prove what was postulated in ancient times in the following theorem:

Theorem: Existence and Uniqueness of a Straight Line Through Two Points

Let $A, B$ be two points of an $n$-dimensional number space $\mathbb R^n$ with $A\neq B$. Then there is exactly one straight line containing the points $A, B.$

Proofs: 1

Proofs: 1

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