While Playfair's formulation is more commonly used today, it's essentially a restatement of Euclid's original Fifth Postulate.
Here's why:
* Euclid's Fifth Postulate: "If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, will intersect on that side."
* Playfair's Axiom: "Through a given point, not on a given line, there passes exactly one line parallel to the given line."
Both statements express the same fundamental concept: there's only one parallel line to a given line through a given point. This concept distinguishes Euclidean geometry from other geometries like hyperbolic and elliptic geometry.