A Finite Projective Geometry Exercise 1.18.
Euclid alone has looked on Beauty bare.
—Edna St. Vincent Millay (1892–1950)

Exercise 1.18.  Identify the axioms for a finite projective plane that are valid in Euclidean geometry. Explain why the others are not valid.

Valid in Euclidean geometry: Axiom P1, Axiom P3, and Axiom P4.
Not valid in Euclidean geometry: Axiom P2. The axiom states that all lines intersect; therefore, there are no parallel lines. But parallel lines exist in Euclidean geometry