Statement
The axiom states that, in the plane,
- If a line intersects one side of a triangle internally then it intersects precisely one other side internally and the third side externally, if it does not pass through a vertex of the triangle.
A more informal version of the axiom is often seen:
- If a line, not passing through any vertex of a triangle, meets one side of the triangle then it meets another side.
In this statement, a side of a triangle is taken to be the line segment joining two vertices of the triangle, so the expression "a line meeting a side" means that the line meets the line forming the side of the triangle internally.
Read more about this topic: Pasch's Axiom
Famous quotes containing the word statement:
“The most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)
“After the first powerful plain manifesto
The black statement of pistons, without more fuss
But gliding like a queen, she leaves the station.”
—Stephen Spender (1909–1995)
“Eroticism has its own moral justification because it says that pleasure is enough for me; it is a statement of the individual’s sovereignty.”
—Mario Vargas Llosa (b. 1936)