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:
“Truth is used to vitalize a statement rather than devitalize it. Truth implies more than a simple statement of fact. “I don’t have any whisky,” may be a fact but it is not a truth.”
—William Burroughs (b. 1914)
“The new statement is always hated by the old, and, to those dwelling in the old, comes like an abyss of skepticism.”
—Ralph Waldo Emerson (1803–1882)
“I think, therefore I am is the statement of an intellectual who underrates toothaches.”
—Milan Kundera (b. 1929)