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 force of truth that a statement imparts, then, its prominence among the hordes of recorded observations that I may optionally apply to my own life, depends, in addition to the sense that it is argumentatively defensible, on the sense that someone like me, and someone I like, whose voice is audible and who is at least notionally in the same room with me, does or can possibly hold it to be compellingly true.”
—Nicholson Baker (b. 1957)
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—William Burroughs (b. 1914)
“The honor my country shall never be stained by an apology from me for the statement of truth and the performance of duty; nor can I give any explanation of my official acts except such as is due to integrity and justice and consistent with the principles on which our institutions have been framed.”
—Andrew Jackson (1767–1845)