Parallel lines are lines which have the same direction; hence parallel lines can never meet, however far they may be produced; for two lines taking the same direction cannot approach or recede from each other.
An Axiom is a self-evident truth, not only too simple to require, but too simple to admit of demonstration.
A Proposition is something which is either proposed to be done, or to be demonstrated, and is either a problem or a theorem.
A Problem is something proposed to be done.
A Theorem is something proposed to be demonstrated.
A Hypothesis is a supposition made with a view to draw from it some consequence which establishes the truth or falsehood of a proposition, or solves a problem.
A Lemma is something which is premised, or demonstrated, in order to render what follows more easy.
A Corollary is a consequent truth derived immediately from some preceding truth or demonstration.
A Scholium is a remark or observation made upon something going before it.