The Demonstration is the proof, in the case of a theorem, that the conclusion follows from the hypothesis; and in the case of a problem, that the construction accomplishes the object proposed.
The Enunciation of a problem consists of two parts, namely, the data, or things supposed to be given, and the quaesita, or things required to be done.
Postulates are the elements of geometrical construction, and occupy the same relation with respect to problems as axioms do to theorems.
A Corollary is an inference or deduction from a proposition.
A Lemma is an auxiliary proposition required in the demonstration of a principal proposition.
A Secant or Transversal is a line which cuts a system of lines, a circle, or any other geometrical figure.
Congruent figures are those that can be made to coincide by superposition. They agree in shape and size, but differ in position. Hence it follows, by Axiom viii., that corresponding parts or portions of congruent figures are congruent, and that congruent figures are equal in every respect.
Rule of Identity.—Under this name the following principle will be sometimes referred to:—“If there is but one X and one Y , then, from the fact that X is Y , it necessarily follows that Y is X.”—Syllabus.
PROP. I.—Problem.
On a given finite right line (AB) to construct an equilateral triangle.
