Elementary Geometry from an Advanced Standpoint

AABC ABCD ADEF algebraic altitude Archimedean postulate base belongs bisector broken line called Cavalieri's principle Chapter circular sector congruent construct contains convex convex polygonal coordinate system defect defined definition denoted dihedral angle distance elements equation Euclidean Euclidean geometry exactly exterior angle theorem FIGURE following theorem formula area Given graph H₁ half planes holds hyperbolic geometry inequality interior intersects isometry Jordan measure K₁ L-line Lemma length M₁ mathematical means measure merely one-to-one correspondence ordered field P₁ pair parallel postulate perpendicular polygonal region polynomial positive integers positive number PROBLEM SET Proof R₁ radius rational numbers real number system rectangle right angle root ruler and compass ruler postulate Saccheri quadrilateral satisfies Section segment sequence Suppose surd surd plane tangent triangular regions upper bound vertices