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an-Nairizi angle ABC angle BAC angles equal Apollonius Arabic Archimedes Aristotle assumed axiom bisected Book Campanus centre circle circumference coincide commentary Common Notion congruent construction definition diameter drawn edition Elements enunciation equilateral triangle Eucl Euclid Euclid's Elements Eudemus Eutocius fact Fihrist follows Geminus geometry given straight line gives gnomon greater Greek Heiberg Heron hypothesis ibid interior angles interpolated isosceles joined lemma less Let ABC magnitude means meet method namely observes Pappus parallel parallelogram passage perpendicular plane Plato porism Posidonius postulate problem Proclus produced proposition proved Ptolemy Pythagoras Pythagorean quoted rectangle rectangle contained reductio ad absurdum reference remaining angle respectively right angles right-angled triangle says Schol scholia scholium segment sides Simplicius solid square on AC suppose surface Suter Theon Theonine MSS theorem things three angles translation triangle ABC twice the rectangle words