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an-Nairizi angle ABC angle BAC angles equal Apollonius Arabic Archimedes Aristotle assumed axiom base BC BC is equal 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 Fihrist follows Geminus geometrical algebra geometry given straight line gives gnomon greater Greek Heiberg Heron hypothesis ibid interior angles intersection joined lemma less Let ABC magnitude means meet method namely observes Pappus parallel parallelogram passage perpendicular plane Plato porism Posidonius postulate problem Proclus produced proof proposition proved Pythagoras Pythagorean quoted rectangle contained reductio ad absurdum reference remaining angle respectively right angles right-angled triangle says Schol scholia segment solid square on AC suppose surface Suter Theon theorem things three angles translation triangle ABC twice the rectangle words