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ABCD AC is equal angle ABC angle ACB angle BAC Axiom base bisected Book centre circle circle ABC circumference common Construction contained Corollary Definition demonstration described divided double draw drawn edition Elements equal equal angles equiangular equilateral equimultiples Euclid fall figure four fourth given straight line greater half Hypothesis impossible join less Let ABC magnitudes manner meet multiple namely parallel parallelogram pass perpendicular plane polygon PROBLEM produced proportionals Q.E.D. PROPOSITION ratio reason rectangle rectangle contained rectilineal figure right angles segment shown sides similar Simson square square on AC straight line &c suppose Take taken THEOREM third touches the circle triangle ABC volumes Wherefore whole