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ABCD AC is equal angle ABC angle ACB angle BAC angle DAE angle DEF angle EDF angles equal Axiom base BC bisected centre circle ABC circumference Constr Construction Corollary DC as BA Definition 15 demonstration double draw equal angles equal to F equiangular equimultiples Euclid Euclid's Elements exterior angle fourth given circle given point given straight line gnomon greater ratio Hypothesis less Let ABC Let the straight multiple opposite angle parallel to BC parallelogram perpendicular plane passing point F polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION rectangle contained remaining angle right angles segment shown sides Simson square described square on AC straight line AB straight lines &c THEOREM third three straight lines touches the circle triangle ABC triangle DEF twice the rectangle Wherefore