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ABCD according added alternately angle BAC antecedent applied base Book called centre circle circle ABC circumference common measure compounded consequent construction contained continued proportion corresponding course cube definition described diameter divided double drawn equal equiangular equimultiples Euclid excess extremes fact fall figure follows four fourth further geometrical given gives greater greatest Hence hypothesis impossible joined least less magnitudes mean proportional measures meet method multiple multitude namely necessary parallel parallelogram pass plane possible prime prime number proof Prop proposition proved ratio reason rectangle rectilineal reference remaining respectively right angles segment sides similar Similarly Simson square straight line suppose taken taking Theon third touch triangle triangle ABC unit VIII whole