English: After Khayyam proved that the two angles at C and D were both right angles, he proves that the two other possibilities, that they were both acute or both obtuse, led to contradictions. If they were acute, CD would be longer than AB, whereas if they were obtuse, CD would be shorter than AB. In each case, Khayyam showed that the lines AC and BD would diverge or converge on both sides of AB, and this would contradict Euclid original postulate.