The process of reasoning from postulates and definitions has been basic to mathematics at least since the time of Euclid. Islamic geometers were well versed in this art, but also spent some effort examining the logical foundations of the method. They were unafraid to revise and improve upon Euclid’s starting points, and they rebuilt the Elements from the ground up in several ways. Khayyam’s Explanation of the Difficulties in the Postulates of  Euclid16 deals with the two most important issues in this context, the parallel postulate and the definition of equality of ratios.