  In the Algebra, Khayyam sets out to deal systematically with all fourteen types of cubic equations. He solves each one in sequence again through the use of intersecting conic sections. In an algebra where powers of x corresponded to geometrical dimensions, the solution of cubic equations was the apex of the discipline. Nevertheless, even here Khayyam was able to advance algebra by considering its unknowns as dimension-free abstractions of continuous quantities.15 Khayyam also considers circumstances under which certain cubic equations have more than one solution. Although he does not handle this topic perfectly, his effort nevertheless stood out from previous efforts.