Solving algebraic problems using geometric tools was not new; in the case of quadratic equations methods like this date back at least as far as the Greeks and probably to the Babylonians.  Predecessors such as al-Khwārizmī (early 9th century) and Thābit ibn Qurra (836–901 CE) already had solved quadratic equations using the straightedge and compass geometry of Euclid’s Elements.  Since negative numbers had not yet been conceived, Muslim mathematicians needed to solve several different types of quadratic equations: for instance, x2 = mx + n was fundamentally different from x2 + mx = n. For cubics, there are fourteen distinct types of equation to be solved. In his “Treatise on Demonstration of Problems of Algebra”14 Khayyam notes that four of these fourteen have been solved and says that al-Khāzin (d. 961/971) was one of the authors, having solved a problem from Archimedes' treatise On the Sphere and Cylinder that al-Māhānī (fl.  ca. 860) had previously converted into a cubic.