Descartes and Newton in dioptrics (for instance, Newton conducted a similar experiment at Trinity College, though using a prism rather than a sphere). In his Kitab Tanqih al-Manazir (The Revision of the Optics), Farisi also saved the latest advancements in color theory by Nasir al-Din al-Tusi on color odering. In contrast to Aristotle (d. 322 BCE), who had suggested that all colors can be aligned on a single line from black to white, Ibn-Sina (d. 1037) had described that there were three paths from black to white, one path via grey, a second path via red and the third path via green. Al-Tusi (ca. 1258) elaborated on this by stating that there are no less than five of such paths, via lemon (yellow), blood (red), pistachio (green), indigo (blue) and grey. No less than 23 intermediate colors on these paths were explicitly mentioned in this text. Fortunately this text was saved since Farisi included it in his Kitab Tanqih al-Manazir (The Revision of the Optics), which was copied numerous times until at least the nineteenth century as part of the textbook Revision of the Optics (Tanqih al-Manazir). Tusi's description of the relations between various colors effectively made color space two-dimensional. Robert Grosseteste (d. 1253) proposed an effectively three-dimensional model of color space. Number theory Farisi made a number of important contributions to number theory. His most impressive work in number theory is on amicable numbers. In Tadhkira al-ahbab fi bayan al-tahabb ("Memorandum for friends on the proof of amicability") introduced a major new approach to a whole area of number theory, introducing ideas concerning factorization and combinatorial methods. In fact Farisi's approach is based on the unique factorization of an integer into powers of prime numbers. While the Greek mathematician Euclid took the first step on the way to the existence of prime factorization, al-Farisi took the final step and stated for the first time the fundamental theorem of arithmetic. Works Asas al-qawa'id fi usul al-fawa'id (The base of the rules in the principles of uses) which comprises an introduction and five chapters dealing with arithmetic, notarial and sales rules, the areas of surfaces and solids, and the last two essays are on algebra. The book is a commentary on the treatise of Al-Baha'i uses in the arithmetic rules of Al-Khawam al-Baghdadi. Tanqih al-Manazir (Arabic: تنقيح المناظر ; The Revision of Ibn al-Haytham's Optics). He completed the writing of this