numeral system, abu'l Wafa was able to extract roots. 980: al-Baghdadi Studied a slight variant of Thabit ibn Qurra's theorem on amicable numbers. Al-Baghdadi also wrote about and compared the three systems of counting and arithmetic used in the region during this period. Eleventh Century Mathematics 10481131: Omar Khayyam. Persian mathematician and poet. "Gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections.". Extracted roots using the decimal system (the Indian numeral system). Twelfth Century Cartography 1100–1165: Muhammad al-Idrisi, aka Idris al-Saqalli aka al-sharif al-idrissi of Andalusia and Sicily. Known for having drawn some of the most advanced ancient world maps. Mathematics 1130–1180: Al-Samawal. An important member of al-Karaji's school of algebra. Gave this definition of algebra: "[it is concerned] with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known." 1135: Sharaf al-Dīn al-Ṭūsī. Follows al-Khayyam's application of algebra of geometry, rather than follow the general development that came through al-Karaji's school of algebra. Wrote a treatise on cubic equations which describes thus: "[the treatise] represents an essential contribution to another algebra which aimed to study curves by means of equations, thus inaugurating the beginning of algebraic geometry." (quoted in ). Thirteenth Century Chemistry Al-Jawbari describes the preparation of rose water in the work "Book of Selected Disclosure of Secrets" (Kitab kashf al-Asrar). Materials; glassmaking: Arabic manuscript on the manufacture of false gemstones and diamonds. Also describes spirits of alum, spirits of saltpetre and spirits of salts (hydrochloric acid). An Arabic manuscript written in Syriac script gives description of various chemical materials and their properties such as sulfuric acid, sal-ammoniac, saltpetre and zaj (vitriol). Mathematics 1260: al-Farisi. Gave a new proof of Thabit ibn Qurra's theorem, introducing important new ideas concerning factorization and combinatorial methods. He also gave the pair of amicable numbers 17296, 18416 which have also been joint attributed to Fermat as well as Thabit ibn Qurra. Astronomy Jaghmini completed the al-Mulakhkhas fi al-Hay’ah ("Epitome of plain theoretical astronomy"), an astronomical textbook which spawned many commentaries and whose educational use lasted until the 18th century. Miscellaneous Mechanical engineering: Ismail al-Jazari described 100 mechanical devices, some 80 of which are trick vessels of various kinds, along with instructions on how to construct them. Medicine; Scientific method: Ibn Al-Nafis (1213–1288) Damascene physician and anatomist. Discovered the lesser circulatory system (the cycle involving the