False position method ibn Luqa (10th century), an Arab mathematician from Baalbek, Lebanon. He justified the technique by a formal, Euclidean-style geometric proof. Within the tradition of medieval Muslim mathematics, double false position was known as "hisāb al-khaṭāʾayn" ("reckoning by two errors"). It was used for centuries to solve practical problems such as commercial and juridical questions (estate partitions according to rules of Quranic inheritance), as well as purely recreational problems. The algorithm was often memorized with the aid of mnemonics, such as a verse attributed to Ibn al-Yasamin and balance-scale diagrams explained by al-Hassar and Ibn al-Banna, all three being mathematicians of
Midfielder as wingers behind a lone striker. In a three-man midfield, specialist wingers are sometimes deployed down the flanks alongside the central midfielder or playmaker. Even more demanding is the role of wing-back, where the wide player is expected to provide both defence and attack. As the role of winger can be classed as a forward or a midfielder, so this role blurs the divide between defender and midfielder. A winger is an attacking midfielder who is stationed in a wide position near the touchlines. Wingers such as Stanley Matthews or Jimmy Johnstone used to be classified as forwards in traditional