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 a wide midfielder, a shuttler, somebody who might be expected to cross a ball but was also meant to put in a defensive shift." A notable example of a right midfielder is David Beckham. The historic position of wing half (half-back) was given to midfielders who played near the side of the pitch. It became obsolete as wide players with defensive duties have tended to become more a part of the defence as full-backs. Defensive midfielders are midfield players who focus on protecting their team's goal. These players may defend a zone in front of their team's defence, or man