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 Midfielder A midfielder is an association football position. Midfielders are generally positioned on the field between their team's defenders and forwards. Some midfielders play a disciplined defensive role, breaking up attacks, and are otherwise known as defensive midfielders. Others blur the boundaries, being more mobile and efficient in passing: they are commonly referred to as deep-lying midfielders, play-makers, box-to-box, or holding midfielders. The number of midfielders on a team and their assigned roles depends on the team's formation; the collective group of these players on the field is sometimes referred to as the midfield. Most managers assign at least one