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key term - Al-kitab al-mukhatasar fi hisab al-jabr wal-muqabala

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Definition

Al-kitab al-mukhatasar fi hisab al-jabr wal-muqabala is a significant mathematical treatise written by the Persian mathematician Muhammad ibn Musa al-Khwarizmi in the 9th century. This work laid the foundations for algebra and introduced systematic methods for solving linear and quadratic equations, reflecting the Islamic contributions to mathematics and astronomy during the medieval period. Its impact extended beyond the Islamic world, influencing European mathematical practices in the centuries to follow.

5 Must Know Facts For Your Next Test

  1. Al-kitab al-mukhatasar fi hisab al-jabr wal-muqabala was one of the first texts to systematically present algebra as a distinct mathematical discipline.
  2. The term 'al-jabr' in the title translates to 'completion' or 'reunion,' reflecting the process of solving equations by balancing and combining terms.
  3. Al-Khwarizmi's work established rules for solving both linear and quadratic equations, making mathematics more accessible and practical.
  4. The book also included applications of algebra to real-world problems, such as inheritance, land distribution, and trade.
  5. The influence of this text can be seen in later European mathematics, especially during the Renaissance when it was translated into Latin, helping to spark advancements in mathematical thought.

Review Questions

  • How did al-kitab al-mukhatasar fi hisab al-jabr wal-muqabala contribute to the development of algebra?
    • Al-kitab al-mukhatasar fi hisab al-jabr wal-muqabala played a crucial role in establishing algebra as a distinct field of study. Al-Khwarizmi organized mathematical principles systematically, providing methods to solve linear and quadratic equations that were previously not clearly defined. This work transformed algebra from a collection of techniques into a structured discipline, laying the groundwork for future developments in mathematics.
  • In what ways did the concepts presented in al-kitab al-mukhatasar fi hisab al-jabr wal-muqabala influence later European mathematics?
    • The concepts from al-kitab al-mukhatasar fi hisab al-jabr wal-muqabala significantly influenced European mathematics by introducing systematic approaches to solving equations. As the text was translated into Latin during the Renaissance, it spread its ideas across Europe, leading to greater interest in algebraic methods. This contributed to the development of more advanced mathematical theories and practices, ultimately shaping modern mathematics.
  • Evaluate the broader significance of al-kitab al-mukhatasar fi hisab al-jabr wal-muqabala within the context of Islamic contributions to science and knowledge during its time.
    • Al-kitab al-mukhatasar fi hisab al-jabr wal-muqabala represents a key moment in Islamic contributions to science and knowledge, showcasing how scholars like al-Khwarizmi advanced mathematical thought while integrating it with practical applications. This treatise not only provided a foundational text for future mathematicians but also exemplified the Islamic Golden Age's emphasis on learning and knowledge exchange. The book's influence transcended cultural boundaries, demonstrating how Islamic scholarship played an essential role in shaping global intellectual traditions.
Al-kitab al-mukhatasar fi hisab al-jabr wal-muqabala - (History of Science) - Vocab, Definition, Explanations | Fiveable | Fiveable