The Compendious Book on Calculation by Completion and Balancing

by Muḥammad ibn Mūsā al-Khwārizmī, Al-khowârizmî

Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala (Arabic for "The Compendious Book on Calculation by Completion and Balancing", in Arabic script 'الكتاب المختصر في حساب الجبر والمقابلة'), also known under a shorter name spelled as Hisab al-jabr w’al-muqabala, Kitab al-Jabr wa-l-Muqabala and other transliterations) is a mathematical book written in Arabic, in approximately AD 820 by the Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī.

The term "algebra" is derived from the al-ğabr in the title of this book, which is considered the foundational text of modern algebra. The al-ğabr provided an exhaustive account of solving for the positive roots of polynomial equations up to the second degree, and introduced the fundamental methods of "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation.

Several authors have also published texts under the name of Kitāb al-ğabr wa-l-muqābala, including Abū Ḥanīfa al-Dīnawarī, Abū Kāmil Shujā ibn Aslam, Abū Muḥammad al-ʿAdlī, Abū Yūsuf al-Miṣṣīṣī, 'Abd al-Hamīd ibn Turk, Sind ibn ʿAlī, Sahl ibn Bišr, and Šarafaddīn al-Ṭūsī.

Genres: Mathematics, Nonfiction, Science

First published January 1, 820

About the author

(perhaps 780 to perhaps 850)

Works of Persian astronomer al-Khwarizmi, fully named Muhammad ibn-Musa al-Khwarizmi, introduced Arabic numerals and algebraic concepts to western mathematics; from his name derives the word algorithm.

This polymath produced vastly influential works in geography. Around 820, people appointed him as the head of the library of the house of wisdom in Baghdad.

See also: محمد بن موسى الخوارزمي

https://en.wikipedia.org/wiki/Al-Khwa...

Reviews

[Tyler · Rating 3 out of 5]

Overall a fairly complex text towards the end. The translators footnotes really helped, of course, and they give you an indication why it was so complex: Abu Hanifah and Islamic inheritance law in general. It can be a confusing mess, but overall very informative as to the substance of the most influential Algebraic text in Islamic history, aside from Abu Kamil’s Algebra. I liked his proof of Pythagorean’s Theorem more than what was in Euclid’s Elements as well (I.47). Overall though, you wont find any problems that aren’t in Diophantus’ Arithmetica. There is a two-variable problem towards the end, but that one gets solved by inheritance law. Overall this was more historically informative than mathematically influential in my opinion, but hey I love history so I gave this 3/5 stars.

[Christopher Byram · Rating 3 out of 5]

I first discovered this book when it was referenced on Khan Academy, in the article 'READ: Thank You for Algebra: Muhammad Ibn Musa al-Khwarizmi', in Unit 4, in the course 'World History Project - Origins to the Present'. The article states that the author is best known for revolutionizing algebra and arithmetic. He didn’t invent algebra, but he did improve the techniques we use to solve algebraic problems. In Arabic, the title of this book is, 'al-Kitāb al-mukhtasar fīhisāb al-jabr wal-muqābala', ('The Compendious Book on Calculation by Completion and Balancing'), and it is is where we get the word 'algebra' (from 'al-jabr' or 'balancing'). This book offered detailed instructions for solving linear and quadratic equations, earning the author the title "father of algebra". Also, the English word 'algorithm' comes from the Latinized spelling of the author's name, 'Algorismi.'

[Faizal Zahid · Rating 5 out of 5]

Bangga dengan al-Khawarizmi tak guna juga tapi tak pernah selak karyanya yang Barat pun baca dan terjemah ke dalam bahasa mereka, kan? Just wow! Mendalam dan terperinci contoh-contoh yang tokoh algebra ni bagi dalam macam-macam aplikasi matematik terutamanya dalam 'al-jabbar wa muqabalah' yang diterjemahkan dalam Latin sebagai 'algebrae et muqabolae' sebab susah nak terjemah secara harfiah. Instead of translating it, they kept the name 'aljabbar' and turned it into 'algebra'. :)

Suka intro dan penutup oleh al-Khawarizmi yang disandarkan kepada Pemilik Segala Ilmu :)

Kena baca banyak kali ni. Insya-Allah, kalau tiba masanya, will read again!