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Primary sourceBookc. 820

Al-Jabr

Muḥammad ibn Musa al-Khwarizmi · c. 820

Al-Khwarizmi's treatise on algebra, written around 820, the first text to treat algebra as its own subject and the source of the word 'algebra'.

This is al-Khwarizmi's own treatise, the founding text of algebra and the source of its name.

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Manuscript title page in Arabic script with a decorated gold-and-brown border. The large heading reads the title of al-Khwarizmi's algebra work, with smaller lines of text beneath in a calligraphic hand, on aged parchment.
Title page from a copy of al-Khwarizmi's Al-Jabr (The Concise Book of Calculation by Restoration and Balancing), c. 820.

About this source

What it is

Al-Jabr is an Arabic mathematical treatise written by al-Khwarizmi around 820 in Baghdad. It explains how to solve equations by 'restoring' (al-jabr) and 'balancing' (al-muqabala) terms, and also covers area, volume and inheritance calculations.

Why it matters

This book gave algebra its name and its first systematic treatment as an independent branch of mathematics. Translated into Latin in the twelfth century, it became the standard algebra textbook in European universities for centuries, showing how al-Khwarizmi's work under Caliph al-Ma'mun shaped mathematics far beyond Baghdad.

Look closer

  • Why do you think al-Khwarizmi wrote out equations in words instead of symbols?
  • What does the long section on inheritance tell you about why people needed algebra in his society?
  • How might a book written in Arabic have reached students in medieval Europe?

This book is part of the curated material that grounds the AI version of Al-Khwarizmi on Humy.ai — when students ask about related events, the AI can quote it and cite it.

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Open manuscript of two facing pages covered in handwritten Arabic script in brown ink on aged, yellowed paper, with small geometric diagrams drawn in red ink with labeled letters near the bottom of each page. The page edges are dark against a black background.Book

Primary source

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Muḥammad ibn Musa al-Khwarizmi · 1342

Black-and-white scan of a medieval Latin manuscript page. A large decorated initial D with ornate knotwork sits at upper left, and the text begins with 'DIXIT algorizmi' in dense handwritten script. A folio number 104 appears at top right.Book

Secondary source

Dixit Algorizmi

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Two facing pages of an Arabic manuscript with black ink text in the margins and a colored diagram in the center: a blue and red river system with branching channels and lakes, a green rectangular panel on the left, and a brown curved shape on the right. Labels in Arabic are written along the diagram.Artifact

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Secondary source

Zij Manuscript, Corpus Christi College MS 283

Title page of an Arabic book. Large decorative calligraphic title reads الفهرست لابن النديم. Below is the date سنة ١٣٤٨ هـ. Lower text gives the publisher's details in Arabic, and a faint pencil note in Latin letters reads al-Nadim, Ibn-abi-Ya'qub at top left.Book

Secondary source

Al-Fihrist

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