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Primary sourceBook1831 translation of 9th-century original

The Algebra of Mohammed ben Musa (English translation)

Fredrick Rosen · 1831 translation of 9th-century original

A page from Rosen's 1831 English translation of al-Khwarizmi's algebra, showing one of his worked geometric problems.

This page presents al-Khwarizmi's own geometric method for solving equations, translated into English.

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Scanned page of an English translation of al-Khwarizmi's algebra text, with printed paragraphs of mathematical prose. Below the text is a diagram of a large square divided into smaller squares labeled G, B, D, zs, H, and A, with the caption 'Demonstration of the Case: a Square and twenty-one Dirhems are equal to ten Roots.'
Muhammad ibn Musa al-Khwarizmi, Algebra, trans. Frederic Rosen, 1831.

About this source

What it is

This page comes from Frederic Rosen's 1831 English translation of al-Khwarizmi's algebra text, originally written in Arabic. It shows a worked mathematical demonstration with a geometric diagram illustrating how a square and a number of units relate to a number of roots, a type of problem typical of al-Khwarizmi's method.

Why it matters

This is the version through which most English-speaking students have read al-Khwarizmi's word problems and geometric proofs. It shows his method of solving equations by relating numbers to geometric shapes, a technique that laid groundwork for algebra as a field of study.

Look closer

  • Why might al-Khwarizmi have used geometric diagrams to solve what we now think of as algebra problems?
  • What does the labelling of the diagram with letters tell you about how mathematical explanations were communicated before modern notation?
  • How is this method similar to or different from how you solve equations in school today?

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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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.Book

Primary source

Al-Jabr

Muḥammad ibn Musa al-Khwarizmi · c. 820

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

Algebra Manuscript, Bodleian MS. Huntington 214

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

Primary source

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Secondary source

Zij Manuscript, Corpus Christi College MS 283

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