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Primary sourceDocument

Risālah fī qismat rubʿ al-dāʾirah

Omar Khayyám

Manuscript of Khayyám's treatise on dividing a quarter circle, linked to his methods for solving cubic equations.

This manuscript shows Khayyám's geometric approach to mathematics, directly from his own treatise.

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Open manuscript book with handwritten Arabic script on yellowed pages, geometric diagrams of circles, arcs and straight lines on the left and right pages, and a hand holding the book's edge at the top.
First page of Risālah fī qismah rubʿ al-dāʾirah. Grand Ayatollah Boroujerdi's digital Library.

About this source

What it is

This manuscript page shows Khayyám's treatise on dividing a quarter circle, including geometric diagrams of circles, arcs and straight lines. It is held in the Grand Ayatollah Boroujerdi's digital library.

Why it matters

This treatise is connected to Khayyám's famous work on solving cubic equations using geometric methods. The diagrams on this page show how he used geometry to work through mathematical problems, a technique that was ahead of its time in the Islamic mathematical tradition.

Look closer

  • What do the geometric diagrams tell us about how Khayyám visualised mathematical problems?
  • Why might combining text and diagrams have been useful for explaining geometry?
  • What does the hand holding the book's edge in the image remind us about how these manuscripts are handled and studied today?

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

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Front cover of a green cloth book titled Rubáiyát of Omar Khayyám, the Astronomer-Poet of Persia, with gold lettering, a gold floral emblem, black decorative arch border, and publisher Houghton, Osgood & Co. at the bottom.Book

Secondary source

Rubáiyát of Omar Khayyám

Edward FitzGerald · 1878

Manuscript page numbered 46 in Arabic script, with a geometric diagram of a rectangle with both diagonals drawn and lettered corners at the top of the page, above several lines of handwritten Arabic text in black ink on aged, yellowish paper.Document

Primary source

Khayyam Geometry Manuscript

Omar Khayyám

Book

Secondary source

The Rubaiyat of Omar Khayyam (First Edition)

Edward FitzGerald · 1859

Painted manuscript page in Persian miniature style: a seated bearded ruler in a crown gestures toward a woman in green kneeling on a rug, while a small attendant in a blue robe stands at a doorway on the left. Persian text fills the bottom panel.Book

Secondary source

Chahar Maqala

Nizami Aruzi · 1155–1157

Wide view of the central courtyard of the Jameh Mosque of Isfahan under a blue sky with clouds. Tall iwans with ornate tiled and muqarnas vaulting frame the square, with a blue-tiled fountain pool in the foreground and a pair of minarets rising behind the central portal.Artifact

Secondary source

Jameh Mosque of Isfahan

841 (rebuilt 1086-1089 under Khayyám's patrons)

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