The Tadhkira Fi Ilm Al Hayia (Arabic: تذكرة في علم الهيئة, “Memoir on Astronomy”) is a treatise on theoretical astronomy composed by Nasir al-Din al-Tusi (1201-1274), the Persian mathematician and astronomer who served at the Maragha Observatory under Ilkhanid patronage. Written in Persian rather than Arabic - unusual for a technical scientific work of its era - the Tadhkira represents al-Tusi's sustained attempt to reform Ptolemaic planetary theory by eliminating what he regarded as its mathematical inconsistencies, most notably the equant point, which Ptolemy had introduced to account for observed planetary motion but which violated the principle of uniform circular motion. The text became a foundational document of the Maragha school and circulated widely across the Islamic world and, eventually, into Latin European astronomical literature.

The Tadhkira is organized as a systematic exposition of the mathematical models underlying planetary motion. Al-Tusi's central contribution in the text is the device now known as the Tusi Couple - a geometric construction demonstrating that linear oscillatory motion can be generated from the combination of two circular motions, one circle rolling inside another of twice its radius. This mechanism allowed al-Tusi to reconstruct Ptolemaic planetary models in a form that preserved uniform circular motion throughout, replacing the equant with a geometrically equivalent but philosophically consistent alternative. The Tadhkira addresses the motions of the Moon, the Sun, and the five known planets, and includes discussion of cosmological structure consistent with an Earth-centered universe. Al-Tusi later produced an Arabic recension of the same work, expanding and revising portions of the Persian original.

The Tadhkira is regarded by historians of science as a key text in the history of planetary theory, and a focus of debate over transmission between the Islamic and European astronomical traditions. Scholars including E. S. Kennedy and George Saliba documented in the latter twentieth century that several geometric devices appearing in the Tadhkira - including the Tusi Couple - also appear, without attribution, in the work of Nicolaus Copernicus, particularly in the De Revolutionibus Orbium Coelestium (1543). The mechanism of transmission remains an open scholarly question. Some historians argue for direct manuscript contact, possibly through Byzantine intermediaries or Italian humanist channels; others hold that parallel independent discovery cannot be excluded. The question bears directly on how the origins of the Copernican revolution are understood. See Tadhkira Fi Ilm Al Hayia - History for fuller treatment. The Tychonic System represents one downstream development in the tradition of geocentric reform that the Maragha school's critiques helped make intellectually urgent.

No consensus exists on the transmission question. Historians of science are divided between independent parallel derivation and some form of direct or indirect manuscript transmission as explanations for the geometric correspondences between the Tadhkira and Copernicus's De Revolutionibus. The Maragha school's broader significance to the history of astronomy is not itself disputed, but its relationship to the Copernican revolution remains an active area of scholarly debate.

Independent Parallel Development
Some historians of science hold that the resemblances between al-Tusi's devices and Copernicus's are the result of independent derivation from shared Ptolemaic problems, and do not require positing manuscript transmission. See this viewpoint.

Direct Transmission to Copernicus
Other scholars argue that the specificity and multiplicity of shared geometric constructions make independent discovery implausible, and that some channel of transmission - direct or indirect - is the more parsimonious explanation. See this viewpoint.

Maragha School as Proto-Scientific Revolution
A broader historiographical position holds that the Maragha school, of which the Tadhkira is a central text, constitutes an autonomous scientific revolution in planetary theory that European astronomy absorbed rather than independently produced. See this viewpoint.

• Tadhkira Fi Ilm Al Hayia - History
• Tadhkira Fi Ilm Al Hayia - Debate
• Tusi Couple
• Maragha Observatory
• Nasir al-Din al-Tusi
• Ptolemaic System
• Tychonic System
• Copernican Revolution
• Islamic Astronomy

1. al-Tusi, Nasir al-Din. Tadhkira Fi Ilm Al Hayia. c. 1260. Persian recension; Arabic

recension composed subsequently.

1. Kennedy, E. S. “Late Medieval Planetary Theory.” Isis 57, no. 3 (1966): 365-378.
2. Saliba, George. A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam. New York: New York University Press, 1994.
3. Saliba, George. Islamic Science and the Making of the European Renaissance. Cambridge,

MA: MIT Press, 2007.

1. Ragep, F. J., ed. and trans. Nasir al-Din al-Tusi's Memoir on Astronomy (al-Tadhkira fi 'ilm al-hay'a). 2 vols. New York: Springer, 1993. The standard critical edition

and translation.

1. Swerdlow, Noel M. “The Derivation and First Draft of Copernicus's Planetary Theory.”

Proceedings of the American Philosophical Society 117, no. 6 (1973): 423-512.