From: Thomas Hockey et al. (eds.). The Biographical Encyclopedia of Astronomers, Springer Reference. New York: Springer, 2007, pp. 623-624

Courtesy of

Khafrī: Shams al‐Dīn Muammad ibn Amad al‐Khafrī al‐Kāshī

Glen M. Cooper

Bornprobably Khafr near Shiraz, (Iran), circa 1470

Diedprobably (Iran), after 1525

Khafrī was an Iranian theoretical astronomer who produced innovative planetary theories at a time well beyond the supposed period of the decline of Islamic science. Little is known about his life. Various Shīʿī writers claim Khafrī as one of their own religious scholars, and the sources assert that he was influential in the program of the Safavid Shāh Ismāʿīl (died: 1524) to make Shīʿism the official Islamic sect of Iran. The fact that Khafrī wrote works in the fields of both religion and astronomy seems to indicate that at his time and place Islamic religious scholars saw no insuperable conflict between science and religion. This appears contrary to the traditional view that science and religion were constantly at odds in Islamic society, and that, long before the lifetime of Khafrī, religious scholars effectively squelched the scientific impulse in Islam. Other examples of Islamic scientists who also were religious scholars include Bahāʾ al‐Dīn al‐ʿĀmilī and Niām al‐Dīn al‐Nīsābūrī.

Khafrī's fame as an astronomer rests mainly on his astronomical treatise al‐Takmila fī shar “al‐Tadhkira” (The completion of the commentary on the Tadhkira). This was a commentary on Naīr al‐Dīn al‐ūsī's important astronomical treatise, al‐Tadhkira fī ʿilm al‐hayʾa (Memoir on astronomy). As was the custom of the time, in both the Arabic and Latin worlds, a scholar often presented his own theories within the context of a commentary on the work of an esteemed author.

Consistent with the Islamic tradition in theoretical astronomy, in which astronomers had sought to reform Ptolemaic astronomy by revising Ptolemy's planetary models into physically consistent forms, Khafrī presented new models. Ptolemy had devised models of planetary motion involving spheres that were required to rotate with nonuniform velocity with respect to poles (the most notorious being the equant) other than their centers. In particular, Khafrī presented new models for the motions of the Moon, the upper planets, and Mercury, some more successful than others in meeting the criticisms of earlier astronomers such as Ibn al‐Haytham.

Khafrī's model for the lunar motion combined the best features of two previous theories, namely those of Muʾayyad al‐Dīn al‐ʿUrī and Qub al‐Dīn al‐Shīrāzī. He managed to employ only spheres that moved uniformly around their own centers, the basic criterion for physical consistency in Islamic astronomy. Khafrī discussed various solutions to the irregular lunar motions, including those of ūsī, Shīrāzī, and himself. However, there are some problems with his model. Because he attempted to make the predictions of his model coincide as closely as possible with the Ptolemaic lunar model, especially at the critical points including quadrature, his model replicated certain errors of Ptolemy's model, including the absurd prediction that the Moon should appear twice its actual size. Ibn al‐Shāir had solved this problem, but Khafrī seems to have been unaware of his work. The fact that Khafrī adheres so closely to Ptolemy's observations and reproduces one of the major predictive failings of Ptolemaic theory suggests that Khafrī was more of a theorist than an observational astronomer.

Khafrī solved the equant problem for the upper planets, Mars, Jupiter, and Saturn, by following ʿUrī's model with a few adjustments, such as introducing a second deferent as well as an “epicyclet,” i. e., an epicycle on an epicycle. Again, this model essentially duplicates all of the Ptolemaic planetary positions while preserving a physically consistent model.

Khafrī described four such models for Mercury's motion, one devised by ʿAlī Qūshjī and three by him. Khafrī employed all of the techniques and theoretical mechanisms devised in the Islamic tradition of mathematical astronomy (the ūsī Couple, epicyclets, etc.) and, in each case, the result was a physically consistent model.

The work of Khafrī raises the important question of the status of theoretical models in science. In the Takmila, Khafrī offered several possible models for the motion of Mercury, each of which was essentially equivalent in predictive power. This seems to imply that for Khafrī, the model apparently was simply a tool for predicting planetary positions. If so, then Khafrī made a significant departure from his predecessors in the entire Graeco–Islamic tradition. Alternatively, Khafrī may have been attempting to find all the possible solutions to a scientific problem, from which the scientist must employ observational criteria to choose the most correct configuration. In any case, it is not yet known what impact, if any, the work of Khafrī had or whether it led to any broad reassessment of the aims of science in Islam.

Two other works by Khafrī are mentioned in several sources, but have yet to be studied: Muntahā al‐idrāk fī al‐hayʾa (The ultimate comprehension of astronomy), written as a refutation or a commentary on the Nihāyat al‐idrāk fī dirāyat al‐aflāk (The ultimate understanding of the knowledge of the orbs) of Shīrāzī; and all mā lā yanall (Resolution of that not [yet] solved).

Selected References

Al‐Khafrī, Shams al‐Dīn (1994). al‐Takmila fī sharḥ al‐tadhkira. (This work has been neither edited nor published in Arabic or English translation. The following manuscripts were consulted by Saliba (1994): Zāhiriyya Library, Damascus, MSS. 6727 and 6782; India Office Library, London, Arabic MS. 747; and Bibliothèque Nationale, Paris MS. Arabe 6085.)

Ragep, F. J. (1993). Naīr al‐Dīn al‐Ṭūsī's Memoir on Astronomy (al‐Tadhkira fī ʿilm al‐hayʾa). 2 Vols. New York: Springer‐Verlag. (Perhaps the most significant study to emerge thus far in the historiography of astronomy in Islam, in which al‐ūsī's treatise was pivotal.)

Rosenfeld, B. A. and Ekmeleddin Ihsanoğlu (2003). Mathematicians, Astronomers, and Other Scholars of Islamic Civilization and Their Works (7th–19th c.). Istanbul: IRCICA, pp. 313–314.

Saliba, George (1994). A History of Arabic Astronomy: Planetary Theories during the Golden Age of Islam. New York: New York University Press. (This is a collection of articles that are useful in that they probe deeply into several discrete figures and issues from the history of Islamic astronomy. Saliba provides helpful clarifications of a number of historical issues, including the nature of the apparent connection between the work of Islamic astronomers of the “Marāgha School” and the achievement of Nicolaus Copernicus.)

——— (1994). “A Sixteenth‐century Arabic Critique of Ptolemaic Astronomy: The Work of Shams al‐Dīn al‐Khafrī.” Journal for the History of Astronomy 25: 15–38. (Detailed survey of the al‐Takmila fī sharḥ al‐tadhkira from which the remarks of the present article were derived.)

——— (1996). “Arabic Planetary Theories after the Eleventh Century AD.” In Encyclopedia of the History of Arabic Science, edited by Roshdi Rashed, pp. 58–127. London: Routledge. (Important survey of the later period of theoretical astronomy in Islam. Presents many helpful descriptions and diagrams of planetary models, and traces the often subtle theoretical modifications from one model to the next.)

——— (1997). “A Redeployment of Mathematics in a 16th‐Century Arabic Critique of Ptolemaic Astronomy.” In Perspectives arabes et médiévales sur la tradition scientifique et philosophique grecque, edited by Ahmad Hasnawi, pp. 105–122. Paris: Peeters. (A speculative description of a possibly significant shift in understanding of the role of mathematical modeling in scientific theory which occurred late in the history of Islamic astronomy, in the work of Khafrī.)