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Khayyam, ‘Umar al-

Although today most renowned for his poetry (especially the quatrains collectively known as The Rubaiyat), ‘Umar al-Khayyam was foremost a mathematician, astronomer, and philosopher. His work on the solutions of cubic equations, the parallel postulate and other issues in Euclidean geometry, and solar *calendar reform each advanced discipline boundaries significantly, and in some cases re-invented them.

Born in Nishapur around 1048 shortly after the Seljuk Turks conquered the area, Khayyam was often beset with political difficulties. He began the life of a scholar at an early age. By 1070, when he received the support of chief justice Abu Tahir of Samarkand, he had already written treatises on *algebra, *arithmetic, and music. At Samarkand he completed his most important work, the Treatise on the Proofs and Problems of Algebra, in which he deals particularly with the solutions of cubic equations. Methods to solve quadratics had been known for millennia; in particular, *al-Khwarizmi’s famous Algebra dealt extensively with them. Without a theory of negative numbers, the equations x² = mx + n and x² + mx = n (for example) must be dealt with separately; al-Khwarizmi had established a classification of the different “species” of linear and quadratic equations that can arise. Khayyam extended this to cubics, arriving at twenty-five different types. For the thirteen cubics that cannot be reduced immediately to equations of lower order, Khayyam applies geometric techniques: he treats the parameters as line segments, and constructs various conic curves from them. Appropriate intersections of these conics produce line segments that satisfy the given equations. Four of the irreducible cubics had been solved by previous authors; in the Algebra, solutions are given to all thirteen. Khayyam also searched for numeric solutions: as he says, “We have tried to express these roots by algebra but have failed. It may be, however, that men who come after us will succeed”—foreshadowing the work of sixteenth-century Italian mathematicians, especially Gerolamo Cardano. Khayyam’s time at Samarkand also produced Difficult Problems of Arithmetic, in which “Hindu methods” of finding square and cube roots are extended to roots of arbitrary order. This work is now lost, but evidence of later writers suggests that Khayyam used the binomial expansion (a + b)ⁿ = aⁿ + na^n-1b + … nab^n-1 + bⁿ to develop his procedure.

In 1074, with the invitation of the Seljuk sultan Malikshah and his vizier Nizam al-Mulk, Khayyam traveled to Isfahan to supervise its new observatory and to establish an astronomical program geared to reforming the calendar for agricultural and economic purposes. Although he was viewed with suspicion for his supposed atheist tendencies, his time at Isfahan was one of the most peaceful and productive periods of his life. Khayyam’s proposed calendar, never implemented, is actually a better fit to the true solar year than the Gregorian calendar. He also supervised the construction of the Zij Malikshah, an astronomical handbook of which only a fragment, a small star catalogue, survives. Khayyam’s major mathematical work composed in Esfahan, the Difficulties in the Postulates of Euclid, contains two major contributions. The first is his treatment of *Euclid’s parallel postulate, the assertion that if two lines cross a given line segment so that the interior angles are less than two right angles, they must eventually meet on that side of the given segment. Many attempts to prove this postulate were made from Greek times up to the discovery of non-Euclidean geometry. Khayyam’s analysis avoids the common trap of assuming implicitly some other statement that turns out to be equivalent to the parallel postulate itself. Instead, he forms what was eventually to be called the “Saccheri quadrilateral,” which is constructed by drawing two equal line segments perpendicularly to either end of a straight line, and connecting the other ends. He appeals to a principle in a (now lost) work of Aristotle, namely, that two convergent lines must meet, to demonstrate that the quadrilateral in fact must be a rectangle. The second contribution in Difficulties was a twofold improvement to the theory of ratios expounded in Euclid’s Elements Book V. Muslim scientists had been dissatisfied with Euclid’s definition of the equality of ratios, and had proposed an alternate approach known as the anthyphairetic definition. Khayyam demonstrates that this is logically equivalent to Euclid, and thus Book V does not have to be rewritten to take into account the substituted definition. Khayyam also worked with the definition of compound ratios, leading to a consideration of ratios of magnitudes as a new kind of number, thus foreshadowing the emergence of irrational numbers and the real number continuum.

The deaths of both of Khayyam’s patrons made it difficult for him to continue his work after 1092. His fall from grace led to the withdrawal of funding for the observatory, and he spent some effort trying to convince the Seljuk court to restore it. He eventually left Esfahan for Merv, the site of the new Seljuk capital in 1118, where he wrote a number of works on topics including algebra, mechanics, astronomy, and geography. He died around 1131, and was buried according to his request in Esfahan, where his tomb still exists today.

In addition to his scientific and poetic writings Khayyam wrote several philosophical treatises, influenced strongly by *Ibn Sina (Avicenna). They include discussions on the subject of a universal science and on questions of the universality of existence. It is difficult to determine Khayyam’s own perspective on these and other philosophical questions, since the authenticity of many of the existing poetic writings is in doubt and the philosophical treatises may have been influenced by Khayyam’s patrons. However, his astronomical and especially his mathematical writings are an enduring testament to a powerful scholar who pursued both foundational questions and the frontiers of science.

See also Astronomy, Islamic; Geography, chorography; Music theory; Planetary tables

Bibliography

Rashed, Roshdi and Bijan Vahabzadeh. Omar Khayyam the Mathematician. New York: Bibliotheca Persica Press, 2000.

Sayili, Aydin. The Observatory in Islam and its Place in the General History of the Observatory. New York: Arno Press, 1981 (reprint of 1960 edition).

Vahabzadeh, Bijan. Al-Khayyam’s Conception of Ratio and Proportionality. Arabic Sciences and Philosophy (1997) 7: 247–263.

GLEN VAN BRUMMELEN AND JULIA XENAKIS

Khwarizmi, Al-

Abu Ja‘far Muhammad ibn Musa al-Khwarizmi is remembered as the founder of *algebra; however, he was a scholar with interests and writings ranging across most of the ancient mathematical sciences. As his name indicates, he was probably of central Asian origin, although little else is known of his early life. From the dedications of his works, it is clear that he wrote for the Abbasid Caliph al-Ma’mun (813–833 C.E.) and was an active member of the circle of scholars in ninth century Baghdad, associated with the *Bayt al-hikma. These scholars worked for many patrons of the highest political and social circles—including caliphs and viziers—and produced a body of knowledge in Arabic that became the basis for advances in Islamic philosophy, medicine, mathematics, and engineering (Gutas). Before he died, sometime in the middle of the century, al-Khwarizmi’s fame was established on the basis of his written works.

Early in his reign, al-Ma’mun expressed a desire for practical *astrology and the mathematics required to support its application. Al-Khwarizmi filled this bill and more. His most famous text was the Handbook for Calculation by Completing and Balancing (Kitab al-muktasar fi hisab al-jabr wa’l-muqabalah). As the title indicates, the book demonstrates two main processes for solving equations. While he may have found both methods in Diophanes’ Arithmetic and probably derived some of his terminology from Indian mathematical practice, it was al-Khwarizmi who brought these elements together. He shows that solvable equations take one of six standard forms. The remainder of the book deals with the practical applications of algebra to problems of inheritance, trade, and legacies, and he uses geometrical figures to explain equations. Confusing and ironic as it may be, al-Khwarizmi did not use any kind of numerical symbols or algebraic notation—all problems were discussed in words. This work became the foundational text of algebra, even within his lifetime. The Latin translation of this text was one of the crucial elements in the so-called Twelfth-Century Renaissance.

Also important to the history of mathematics, al-Khwarizmi wrote a small work on Calculation with Hindu Numerals. This book was clearly written after the Algebra, to which it refers. Like the Algebra, it appears to be the first work of its kind, treating the Hindu numbers and place-value notation as derived from Indian mathematics. It teaches the use of the numerals, the basic arithmetical operations, fractions, and the extraction of square roots. This work was not of great consequence in the Arabic-speaking world and the Arabic original has not survived. However, it had a revolutionary impact in Europe, in its Latin translation titled Algoritmi de numero Indorum (Khwarizmi on Indian Numbers), the deformation of his name yielding the modern mathematical term, algorithm. His third major work was his astronomical tables, or Zij al-Sindhind. This book described the positions of the planets, the Moon, and the Sun, based in a calendar and a specific location. It then included the tables and the instructions for computations of the positions of the heavenly bodies. Like the mathematical works, this was based on a Sanskrit original, known as Siddhanta. His tables indicate familiarity with Greek and Persian tables, as well as the Indian text; as in his other works, he was attempting a synthesis of the knowledge from the legacy of sources created in earlier civilizations. Surprisingly, none of the tables was correlated with observation, even though contemporary Baghdadi astronomers had already found more accurate values for some astronomical phenomena. Perhaps most surprising, the original text was based on the Yazdigird III calendar rather than the Hijra calendar. Because of its practical importance, this work had wide diffusion, appearing in Muslim Spain within his lifetime. Here, his original tables were studied by *Maslama of Madrid and his pupils whose adaptation, more accurate than the original, adjusted the tables to make them useful to astronomers in the West. This version was then translated by *Adelard of Bath and *Pedro Alfonso, and it is only this Latin version that survives complete whereas in Arabic only selections from the original survive.

Al-Khwarizmi’s two other surviving works are the Geography and the Extraction of the Jewish Calendar. It appears that the Geography represents an important advance over *Ptolemy’s work of the same name. It has been speculated that al-Khwarizmi’s work was based on a world map constructed by a collection of scholars for al-Ma’mun; the Geography represents superior knowledge of the Islamic lands and the areas visited by Muslim traders and merchants. The work on the Jewish calendar is curious. He says that he wrote it because an explanation of that calendar was necessary for those who happen to use it. Its occasion or purpose remains obscure; perhaps it was used by historians and writers trying to reconcile the differences between the Islamic and Christian calculations of the annus mundi.

Al-Khwarizmi wrote several other books which do not seem to have survived: a Book on the Construction of the Astrolabe, a Book on the Use of the Astrolabe, a Book of the Sundial, and a Chronicle which is frequently quoted by later historians.

Al-Khwarizmi is one of the most influential medieval mathematicians and astronomers. While his creativity was inspired by borrowing, the developments, especially of algebra, were his own. Even though he was only one of a circle of savants working in al-Ma’mun’s Baghdad, he is the only one who created a branch of knowledge and gave his name to a process: algebra and algorithm. Because he brought disparate elements together in a new structure of scientific knowledge, others were able to advance the science beyond his foundations. It is fair to characterize his work as more “practical” than “theoretical”: his algebra, his astronomical tables, his geography, and his lost works all fulfill useful purposes. But precisely for this reason his works endured, especially in Western Europe.

See also Astronomy, Islamic; Commercial arithmetic; Geography, chorography; Planetary tables

Bibliography

Al-Khwarizmi. The Astronomical Tables of al-Khwarizmi. Edited by Otto Neugebauer. Copenhagen: Royal Danish Academy of Sciences and Letters, 1962.

Gutas, Dimitri. Greek Thought, Arabic Culture. London: Routledge, 1998.

Kennedy, E.S. “Al-Khwarizmi on the Jewish Calendar.” Scripta Mathematica (1964) 27: 55–59.

———. A Survey of Islamic Astronomical Tables. Philadelphia: American Philosophical Society, 1956.

Pingree, David. “Indian Astronomy in Medieval Spain.” In From Baghdad to Barcelona, 2 vols. Edited by Julio Samso and Josep Casulleras. I: 39–48 Barcelona: Anuari de Filologia XIX, 1996.

Roshdi, Rashid. “Al-Khwarizmi’s Concept of Algebra.” In Arab Civilization: Challenges and Response. Edited by G.N. Atiyeh and I.M. Oweiss. 98–111. Albany: SUNY Press, 1988.

Van Dalen, Benno. “Al-Khwarismi’s Astronomical Tables Revisited.” In Samso and Casulleras, I: 195–252.

MICHAEL C. WEBER

Kilwardby, Robert

Robert Kilwardby died at the papal court in Viterbo, Italy, on September 11, 1279. Although aspects of his career as an intellectual and churchman are known, nothing is really known about his early life except that he studied at Paris. It would be nice to know if he studied with the natural philosopher Richard Fishacre at Oxford in the early 1240s, for instance: it is possible and some of their ideas are similar. He was teaching in the arts faculty of the University of Paris in the late 1240s but left sometime around 1250 to begin the study of theology. This switch is of great significance when trying to understand his central role in the *Condemnation of 1277. As a member of the arts faculty in the 1240s Kilwardby could not teach theology or touch on theological issues. His reputation as one of the most able commentators on Aristotle during this period still stands: no mean accomplishment for it was only just at this moment that Aristotle was really being read and taught in Christian Europe. Kilwardby would later come to be highly regarded as a theologian and this reputation, combined with his elevation in 1273 to the office of Archbishop of Canterbury, made him a powerful churchman. As a churchman he appears to have been extremely conscientious in his duties—and that was not universally true in the Middle Ages—and known for his piety. He went on a pastoral visitation of his province, for example, despite the invariable hardships of sustained travel in those days.

Among Kilwardby’s most important works are De ortu scientiarum (1250); his Sentences-commentary (1252); and his Letter to Peter Conflans (1277). Perhaps the common theme of these works is an interest in harmonizing oppositions. For example, in a short metaphysical work, De natura relationis, Robert tries to show that a substance can also be a relation. While this claim would confound anyone who had read Aristotle’s Categories, any reader of his Metaphysics would likewise be amazed at Kilwardby’s argument in his Sentences-commentary that one and the same thing (res) can be genus, species, and individual substances. However, it must not be thought that Kilwardby was dismissive of Aristotle or that he had some perverse cast of metaphysical mind. In fact, intense scrutiny of Aristotle and radical reworkings of his categories of thinking were pretty much the bread and butter of philosophers and theologians in the second half of the thirteenth century. Henry of Ghent and *Johannes Duns Scotus are the most famous of Aristotle’s transformers, of course, but like Kilwardby they brought a fundamentally theological vision to bear on Aristotle and alter his categories of thought for deep, thoroughly worked out, theological reasons. Henry and Scotus were thoroughgoing metaphysicans but Robert often tried to justify his transformations of Aristotle by appealing to biology.

Robert Kilwardby (left) performs the Archbishop of Canterbury’s traditional ceremonial duty at the coronation of Edward I (r. 1272–1307) as king of England at Westminster Abbey in August 1274. (Color lithograph c. 1910.) (Mary Evans Picture Library)

Although Robert Kilwardby had yet to study theology when he wrote his famous work on the origin and order of the sciences, De ortu scientiarum is nevertheless a remarkable presentation of Christian Platonism, a profoundly theological metaphysics, and this despite the fact that Aristotle’s Metaphysics is the most cited work within it and second most cited is the Posterior Analytics. But this is of a piece with Robert’s interest in reconciliation. Although Robert’s cosmology was thoroughly Platonic, his use of Aristotle was not mere window-dressing. Like Bonaventure, Robert argued that the inner reality of the physical world was music but unlike Bonaventure he wanted Aristotle as one of his authorities for his opinions. Thus Robert was the first to define music, a science that was taught as part of the *quadrivium in the arts faculty, as numerus harmonicus. He derived the idea of music as a mathematical science from Aristotle’s position in the Posterior Analytics that music is a subordinate science to *arithmetic, and so one of the scientiae mediae, sitting between mathematics and physics in the hierarchy of the sciences. Robert’s definition became a source for later medieval musical theorists who like him espoused a strongly Platonic cosmology: and it was a fairly common position in the Middle Ages to defend Platonism by the idea that music as a structuring principle of the natural order sat close to the core of reality.

Robert’s commitment to Platonism never left him and was certainly reinforced by his reading of Augustine and taking him as a mentor in theology after 1250. This theologico-philosophical position is the backdrop for Robert’s well-known, and much-debated, intervention in the academic affairs of the University of Oxford. There, in 1277, he condemned a number of propositions ranging from issues in grammar to natural philosophy. Among the issues condemned, and by far the most significant and wide-ranging, was the thesis that there is a single substantial form in man. Robert was a defender of the common position in the Middle Ages that the human being is made up of a plurality of substantial forms. This position was a commonplace in medical literature until the seventeenth century. His 1277 Letter to Peter Conflans is a defense of this thesis almost exclusively in terms of medicine and biology, albeit with a strong metaphysical accent. Defending the plurality thesis in this way, with reasoning drawn from embryology, comparative anatomy, and physiology was quite common. Famously, it was not the position held by *Thomas Aquinas, nor did Thomas draw on biology for his defense of the unicity thesis. Although there is debate about this, a consensus does exist that Robert did take a swipe at his Dominican confrere in 1277 when condemning the unicity thesis. However that may be, what is crucial here is that the plurality position suited Augustinian Platonism and a theology in which a powerful contrast exists between humans as divided in substance and God as utterly one in being. Robert had elaborate theological and scientific reasons for handing down his 1277 condemnations and his action cannot merely be cast as some “conservative backlash” against, or fear of, Arabo-Aristotelian scientism: and sadly, one reads such opinions in a fair chunk of the literature on Robert and 1277.

See also Aristotelianism; Music theory; Plato

Bibliography

Primary Sources

Robert Kilwardby. De ortu scientiarum. Albert G. Judy, ed. London: British Academy, 1976.

———. On Time and Imagination. O. Lewry, ed. Oxford: Oxford University Press, 1987.

———. Quaestiones in libros I-IV Sententiarum. Ed. Johannes Scheider (I); Gerhard Leibold (II); E. Gössmann, G. Leibold (III); Gerd Haverling (IV). Munich: Bayerisches Akademie der Wissenschaften, 1986–1995.

Secondary Sources

Judy, A.G. “Introduction.” In De ortu scientiarum. London: British Academy, 1976.

McAleer, G.J. The Science of Music: A Platonic Application of the Posterior Analytics in Robert Kilwardby, De ortu scientiarum. Acta Philosophica (2003) 12: 323–335.

———. The Presence of Averroes in the Natural Philosophy of Robert Kilwardby. Archiv für Geschichte der Philosophie (1999) 81: 33–54.

Sharp, D. E. The 1277 Condemnation of Kilwardby. New Scholasticism (1934) 8: 306–318.

———. The Philosophy of Richard Fishacre. New Scholasticism (1933) 7: 283–297.

Sommer-Seckendorff, Ellen Mary Frances. Studies in the Life of Robert Kilwardby. Rome: Istituto Storico Domenicano, 1937.

G.J. MCALEER

Kindi, Al-

Very little is known of the life of Abu Yusuf Ya’qub ibn Ishaq al-Kindi, called “The Philosopher of the Arabs”: descended from the south-Arabic tribe of Kinda (hence his name). He was born in Kufa (first capital of the Abbasid empire) in Iraq, around 800. He got his intellectual education first in Basra, of which his father was governor, then in Baghdad, where he carried on his scientific career and where he died, after 866. He was a member of a group of philosophers in the circle of the caliph al-Ma’mun (813–883) and the *Bayt al-Hikma and made some of the early translations of Aristotle, Proclus, and Plotinus from Greek, all of them now lost. Al-Ma’mun’s successor, al-Mu‘tasim, appointed al-Kindi as the tutor of his son Ahmad. Somehow out of favor during the reign of al-Wathiq, al-Kindi regained some favor with al-Mutawakkil before falling into disgrace due to the intrigues of other scientists (the Banu Musa or Abu Ma‘shar) who were also his rivals.

Al-Kindi then divided his activities between Kufa, Basra and Baghdad, the three most prestigious cities of the Abbassid empire, centers during the ninth century of an intense intellectual activity, supported by political power: the passage under the Arab domination of non-Arabic-speaking nations, heirs of rich intellectual traditions, induced a fertile cultural and social mixing. Contemporary to the studies of grammar, linguistics and hermeneutics in the schools of Kufa and Basra, the religious speculation, stirred by controversies arousing of the confrontation with believers of other religions (Christians, Jews, Zoroastrians…) became more dialectical. At the same time the Arabo-Islamic culture appropriated and developed for its own account scientific and philosophical elements elaborated in Persia, India, and and also Greece: the massive movement of translation of the Hellenistic heritage coincided with the first scientific researches. This century is one of the most brilliant of the universal history.

Al-Kindi is a good example of an encyclopedic thinker, nurtured on Greek thought and, at the same time, involved in the religious controversies of the time, he is the author of a very vast work, of which unfortunately very little is left: while the biobibliographer Ibn al-Nadim (writing approximately one hundred fifteen years after al-Kindi’s death) ascribes to him in his *Fihrist more than two hundred seventy works, no more than thirty have survived. Al-Kindi’s interests embraced almost all sciences, to which he developed, starting from the premises of Greek science, a personal and original interpretation. He is in particular the author of the most substantial work on optics since late antiquity.

Philosophy

Al-Kindi’s philosophy was especially indebted to *Plato and Aristotle, who for him had intrinsically the same doctrine (we recognize here one of the syncretistic aspects of late Greek thought). His philosophy integrates problems and concepts originating in various currents of Neoplatonism (Proclus, Plotinus). His thought is also closely related to kalam, or rational Islamic theology; in particular its mu’tazilite branch, which played an important role in the introduction of elements of Greek philosophy into the Islamic thought, as well as some of the key subjects he studies, such as the unicity of God, man’s free will, and the thesis of the “created” Qu’ran.

Al-Kindi, relying on the principle that reason is an attribute specific to mankind, considers that philosophy has to explain by its own methods the truths expounded in the Qu’ran in a condensed form. Inasmuch as for him, philosophical truth accords on the whole with revealed truth, there is no conflict between reason and religious faith. He develops this thesis in several works, including his First Philosophy and the epistle On the Number of Aristotle’s Books. The central theme is that prophetic science and human science have the same content, the only difference being that the first one is instantaneous, gained without effort or prior knowledge, because it comes from God. First Philosophy contains a violent criticism of those who, under cover of religion, denigrate philosophical speculation.

Most of al-Kindi’s works are epistles (risala), rather short texts, rigorously organized, dealing with well defined subjects (this style of writing will become afterwards rather common amongst philosophers writing in Arabic). Al-Kindi devotes, inter alia, several epistles to the proof of the finitude of the world in time and in space and to the fact that the infinite exists only potentially (a problem already tackled in his First Philosophy), thus breaking with Aristotle’s cosmology and incorporating some Neoplatonic concepts (such as those found in the Theology of Pseudo-Aristotle or in Proclus’ book on The Pure Good).

Optics

Al-Kindi’s work in the field of optics is double-faceted: while it is directly indebted to Hellenistic optics—most of the Greco-Hellenistic texts on the subject were translated into Arabic early, as far back as the ninth century—it is nevertheless forward-looking and opens several new fields of research.

In antiquity, Optics was, strictly speaking, a geometry of the perception of space and optical illusions (as in *Euclid’s Optica); it was based on the doctrine of the emission by the eye of a visual ray, the nature of which is only geometric. This ray is just a segment of a straight line joining two points, referring neither to the physical nature of light nor to the physiology of the eye. The theory of the “visual ray,” often criticized by philosophers, is the theory espoused by the supporters of geometrical optics, except when they study burning-mirrors (a set-piece of ancient science whose subject is the reflection of solar rays).

Al-Kindi supports the theory of the visual ray, but for him vision is due to a radiant power issuing from the eye and forming the air into straight lines. This now endows the visual ray with a physical reality: it becomes “a light power which impresses a luminosity in all the air it comes across… such as a living limb by which the pupil feels all the bodies it touches.” With al-Kindi, optics becomes a field falling within the province both of geometry and physics. This physical conception of the visual ray leads al-Kindi to take into account the duality of light versus vision and to study, not only the way the objects are seen, but also the propagation of luminous rays and the physical properties of light. These multiform links forged between light and vision created a dilemma that was only resolved a century and a half later by *Ibn al-Haytham who, definitively giving up the theory of the visual ray, developed the hypothesis that light rays, entering the eye, are the true cause of vision.

Al-Kindi’s On Solar Rays, at the cusp of late antiquity and the nascent Arabic tradition, is the first Arabic text to deal with burning-mirrors. His purpose in this treatise was to remedy the inadequacies in Anthemius of Tralles’ study and to complete it. The optical works of al-Kindi influenced his successors, particularly Ibn al-Haytham.

See also Archimedes; Aristotelianism; God in Islam; Optics and catoptrics; Pseudo-Aristotle; Ptolemy; Thabit ibn Qurra

Bibliography

D’Ancona Costa, C. Aristotele e Plotino nelle dottrina di al-Kindi sul primo principio. Documenti e studi sulla tradizione filosofica medievale 1993.

Guerrero, Rafael and Emilio Tornero. Obras filosóficas de al-Kindi. Madrid: Coloquio, 1986.

Ivry, A. L. Al-Kindi’s Metaphysics. A Translation of Ya’qub ibn Ishaq al-Kindi’s Treatise “On First Philosophy” with introduction and commentary. Albany: State University of New York Press, 1974.

Jolivet, Jean. L’intellect selon al-Kindi. Leiden: E.J. Brill, 1971.

Rashed R., and J. Jolivet. Oeuvres philosophiques et scientifiques d’al-Kindi, vol. 1 L’optique et la catoptrique, vol. 2 Métaphysique et cosmologie. Leiden: E.J. Brill, 1997–1998.

HÉLÈNE BELLOSTA

Kosmas Indikopleustês

A Greek merchant in the first half of the sixth century, Kosmas traveled from Alexandria to Eastern Africa and Arabia and supposedly sailed also to India and Sri Lanka (hence his qualification of Indikopleustês, that is, Sailor to India). He has been identified as the person to whom the physician Alexander of Tralles (sixth century) dedicated his treatise On fevers. If so, Kosmas was the son of the physician who taught medicine to Alexander at an unspecified place (perhaps Tralleis rather than Alexandria, as recently suggested). In contact with Alexander since his youth, he remained a life-long friend, even though he moved abroad, according to Alexander’s own words. In his old age, he became a monk at the Rhaitu monastery in the Sinai.

Kosmas is best known for his work Christianikê topographia (Christian Topography), comprising twelve books in which he proposed a Christian conception of the universe. The program was not new, but dated back to the Fathers of the Church. During Kosmas’ life, however, Christianization of society, science and culture was enforced, particularly under the Byzantine emperor Justinian I (b. c. 482, emperor 527, d. 565): when the philosophical school of Athens—where classical, viz., pagan, philosophy was taught—was closed in 529, some teachers, who moved from Athens to Alexandria, were later called to Constantinople by the Emperor, and medicine, for example, was transformed by means of the development of the cult of Kosmas and Damianos (martyred in the late-third century). In this context, the conceptions of the Earth and the universe inherited from antiquity were to be replaced by a new one, compatible with the Old Testament and the account of the creation of the world. The topic was the object of a philosophico-scientific polemic illustrated by such philosophers as Proclus (410 or 412–485) and John Philoponus (c. 490–after 567). It opposed not only Christians and pagans according to a traditional interpretation, but also Christian heterodox groups (among others the Nestor-ians) and Christian orthodoxy. Kosmas refuted the Aristotelico-Ptolemaic cosmology and proposed a literalist interpretation of the biblical text, following the Syro-Antiochean tradition of biblical exegesis, traditionally opposed to the Alexandrian school. In this view, the Earth is a rectangular plate of four hundred travel days from west to east, and two hundred from north to south, surrounded by the Ocean. At the northern end of the Earth, a cone-shaped mountain rises up, which hides the Sun during the night. The firmament is a two-story vault like Moses’ tabernacle, which is built on vertical walls: the first story is perishable, and the second divine and eternal.

The scientific interest of the Topography is not limited to illustrating the creation of a new cosmography and geography, but resides also in the wealth of information of all kinds (not only natural history, but also ethnography and history of religions, for example) that Kosmas gathered on the basis of personal observation or hearsay. Among other things, he described the life of the Near East, not only the expansion and rituals of Christian Church(es), but also trade activity, including the rivalry between the Persian and the Byzantine empires, the natural environment with the plants and animals of India, such as pepper and coconut, or unicorn, buffalo, giraffe, and hippopotamus, and he even made a copy of a Greek inscription in Adulis from the so-called Monumentum Adulitanum.

The work is known in more than thirty Byzantine manuscripts, three of which are illustrated (Vaticanus graecus 699, ninth century; Florentinus, Mediceus Laurentianus, 9.28, eleventh century; Sinaiticus graecus 1186). It was translated into Slavonic between the twelfth and thirteenth century and was influential in Kievan Rus, as well as in the Nestorian Near East, and in popular medieval geography. Fragments of the Topography were published in the seventeenth century, and the full text in 1707 by Bernard de Montfaucon in his Collectio nova patrum et scriptorum graecorum.

See also Geography, chorography; Travel and exploration

Bibliography

Anastasos, M.V. The Alexandrian Origin of the Christian Topography. Dumbarton Oaks Papers (1946) 3: 73–80.

Pigulevskaia, N. V. Byzanz auf den Wegen nach Indien. Aus der Geschichte der byzantinischen Handels mit dem Orient vom 4.-6. Jh. Berlin and Amsterdam: Hakkert, 1969.

Wolska-Conus, W. La Topographie chrétienne de Cosmas Indicopleustès, théologie et science au VIe siècle. Paris: Presses Universitaires de France, 1962.

———. Cosmas Indicopleustes, Topographie chrétienne. Introduction, texte critique, illustration, traduction et notes. 3 vols. Paris: Éditions du Cerf, 1968.

———. La «Topographie Chrétienne» de Cosmas Indicopleustès. Hypothèses sur quelque thèmes de son illustration. Revue des Etudes Byzantines (1990) 48: 155–191.

ALAIN TOUWAIDE