Medieval Science, Technology and Medicine

Elements and Qualities

According to Aristotle’s *cosmology, the universe is divided into two distinct realms. In his geocentric account, beyond the border of the sphere of the Moon, all bodies are composed of the element ether. These bodies are eternal, experience neither generation nor corruption, and move in circles around the Earth. Below the sphere of the Moon, in the terrestrial region, all bodies are composed of mixtures of the four elements: earth, water, air, and fire. These elements were considered to be simple substances, and the matter from which all terrestrial substances were composed. They never exist separately in a pure form, and are characterized by four primary qualities: the hot, the cold, the wet, and the dry. These elements and their defining qualities explain the passive properties and active powers of corporeal substances. By and large medieval philosophers accepted Aristotle’s framework as laid out in De generatione et corruptione, Meteorologica IV, the Physics, and the De caelo, although they debated some of the finer points of his theories. The general correspondence between Aristotle’s elements and those of *Plato as described in the Timaeus gave additional authority to this understanding of the elements. Furthermore, medieval physicians, who derived their theories from Greek medical works attributed to *Galen and *Hippocrates, also used the prime qualities to define the temperaments of the body and to explain the causes of health and disease.

Elements and the Prime Qualities

In typical medieval accounts each element is defined by two of the four primary qualities. The qualities are divided into two groups: active and passive. The two opposites, the hot and the cold, are active, while the wet and the dry are passive. Each element is defined by one active and one passive element. Thus earth is cold and dry; water is cold and wet; air is hot and wet; and fire is hot and dry. The elements transform into each other when one of their prime qualities turns into its opposite. For example, earth changes into water when it becomes wet, and water becomes air when it becomes hot. Elements can only transform one quality at a time. Therefore, earth must transform first into either water or fire before turning into air, its polar opposite.

Schematic diagram showing the relation between each of the elements and the qualities that compose them.

Even though all the elements are defined by two primary qualities, one particular quality predominates in each element. Thus earth is dry; water is cold; air is wet, and fire is hot. The qualities themselves can be thought of both as tangible properties, such as heat, coldness, etc., as well as powers or principles of organization. The four primary qualities and their effects were thought to be responsible, either directly or indirectly, for all qualitative change, generation, and corruption in the sublunary realm. The active qualities “act” by participating in the generation and corruption of substances. The hot assimilates like substances and separates unlike ones, while the cold brings together both like and unlike substances. The passive qualities are responsible for the shape of the substance in which they inhere. Thus wet substances are topologically fluid and conform to the shape of a container, while dry ones are solid and retain their shape. There was some debate over the rigid distinction between passive and active qualities, and some medieval scholars argued that the active qualities were only relatively more active than the passive ones, and that the passive qualities were in fact active. In particular it was argued that the wet was active since wet substances could turn dry substances into liquids through dissolution.

Medieval interpreters of Aristotle devoted much energy to discussions of how the four elements combine in mixtures. Since all sublunary bodies are composed of the four elements, it was a fundamental question of terrestrial physics. Approaches relied on the notions of substantial forms and matter, key concepts to Aristotelian theories of *hylomorphism. In particular, they questioned in what sense the elements acted as the matter of composites, and in what manner the qualities persisted in these mixtures. Since the elements did not remain perfectly complete in, for example, small particles side by side in composites, but rather fused to make new mixtures, scholars debated whether the substantial forms or the qualities of the elements were diminished or persisted intact.

Elements, Cosmology, and Secondary Qualities

While the elements are defined by the prime qualities, they are also distinguished by what is described in Aristotelian terms as their natural place. In this schema, each of the elements has a characteristic tendency to move to a particular region closer to or further away from the center of the Earth. The element earth was thought to be the heaviest, followed by water, which tends toward the surface of the Earth. Air naturally moves toward the region above the Earth; and fire, the lightest element, moves away from the Earth. Because of their natural motions, earth and fire were known as extreme elements (elementa extrema), while water and air were termed middle elements (elementa media). Since all sublunary bodies are compounds of the four elements, a given body’s weight, or tendency to move toward the center of the Earth, was thought to be determined by the relative amounts of each element that it contains. Some scholars believed that the weights of compounds of the elements, that is, the weight of every terrestrial body, could be understood in terms of ratios of the elements that composed the given body. Additionally, the tendency of each of the elements to move toward its natural place partially explains why bodies in the sublunary region were constantly in a state of generation and corruption. No compound of the elements can be eternal because of the natural tendency of its components to break apart and move in different directions. Meanwhile, the temporally finite persistence of a body was dependent on the organizing powers of its substantial form that unified a compound of the elements.

Secondary qualities other than heaviness and lightness were said to derive from the hot, the cold, the wet, and the dry. Secondary tangible qualities, such as fineness and coarseness or hardness and softness, stemmed directly from the prime qualities. For example, the dry causes hardness. Other sensible but not tangible secondary qualities, such as color and odor, were widely regarded as the result of local motions (motus locales), which in turn were caused by the power of the active qualities to assimilate and separate substances, or the natural motions inherent to each of the elements.

Applications of the Elements and Qualities

The qualities were prominent not only in matter theory but also in medieval understanding of *meteorology and medical theory. The four seasons could be characterized by combinations of the primary qualities, just as the elements could be. Furthermore, according to Aristotelian meteorology, two exhalations characterized by the prime qualities, one wet, the other hot and dry, occurred in cycles between the surface of the Earth and the sphere of Moon. These cyclic exhalations caused atmospheric changes. Perhaps more significantly, the qualities were seen to be essential for medical diagnoses and cures. Standard medical textbooks of the Middle Ages, such as the Canon of Avicenna (*Ibn Sina), introduced students to medical theory with discussions of the elements and qualities. These were seen as pertinent topics for medical students because they could be used to explain pharmaceuticals and other cures, such as baths and diets.

Under the standard Galenic view, the human body was thought to contain four humors: black bile, blood, phlegm, and yellow bile. Each of these humors was characterized by one passive and one active primary quality, as well as associated with a corresponding season. This theory holds that black bile is cold and dry; phlegm is cold and wet; blood is hot and wet; and, yellow bile warm and dry. Health was widely considered to be the balance of these humors, while disease resulted from the predominance of one or more the humors. Thus explanation of cures depended on identifying the primary qualities of the components of the regimen. If a patient was diagnosed to be excessively hot, a drug or some other cure with a cooling property might be prescribed. As a result, discussions of the elements and the primary qualities abound in medical commentaries on the Canon and other texts used for teaching medicine in medieval universities.

The universal nature of the elements and the prime qualities, their broad correspondence to everyday experience, and the authority of ancient and medieval texts ensured their place in medieval accounts of the sublunary world. The explanatory power of these simple bodies was particularly broad, and thus the success of this theory was due in part to its applicability to a wide range of phenomena and branches of learning. As a result it was only with great reluctance and much polemic that the scientific world sought a more pluralistic understanding of the material elements of the world in the seventeenth and eighteenth centuries.

See also Aristotelianism; Experiment, experimenta;

Bibliography

Aristotle. De generatione et corruptione. Translated by C. J. F. Williams. Oxford: Clarendon Press, 1982.

Galen. “On Mixtures.” In Selected Works. Translated by P. N. Singer. Oxford: Oxford University Press, 1997.

Lang, Helen S. Aristotle’s Physics and its Medieval Varieties. Albany: SUNY Press, 1992.

Lang, Helen S. The Order of Nature in Aristotle’s Physics: Place and the Elements. New York: Cambridge University Press, 1998.

Maier, Analiese. On the Threshold of Exact Science. Edited and Translated by Steven D. Sargent. Philadelphia: University of Pennsylvania Press, 1982.

McKeon, Richard P. “Medicine and Philosophy in the Eleventh and Twelfth Centuries: The Problem of the Elements.” The Thomist (1961) 24: 75–120.

CRAIG MARTIN

Encyclopedias

During the thirteenth century several voluminous texts were written in Latin and vernacular languages in which their authors attempted to gather the knowledge of their time for non-specialist audiences. Although it is strictly anachronistic to describe such works as “encyclopedias”—the first recorded use of the term in English is dated 1525—these medieval works satisfy the definition: their contents are arranged under several rubrics and focus on various fields such as theology, astronomy, mathematics, biology, and even daily life.

Among the most influential encyclopedias of the Middle Ages are De naturis rerum by *Alexander Nequam (end of the twelfth century), De natura rerum by *Thomas of Cantimpre (c. 1200–c. 1280), De proprietatibus rerum by *Bartholomaeus Anglicus (thirteenth century), Le livre du trésor (The Book of the Treasure) by Brunetto Latini (c. 1220–c. 1294), and Speculum maius by *Vincent of Beauvais (c. 1199–c. 1265). (The last named work is divided in three Specula: naturale, historiale, and doctrinale.) All five of these texts are composed of a collection of topics, which are classified by chapters and books. The works deal mainly with the “things of nature” (naturae res) or the “nature of things” (natura rerum), in other words, with all the elements surrounding humans on Earth and in heaven.

Although there was a profusion of encyclopedias in the thirteenth century, the form is much older than that: the originator is widely held to be *Isidore of Seville (d. 636), with his Etymologiae, a work that took as one of its major references the Historia naturalis of Pliny the Elder (23–79 C.E.). Isidore was soon imitated by *Bede, the English author of a De natura rerum, and by the German abbot of Fulda, Rabanus Maurus (c. 776–856) in his De rerum naturis. Also classifiable as an encyclopedia is the imago mundi, a form of geographical text that described the inhabited areas of the world and built a discourse on other disciplines such as astronomy. Leading examples of imagines mundi were by Honorius (twelfth century; Latin) and Gossuin de Metz (thirteenth century; French). Similar, too, were didactic texts that took the form of dialogues between master and pupil—works such as those of Placides and Timéo or the Livre de Sydrach (late thirteenth century), in which there are several reflections on natural phenomena.

The Founder

Isidore of Seville’s Etymologiae played a major role in the transmission of ancient culture. Its title comes from the belief—common in the Middle Ages—that words are inextricably linked with the objects they describe. Thus, the practice of etymology is regarded as the best way both to discover the true “nature of things” and to organize the various rubrics of the encyclopedia. As a consequence, the encyclopedic text is not merely a simple compilation: it is organized according to a method that may be termed “the encyclopedic transposition process.” Such a process is based on the transposition of the “scholarly knowledge”—mainly provided by ancient Latin texts, the Bible, and the writings of the Fathers of Church—into a more accessible fund of information. The idea of encyclopedic transposition is set out in a passage in the Etymologiae in which Isidore clarifies his method. According to him, the compiler is like an alchemist who combines various substances, bringing together the elements, the bonds, and the catalysts that produce, at the end of the process, a new form of matter.

Through the twenty books of the Etymologiae, Isidore influenced the whole medieval encyclopedic genre, especially through the coherence of his approach, which tends to limit references to the supernatural. The seven liberal arts occupied the main place in Isidore’s text. They were put in an order that would be influential throughout the Middle Ages: grammar, rhetoric, dialectic, *arithmetic, geometry, music, and astronomy/*astrology. Moreover, the Etymologiae constitutes a turning point in the history of the encyclopedic style by gathering information on the things of nature without reference to scholarly disciplines. These objects of knowledge can be divided into three categories as they appear in Isidore’s work: humans, lower nature (divided into three fundamental types: animals, plants, and minerals), and objects transformed by human activity (thus opening the path to mechanical arts). Later encyclopedists who worked on the things of nature were influenced by Isidore’s ideas. They went further and apprehended nature in a more naturalistic way. This process was facilitated at the end of the twelfth century by the diffusion among encyclopedists of the works of Aristotle and various Arabic authors on the philosophy of nature.

The Golden Age of the Encyclopedic Genre

What is known as “medieval encyclopedism” is linked principally to the thirteenth century, during which most of the major works in the genre were written. With the growth of cities, the creation of *universities, the rise of urban intellectuals and an audience increasingly eager for knowledge but without a grounding in Aristotle and scholastic techniques, new cultural expectations appeared. In addition, following the Arabic and Latin translations of the twelfth century that brought new scientific learning to the Latin West, the general need for knowledge seemed to expand, and there was a consequent increase in the number of popular works. However, encyclopedists remained faithful to Isidore’s tradition: etymology was still frequently used to introduce a topic, and references to the originator himself (“ut dixit Isidorus”) remained numerous in later works. The modern study of encyclopedic texts written during this productive period involves not only reference to the works themselves but also consideration of what a medieval encyclopedia could really be.

It is also instructive to examine the words used by medieval authors to define what are now known as “encyclopedias.” Two terms are recurrent: “speculum” and “natura rerum” or its equivalents. The first, systematically used by Vincent of Beauvais and often appearing in the prologues of encyclopedias, indicates that the encyclopedia is a book that reflects nature, in the manner of a mirror. In medieval representations, “mirror” also refers to the learning process: through it readers discover how to apprehend the things of nature and their wonders. They can then understand the will and power of God. Moreover, in the prologue, authors normally state their intention of dealing with the things of nature, i.e., the main elements of Creation. Lists compiled by encyclopedists show that their works aim at building an overview of these elements. In other words, they show a propensity to compose a summa (general survey).

Miniature showing construction of a tower from the early encyclopedic work The Sacred and Profane in the Codex of Monte Cassino (1023). (Corbis/Bettmann)

In the Livre du Trésor, Brunetto Latini states that he has tried to “briefly write a Summa.” The two terms—“briefly” and “summa”—may seem contradictory. However, they do not appear paradoxical to the author, who proceeds to explain his method of building a summa from collected data. The double reference to brevity and summa appears in the prologue of most medieval encyclopedias and seems to have been regarded as a necessary part of the exordium. Thus, the fact that such texts are often voluminous is not contradictory. For medieval encyclopedists, brevity was not necessarily the same as concision: their method was to compile the most relevant and important parts of the work of other philosophers; their effectiveness was measured by their choice of what to include, not by the number of words in the finished product.

Organization of Knowledge

In order to compile and arrange a large amount of data, encyclopedists had to structure their discourse. This was one of the fundamental premises of encyclopedic writing. Another was that the text was not written only to be consulted: according to Gossuin de Metz in his Image du monde, the work, in order to be effective, had to be read as a whole.

But a more modern idea of consultation progressively appears. It is linked with the emergence of rubrics classified by alphabetical order, then with the use of indexes (in, for example, the work of Bartholomaeus Anglicus and Vincent of Beauvais). However, this alphabetical order was never complete, and generally took the form of a “system of the world.” For example, Vincent of Beauvais tried to build his text according to the structure of the Bible; Bartholomaeus Anglicus attempted to make his work conform to a neo-Platonic hierarchy of creatures, from God to matter; Brunetto Latini followed a Stoic division of sciences. Of course, considering the abundance of information, no encyclopedist managed to build a complete classification. One sees above all various kinds of juxtapositions, often marked by inconsistencies. These inconsistencies are all the more obvious as encyclopedists did not analyse their sources: they were then bound to repeat what earlier authors had said, sometimes in a contradictory way.

One can note in prologues the recurrence of the terms “brief summa,” “to compile,” “compilation,” and “compendium.” Most of the time, the encyclopedist specifies that he does not use his own knowledge, except to structure discourses extracted from the work of authorities. Consequently, a medieval equivalent for “encyclopaedia” could be “brief summa.” A summa is a kind of aggregate of the things of nature, i.e., a mirror-book of nature. In that respect, nature is itself a mirror of God. Each summa is brief because it is based on sources from which the encyclopedist extracts some data. Moreover, brevity implies a structure: the encyclopedist methodically organizes the philosophers’ discourses.

The medieval encyclopedia is thus a literary genre between the accessus and the account of a synthetic vision of the Creation. Throughout prologues, the numerous quotations from the authorities, whose names and/or works are specified, reveal some of the conscious process by which scholarly knowledge was rendered into encyclopedic knowledge. The encyclopedist writes for an audience that has little time to spare, such as the mighty or people who lack the knowledge to read the scholarly works on which his work is based. He considers himself a teacher aiming at a large audience. Among his goals are to improve the reader’s understanding of the Bible; to help preachers and train princes; to encourage people to study and then improve their moral standards; and to facilitate the reading of more technical texts.

Many medieval encyclopedias were highly successful. For example, the De proprietatibus rerum was translated into five languages beginning in the fourteenth century. The texts survive in many manuscripts of this period, and from the fifteenth century to the eighteenth century many encyclopedias also appeared in several editions. Numerous marginalia in the manuscripts and borrowings from medieval encyclopedias by many authors show that these texts were frequently consulted. Library catalogues also contain many references to these works. Thus it is clear that medieval encyclopedias played a major role in the culture of the Middle Ages and in the diffusion of scientific knowledge among a large audience.

See also Aristotelianism; Astronomy, Latin; Bestiaries; Herbals; Lapidaries; Music theory; Natural history; Quadrivium; Vocabulary

Bibliography

Binkley, P., ed. Premodern Encyclopaedic Texts. Leiden: E.J. Brill, 1997.

Lusignan, S., M. Paulmier-Foucart and A. Nadeau, eds. Vincent de Beauvais. Intentions et réceptions d’une œuvre encyclopédique au Moyen Âge. Paris: Vrin, 1990.

Lusignan, S and M. Paulmier-Foucart, eds. Lector et compilator, Vincent de Beauvais, frère prêcheur. Un intellectuel et son milieu au XIIIe siècle. Grâne, France: Créaphis, 1997.

Ribémont, B. De natura rerum. Études des encylopédies du Moyen Âge. Orléans: Paradigme, 1995.

———. Le Livre des propriétés des choses, une encyclopédie au XIVe siècle. Paris: Stock, 1999.

———. Les Origines des encyclopédies médiévales. D’Isidore de Séville aux Carolingiens. Paris: Champion, Bibliothèque du Moyen Age, 2001.

———. Littérature et encyclopédies du Moyen Âge. Orléans: Paradigme, coll. Medievalia, 2002.

———. La “renaissance” du XIIe siècle et l’encyclopédisme. [Essais sur le Moyen Age 27] Paris, France: Champion, 2002.

Seymour, M.C. Bartholomaeus Anglicus and his Encyclopedia. London: Variorum, 1992.

B. RIBÉMONT

Eriugena, John Scottus

The Irish-born Johannes Eriugena—his seventeenth-century editor Thomas Gale named him “Johannes Scotus Erigena”—was “master” (magister) of the cathedral school at Laon and a scholar at the court of King Charles the Bald of France. In 850–851, Bishop Pardulus of Laon refers to “a certain Irishman, named Johannes, who is at the palace of the king.” The appelation “scottus” or “scotigena” means “Irish”; the Vatican Librarian Anastasius, for instance, refers to him as “Joannes Scotigena.” The name “Eriugena” (“Irish born”)—corrupted to “Erigena” in twelfth-century catalogues—was a pen-name used to sign his translation of Pseudo-Dionysius.

Eriugena was probably born before 800 and died sometime around 877. Recognized for his erudition, he had a wide knowledge of Latin Christian sources: St. Augustine, *Martianus Capella, *Macrobius, Cassiodorus, *Bede, *Isidore of Seville, Ambrose, Hilary of Poitiers, and Jerome. He refers occasionally to *Boethius (Opuscula sacra) and possibly knew his Consolation of Philosophy (glosses, possibly in his hand, survive). Two partial commentaries, Annotationes in Marcianum (c. 840–c. 850), on Martianus’ liberal arts handbook De nuptiis Philologiae et Mercurii (The Marriage of Philolology and Mercury) survive. Pierre Duhem thought that Eriugena, in Book Seven of this Commentary, offers a version of the non-Ptolemaic system subsequently associated with Tycho Brahe. In fact, Eriugena is accurately reporting Martianus’ version of Heraclidus of Pontus’ theory, but remarkably places Mars and Jupiter also in orbit around the Sun.

In the late 840s Eriugena was commissioned by two bishops to refute a treatise by a Saxon monk, Gottschalk (806–868), who interpreted St. Augustine as teaching a “twofold” or “twin predestination” (gemina praedestinatio) of the elect to heaven and of the damned to hell, based on the opinion of Isidore of Seville, Sententiae II, 6, I. Eriugena’s De divina praedestinatione (On Divine Predestination, c. 851) rebuts Gottschalk, rejecting any predestination toward evil by appealing to God’s unity, transcendence and goodness. This treatise proceeds through a rationalistic, dialectical analysis of key theological concepts, relying on argument rather than Scripture (something criticized by contemporaries, see PL CXV 1294a). Eriugena holds that “true philosophy is true religion and conversely” (following Augustine, De uera religione 5, 8).

In De divina praedestinatione Eriugena maintains that God wants all humans to be saved and does not predestine souls to damnation. Humans damn themselves through their own free choices: “Sin, death, unhappiness are not from God.” God is outside time and cannot be said to foreknow or predestine. Eriugena locates Gottschalk’s errors as midway between the Pelagian heresy that downplays divine grace, and the opposing heresy that denies human freedom. In turn Eriugena himself, due to his emphasis on free will, was accused of “Origenism” and “Pelagianism.” Eriugena’s treatise was condemned at the councils of Valence (855) and Langres (859): one reason for the verdict on the work was its reliance on “dialectic” (dialectica).

Around 860, Eriugena translated the works of (Pseudo-) Dionysius the Areopagite—his Divine Names, Mystical Theology, Celestial Hierarchy, and Ecclesiastical Hierarchy. He subsequently wrote a long commentary, Expositiones in hierarchiam coelestem, on the Celestial Hierarchy. In his Divine Names, Dionysius draws on Proclus’ Commentary on the Parmenides to argue that affirmations are less worthy than negations in referring to entities that transcend being, since negations strip something away whereas affirmations involve “possession of form.” Negations concerning God (such as, for example, “God is not good”) are “more true” than affirmations (such as “God is good”). Divine names apply metaphorically and not literally to God, who is “beyond all that is.” Pseudo-Dionysius maintains that God is not known directly except through theophaniai, divine appearances (Divine Names, ch. 7, PG III 869c-d). Eriugena also translated and commented on the work of Maximus Confessor, giving him access to a rich Greek Christian anthropology. These translations gave him both a familiarity with and a preference for the Eastern Fathers.

Eriugena’s dialogue, Periphyseon or De divisione naturae (On the Division of Nature), enthusiastically adopts the Areopagite’s main ideas, chiefly, his distinction between affirmative (kataphatic) and negative (apophatic) theology. He even extends the dialectic of affirmation and negation beyond theology to statements about human nature (“man is not an animal” is more true than “man is an animal”). Overall his outlook is rationalistic; true philosophy is true reason (vera ratio); authority is but right reason (Periphyseon, I.511b). One should introduce the “opinions of the holy Fathers” only where “the gravest necessity requires that human reason be supported for the sake of those who, being untrained in it, are more amenable to authority than reason” (Periphyseon IV.781c-d).

Eriugena’s cosmology includes original views on creation, matter, space, and time, corporeal body, the nature of paradise and hell, and so on. For example, heaven and hell are not places. Paradise is perfect human nature (Periphyseon IV.840a), whereas souls trapped in their own fantasies are in “hell.” He defines nature (natura) very broadly as the “totality of all things” including both beings and non-beings, both God and creation. All things emerge from and return to the one God, Who is beyond being and non-being. God “creates Himself by manifesting Himself in theophanies” (Periphyseon I.446d). This self-manifestation (I.455b) is identical with the speaking of the Word and the creation of all other things, since all things are contained in the Word. The Word contains the divine Ideas or “primary causes” (causae primordiales) of all creation, which proceed into their created effects. The timeless primordial causes are contrasted with the “mutable and imperfect and as yet formless procession of this sensible world” (Periphyseon II.549b).

Four Divisions of Divine Nature

Eriugena divides the divine nature into four “divisions” (divisiones), or “species” or “forms,” namely:

nature which creates and is not created,
nature which creates and is created,
nature which is created and does not create, and
nature which is neither created nor creates.

God is present in all four divisions. The outgoing of all things in creation is balanced by their “return” (epistrophe, reditus, reversio) to God. There is a general return of all things to God. Corporeal things will return to their incorporeal causes, the temporal to the eternal, the finite will be absorbed in the infinite. The human mind will achieve reunification with the divine, and then the corporeal, temporal, material world will become essentially incorporeal, timeless and intellectual. The elect achieve “deification” (deificatio, theosis), merging with God as lights blend into the one light, as voices blend in the choir, as a droplet of water merges with the stream. God shall be all in all (omnia in omnibus, V 935c).

Eriugena controversially claims that God and the creature are ultimately “one and the same” (Periphyseon, III.678c), and that God is the “essence of all things” (essentia omnium) or “form of all things” (forma omnium), expressions that led to the accusation of pantheism. However, Eriugena also stresses the divine transcendence: God is the non-being above being as well as the principle or form of all things.

Eriugena’s Periphyseon had influence in the schools of Laon, Auxerre, and Corbie, and was popular in the twelfth century, especially when circulated in the “edition” of William of Malmesbury and in the paraphrase, Clavis physicae, of Honorius Augustodunensis. His version of Dionysius was also influential in the twelfth and thirteenth centuries. Linked with two heretical Paris theologians, David of Dinant and Amaury of Bène, Periphyseon was condemned in 1210 and 1225. Meister Eckhart of Hochheim (c. 1260–c. 1328) and Nicholas of Cusa (1401–1464) were both familiar with the Periphyseon.

See also God in Christianity; Nature: the structure of the physical world

Bibliography

Primary Sources

Barbet, Jeanne. Iohannis Scoti Eriugenae Expositiones in Ierarchiam coelestem, Corpus Christianorum. Continuatio Mediaevalis XXI, Turnhout: Brepols, 1975.

Cappuyns, Maiul. Le De imagine de Grégoire de Nysse traduit par Jean Scot Erigène. Recherches de théologie ancienne et médiévale (1965) 32: 205–262.

Contreni, John J. and Pádraig P. Ó Néill. Glossae Divinae Historiae. The Biblical Glosses of John Scottus Eriugena. Firenze: Sismel–Edizioni del Galluzo, 1997.

Floss, H.-J., ed. Johannis Scoti Opera quae supersunt Omnia. Patrologia Latina CXXII. Paris, 1853.

Gale, Thomas. Joannis Scoti Erigenae De Divisione Naturae Libri Quinque Diu Desiderati. Accedit Appendix ex Ambiguis S. Maximi Graece et Latine. Oxford: Sheldonian Theatre, 1681.

Jeauneau, Édouard. Jean Scot: Commentaire sur l’Evangile de Jean. Sources Chrétiennes 180. Paris: Cerf, 1972.

———. Jean Scot: L’Homélie sur le Prologue de Jean. Sources Chrétiennes 151. Paris: Editions du Cerf, 1969.

———, ed. Maximi Confessoris Ambigua ad Iohannem iuxta Iohannis Scotti Eriugenae latinam interpretationem. Corpus Christianorum Series Graeca, 18. Turnout/Leuven: Brepols/Leuven University Press, 1988.

———, ed. Iohannis Scotti seu Eriugenae Periphyseon, liber primus. Corpus Christianorum Continuatio Medievalis 161. Turnhout: Brepols, 1996.

———, ed. Iohannis Scotti seu Eriugenae Periphyseon, liber secundus. Corpus Christianorum Continuatio Medievalis 162. Turnhout: Brepols, 1997.

———, ed. Iohannis Scotti seu Eriugenae Periphyseon, liber tertius. Corpus Christianorum Continuatio Medievalis 163. Turnhout: Brepols, 1999.

———, with the assistance of Mark A. Zier, eds. Iohannis Scotti Eriugenae Periphyseon (De Divisione Naturae) Liber Quartus. English Translation by John J. O’Meara and I.P. Sheldon-Williams, Scriptores Latini Hiberniae Volume XIII. Dublin: Dublin Institute for Advanced Studies, 1995.

Laga, Carl and Carlos Steel, eds. Maximi Confessoris Quaestiones ad Thalassium II. Q. LVI-LXV una cum latina interpretatione Iohannies Scotti Eriugenae. Corpus Christianorum Series Graeca, 22. Turnhout/Leuven: Brepols/Leuven University Press, 1990.

Lutz, Cora, ed. Iohannis Scotti Annotationes in Marcianum. Cambridge, MA: Medieval Academy of America, 1939.

Madec, Goulven, ed. Iohannis Scotti de divina praedestinatione. Turnhout: Brepols, 1978.

Sheldon-Williams, I.-P. Iohannis Scotti Eriugenae Periphyseon. Volumes I–III, Dublin: Institute for Advanced Studies, 1968, 1972, and 1981.

Secondary Sources

Allard, Guy, ed. Jean Scot écrivain. Montréal: Bellarmin, 1986.

Beierwaltes, Werner. Eriugena. Grundzüge seines Denkens. Frankfurt am Main: Vittorio Klostermann, 1994.

———, ed. Eriugena Redivivus. Zur Wirkungsgeschichte seines Denkens im Mittelalter und im Übergang zur Neuzeit. Heidelberg: Carl Winter Universitätsverlag, 1987.

———, ed. Begriff und Metapher. Sprachform des Denkens bei Eriugena. Heidelberg: Carl Winter Universitätsverlag, 1990.

———, ed. Eriugena. Studien zu seinen Quellen. Vorträge der III. Internationalen Eriugena-Colloquiums, Freiburg im Breisgau, 27.-30. August 1979. Heidelberg: Carl Winter Universitätsverlag, 1980.

Bett, Henry. Johannes Scotus Erigena: A Study in Medieval Philosophy. New York: Cambridge University Press, 1925.

Brennan, Mary. A Guide to Eriugenian Studies. A Survey of Publications 1930–87. Paris: Editions du Cerf, 1989.

———. A Bibliography of Publications in the Field of Eriugena Studies 1800–1975. Studi Medievali (1977) ser. 3a, 28: 401–447.

———. Materials for the Biography of Johannes Scottus Eriugena. Studi Medievali (1986), ser. 3a, 27: 413–460.

Brennan, Mary, tr. John Scottus Eriugena. Treatise on Divine Predestination, with an Introduction by Avital Wohlman, Notre Dame: University of Notre Dame Press, 1998.

Cappuyns, Maiul. Jean Scot Erigène: sa vie, son oeuvre, sa pensée. Louvain: Abbaye de Mont César, 1933.

Carabine, Deirdre. John Scottus Eriugena. Oxford: Oxford University Press, 2000.

Gardner, Alice. Studies in John the Scot: A Philosopher of the Dark Ages. London: Oxford University Press, 1900.

Gersh, Stephen. From Iamblichus to Eriugena. Leiden. E.J. Brill, 1978.

Huber, Johannes. Johannes Scotus Erigena: Ein Beitrag zur Geschichte der Philosophie und Theologie im Mittelalter (1861). Hildesheim: Olms, 1960.

Jeauneau, Édouard. Études érigéniennes. Paris: Études Augustiniennes, 1987.

Leonardi, Claudio and E. Mesesto, eds. Giovanni Scoto nel suo tempo: L’organizzazione del sapere in età carolingia. Spoleto: Centro Italiano di Studi sull’Alto Medioevo, 1989.

Madec, Goulven. Jean Scot et ses auteurs. Annotations érigéniennes. Paris: Études Augustiniennes, 1988.

Marenbon, John. From the Circle of Alcuin to the School of Auxerre: Logic, Theology and Philosophy in the Early Middle Ages. New York: Cambridge University Press, 1981.

McEvoy, James J. and Michael Dunne, eds. History and Eschatology in John Scottus Eriugena and His Time. Proceedings of the Tenth International Conference of the Society for the Promotion of Eriugena Studies, Maynooth and Dublin, August 16-20, 2000. Leuven: Leuven University Press, 2002.

McGinn, Bernard and Willemien Otten, eds. Eriugena. East and West. Notre Dame: Notre Dame University Press, 1994.

Moran, Dermot. The Philosophy of John Scottus Eriugena. A Study of Idealism in the Middle Ages. New York: Cambridge University Press, 1989.

———. Pantheism from John Scottus Eriugena to Nicholas of Cusa. American Catholic Philosophical Quarterly 1990, Vol. LXIV No. 1 (Winter): 131-152.

———. “Time, Space and Matter in the Periphyseon: an Examination of Eriugena’s Understanding of the Physical World.” In At the Heart of the Real, edited by F. O’Rourke. Dublin: Irish Academic Press, 1992.

———. “Origen and Eriugena: Aspects of Christian Gnosis.” In The Relationship Between Neoplatonism and Christianity, edited by T. Finan and V. Twomey. Dublin: Four Courts Press, 1992.

———. “Eriugena’s Theory of Language in the Periphyseon: Explorations in the Neoplatonic Tradition.” In Ireland and Europe in the Early Middle Ages IV. Language and Learning, edited by Próinséas Ní Chatháin and Michael Richter. Frankfurt: Klett-Cotta, 1996, 240–260.

———. Idealism in Medieval Philosophy: The Case of Johannes Scottus Eriugena. Medieval Philosophy and Theology (1999) 8: 53–82.

O’Meara, John J. Eriugena. Cork: Mercier Press, 1988.

Otten, Willemien. The Anthropology of Johannes Scottus Eriugena. Leiden: E.J. Brill, 1991.

——— and Ludwig Bieler, eds. The Mind of Eriugena. Dublin: Irish University Press, 1973.

Riccati, C. Processio et explicatio: La Doctrine de la création chez Jean Scot et Nicolas de Cues. Naples: Bibliopolis, 1983.

Rudnick, Ulrich. Das System des Johannes Scottus Eriugena. Eine theologisch-philosophische Studie zu seinem Werk. Frankfurt am Main: Peter Lang, 1990.

Schrimpf, Gangolf. Das Werk des Johannes Scottus Eriugena im Rahmen des Wissenschaftsverständnisses seiner Zeit. Eine Hinführung zu Periphyseon. Münster: Beiträge zur Geschichte der Philosophie und Theologie des Mittelalters, 1982.

Sheldon-Williams, I.-P. “The Greek Platonist Tradition from the Cappadocians to Maximus and Eriugena.” In The Cambridge History of Later Greek and Early Medieval Thought, edited by A.H. Armstrong. New York: Cambridge University Press, 1970.

Sheldon-Williams, I.-P. and J.J. O’Meara, tr. Eriugena. Periphyseon (The Division of Nature). Montreal/Paris: Bellarmin, 1987.

Uhlfelder, Myra and J. Potter, tr. John the Scot. Periphyseon. On the Division of Nature. Indianapolis: Bobbs-Merrill, 1976.

Van Riel, Gerd, Carlos Steel and James J. McEvoy, eds. Iohannes Scottus Eriugena. The Bible and Hermeneutics. Proceedings of the Ninth International Conference of the Society for the Promotion of Eriugena Studies, held at Leuven and Louvain-La-Neuve, June 7–10, 1995. Leuven: Leuven University Press, 1996.

DERMOT MORAN

Euclid

Euclid lived around 300 B.C.E. in Alexandria. He authored the most influential textbook in the history of mathematics, the Elements. Additionally, he wrote at least five other geometrical works (Data, Porisma, On Divisions, Conics, Plane loci, Pseudaria), one text on astronomy (Phainomena), an influential text on optics (Optics) and a work on theoretical music (Elements of Music). Others texts on mechanics and on mirrors ascribed to him are not believed to be his works.

Certain axioms, postulates, definitions and theorems of the Elements have been contested since antiquity. During the greater part of the twentieth century, it was believed that Heiberg had successfully established the genuine Euclidean text in a critical edition. This belief was questioned at the end of the century by the works of Knorr, Vitrac, Djebbar, and Rommevaux. Similar shifts of understanding and approach occurred in the course of the century with regard to the medieval transmission of Euclid’s Elements. This transmission embraces translations into Latin, Arabic, Syriac, and Hebrew either from Greek or from Arabic texts. A further strand of transmission, often ignored, comprises the translation from Arabic into Persian. The multiplicity of texts translated from one language into the other and transferred from one scholarly culture to the other makes the study of the history of Euclid’s Elements one of the most difficult, but also most fascinating, subjects in textual history of medieval mathematics.

The first interest in the text is documented at the beginning of the Abbasid dynasty (750–1258), when caliph al-Mansur (r. 754–775) asked for a Greek manuscript. Yahya ibn Khalid (d. 805), vizier of al-Mansur’s grandson Harun al-Rashid (r. 786–809), sponsored the first known Arabic translation by al-Hajjaj ibn Yusuf ibn Matar (d. after 825). No trace of this translation seems to be preserved. During the reign of Harun’s second son, al-Ma’mun (r. 813–833), al-Hajjaj produced a second version, the character of which is highly disputed. While Arabic historical sources imply that this second version was a new translation, current research sees it more as a substantially revised edition. Fragments of this version or of editions based on it are extant in at least four different groups in Arabic and Latin, but the relationship between these four groups is far from being firmly established.

The second major textual transmission of the Elements had its start in the last third of the ninth century, when Ishaq ibn Hunayn (830–911) translated in Baghdad a different Greek version. This translation was edited and modified by his colleague *Thabit ibn Qurra (d. 901). Ishaq’s translation is apparently lost except for a very small number of fragments. The extant manuscripts that are acknowledged as representing the two translation efforts contain highly mixed texts with substantial differences in some books. There is no agreement among historians as to what relationship exists between these manuscripts and the three scholars of the ninth century.

Parallel to the efforts of translating, scholars began in the early ninth century to edit the translated text according to either philosophical or mathematical priorities. Almost all evidence for this work seems to be lost except for small fragments of *al-Kindi (d. c. 870) and al-‘Abbas b. Sa’id al-Jawhari (d. c. 860). The most important versions among those extant are the editions compiled by *Ibn Sina (d. 1037), Athir al-Din al-Abhari (d. 1263), Mu’ayyad al-Din al-‘Urdi (d. c. 1266), Muhyi’l-Din al-Maghribi (d. c. 1290), *Nasir al-Din al-Tusi (1201–1274), and an anonymous version printed in Rome in 1594. The most influential of these revised editions was the one composed by al-Tusi. As pointed out recently by De Young, Tusi’s text indicates that until the thirteenth century both major Arabic traditions (Hajjaj and Ishaq-Thabit) were used by scholars across the Muslim world. After the thirteenth century, they were replaced by al-Tusi’s edition.

Other works on Euclid’s Elements aimed to solve doubts, fill lacunae or add variants as well as new aspects. The most important authors of these kinds of commentaries were Abu’l-‘Abbas al-Fadl al-Nayrizi (d. c. 922), Abu Sahl al-Kuhi (fourth/eleventh century), Ahmad ibn Muhammad al-Sijzi (d. c. 1025), *Ibn al-Haytham (d. c. 1041), *‘Umar al-Khayyam (1048–1131), Muhyi’l-Din al-Maghribi (c. 1220–c. 1283), and Shams al-Din al-Khafri (d. 1550).

Translations of the Elements

Only a few Syriac texts are extant that testify to an interest in Euclid’s work among Nestorian and Jacobite Christians. None is known for the period before 700. An undated fragment of Book I was edited in 1924. Historians continue to debate about the language from which it was translated (Greek or Arabic) and about its relationship to the Arabic and Arabic-Latin transmission. The second known Syriac extract of the Elements came from the pen of the Jacobite patriarch Abu’l-Faraj ibn al-‘Ibri (1226–1286). It is related to the Arabic editions of the thirteenth century, but the precise character of this relationship has yet to be established.

The most influential translation from Greek into Latin before 1200 was made by *Boethius (c. 480–524/5) in c. 500. The four fragments that survive from this translation either come from northeast France (Corbie) or from Lorraine. Each of them was transmitted within another text or set of texts: B(Ma) belongs to Cassidorus’ Institutiones; B(Mb) belongs to Corpus Agrimensorum; B(Mc) belongs to Geometria I; B(Md) belongs to Geometria II. Folkerts reconstructed from the last named Boethius’ original translation of books I–IV and of the definitions of Book V.

In the twelfth century, a new Latin translation of the Elements was made from a Greek text in Southern Italy or Sicily. Folkerts proposed *Leonardo Fibonacci (1170?–1250?) as the compiler of the present form of the text, which is not identical with the original translation. Furthermore, at least three other Latin translations from Arabic have been made by *Adelard of Bath (c. 1116–1142), *Hermann of Carinthia (c. 1110–1154 or 1160) and *Gerard of Cremona (c. 1114–1187). The relationship between these translations and Arabic versions of the Elements has been repeatedly debated, but no general consensus could be reached.

Robert of Chester (fl. 1136–1157) was the compiler of an edition of the Elements (previously called Adelard II) that combined extracts from Adelard of Bath’s and Hermann of Carinthia’s translations with independent work, partially based on additional Arabic manuscripts. This edition dominated the Latin transmission until the mid-thirteenth century. Four other compilations that mix various textual forms of the Elements such as Boethius, Robert of Chester and unidentified Arabic material originated in the course of the twelfth century—the Liber Ysagogarum Alchorismi (chapter on geometry in Book IV), the version of an anonymous compiler from northern Germany, the version of an anonymous compiler possibly linked to Chartres and the edition, previously known as Adelard III, but identified by Knorr as the work of an Englishman, John of Tynemouth (twelfth/thirteenth century?).

Latin scholars continued to edit, rework, and comment on the Elements in the following two and a half centuries before the editio princeps of the Greek text appeared in 1533. The version that dominated this period was produced by *Campanus de Novara (c. 1210–1296) in the 1350s. He adopted most of the enunciations from Robert, but provided his own proofs. Campanus had didactic interests and hence strove to make the text self-contained. The result became one of the most important books in the curriculum of the medieval university. Other important commentaries on or editions of (parts of) the Elements were composed by *Albertus Magnus (c. 1206–1280), *Roger Bacon (1214–1294) and *Nicole Oresme (c. 1323–1382).

Additionally to the Elements, Gerard of Cremona translated three Arabic commentaries on this work—the Arabic translation of Pappus of Alexandria’s (fl. 300) commentary on Book X, al-Nayrizi’s comments on and additions to Euclid’s text (extant only Book I–Book VII, definitions) and an anonymous Arabic commentary on Book X.

The Hebrew transmission of the Elements consists of texts derived from the Ishaq–Thabit tradition and some fragments affiliated to the Hajjaj tradition. The main translators were Moses ibn Tibbon (*Profatius Judaeus) and Jacob ibn Makhir (1236?–1305?). Additionally, Hebrew scholars composed about fifteen commentaries and adaptations based on Arabic editions. An anonymous scholar translated the enunciations of Adelard of Bath’s Arabic-Latin translation to which he added the diagrams. A Hebrew compilation, from which Book I and II are extant, quotes from Campanus’ edition. According to Lévy, it may have been the work of Moses Provensali (fl. c. 1550).

The first Persian texts related to the Elements were written in the late tenth and early eleventh centuries. They are mainly chapters on geometry in encyclopedias based on earlier Arabic encyclopedias. The earliest Persian summary of an Arabic edition of the Elements was also produced in this period. The first known Persian translation of the entire work is found in Qutb al-Din al-Shirazi’s encyclopedia Durrat al-taj li-ghurrat al-Dibaj, written in 1282. It is related to al-Tusi’s Arabic edition, but the character of the relationship needs yet to be established. Until the nineteenth century, at least fourteen other Persian works on all or parts of the Elements appeared, among them at least three new translations.

Euclid’s Other Works

The second most influential Euclidean work within Islamic societies was the Data. It was used by scholars as a guidebook for approaching and solving geometrical problems. Included in the so-called Middle Books, which had to be studied after the Elements and before Ptolemy’s Almagest, it became available for mathematical training in the context of the madrasa, although it was not taken up in each and every one of them. Three Arabic translations of the Data are known and possibly extant. One was made in the circle of al-Kindi. The other two may have been the work of al-Hajjaj ibn Yusuf ibn Matar and Hunayn ibn Ishaq. One Arabic version of the Data was translated into Latin by Gerard of Cremona. On Divisions is extant in Arabic fragments in works by al-Sijzi and Abu’l-Wafa’ al-Buzjani (940–998) and in an anonymous compilation. Latin quotations come from this background rather than from a direct knowledge of the Euclidean text. Traces of the Porisms are found in the anonymous Arabic translation Book of Assumptions of a lost Greek work by an unidentified author transliterated in Arabic as Aqatun and in works by al-Sijzi and Ibrahim ibn Sinan (908–946).

Euclid’s Optics, which like the Elements has a complex textual history, was translated in one of its versions into Arabic by Hiliya ibn Sarjun (fl. early ninth century?). The author of the second Arabic version is unknown. The textual transmission included a substantial transformation of its theoretical content. It involved al-Kindi, who compiled an edition of the text as well as other treatises on Euclidean and Pseudo-Euclidean optical writings. As in the case of the Elements and the Data, al-Tusi reedited the Optics. Parallel to al-Tusi, Ibn Abi Jarada (c. 1277) composed a paraphrase. The Latin transmission of the Optics is also fairly diverse. Three Arabic-Latin versions and a Greek-Latin version are known to exist. They were studied by Catholic scholars such as *Roger Bacon, *John Pecham, and *Witelo. The Hebrew and the Persian transmission of the work did not yet attract much attention.

Ancient sources know nothing about two texts on mechanics ascribed in Arabic sources to Euclid—the Maqala fi’l-mizan (Treatise on the Balance) and Kitab fi’l-thiql wa’l-khiffa (Book on Heaviness and Lightness); the latter was edited by Thabit ibn Qurra; the translator or editor of the former is unknown. The axiomatic and deductive structure situates the two texts clearly in a Euclidean framework. Bulmer-Thomas proposed to regard them as parts of one single larger Greek text, now lost. Several scholars from Islamic societies between the ninth and thirteenth centuries contributed to a new science of mechanics by merging the content and methodology of the Pseudo-Euclidean texts into the dynamic tradition of the Pseudo-Aristotelian Problemata Mechanica to which they added concepts and methods taken from the works of *Archimedes (c. 287–212 B.C.E.). On this basis, according to Abattouy, Muzaffar ibn Isma’il al-Isfizari (fl. 1048–1116) achieved a unified theory of the balance. The second Pseudo-Euclidean text plus several Arabic texts on mechanics were translated by Gerard of Cremona and other scholars into Latin and provided the basis for the works of *Jordanus de Nemore (fl. c. 1220) and others in Europe.

See also Abraham bar Hiyya; Algebra; Aristotelianism; Optics and catoptrics; Quadrivium; Uqlidisi, Al-; Weights, Science of

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SONJA BRENTJES

E

Elements and Qualities

Elements and the Prime Qualities

Elements, Cosmology, and Secondary Qualities

Applications of the Elements and Qualities

Bibliography

Encyclopedias

The Founder

The Golden Age of the Encyclopedic Genre

Organization of Knowledge

Bibliography

Eriugena, John Scottus

Four Divisions of Divine Nature

Bibliography

Primary Sources

Secondary Sources

Euclid

Translations of the Elements

Euclid’s Other Works

Bibliography

Primary Sources

Secondary Sources

Eyeglasses

Bibliography