Medieval Science, Technology and Medicine

Scholasticism

The term “scholasticism” generally refers to both a historical movement and a systematic method that arose during the Middle Ages and (notwithstanding the derogatory views of Renaissance humanists, who first coined the term) exerted enormous influence on the intellectual culture of the period.

Perhaps the most fundamental issue concerned with the history of Scholasticism is its origin. Early scholars contended that elements of scholastic method and the culture of Scholasticism go all the way back to antiquity and Aristotle in particular. But while it is certainly the case that there were ancient schools, that Aristotle discussed a dialectical procedure in his writings, and that medieval scholars drew on those discussions in formulating their scholastic method, the causal connection is at best remote rather than proximate. Early scholars, such as Endres and Grabmann, pointed instead to a confluence of related developments in different disciplines. As Europe emerged from the tenth-century invasions and the consequent social and political instabilities they produced, both the Church and emerging states sought to collect and compile legal codes, a movement that was assisted by the recovery of Roman law. But it is instructive to note that when Roman law came to light in Italy at the end of the eleventh century, it was the Digest—a compilation of the legal opinions of Roman jurists—and not the Code or the Novels that attracted the greatest interest. Earlier in the century, both Burchard of Worms (d. 1025) and Ivo of Chartres (c. 1040–1115) compiled large collections of rules governing all manner of Christian behavior. At the same time, the Church came to recognize that doctrinal pronouncements by the Fathers and the popes were in an equal state of disorganization, and frequently contradiction, as *Peter Abelard (1079–1142) observed in his Sic et non. Grabmann and others observed that some of the earliest examples of scholastic method arise in the contexts of assimilating and reconciling discordant legal and doctrinal pronouncements, as Gratian did for canon law in his Decretum (1140) and *Peter Lombard (1095/1100–1160) did for theology in the Sentences (written 1155–1157).

While Grabmann recognized that Abelard could not be the father of this movement or method (both because the technique was already in place before his time and because the Sic et non failed to adopt the various methodological rules he set forth in the prologue), he generally considered Scholasticism a Western creation, with some influence from Byzantine writers such as Photius (820–897). In reaction to this general consensus, George Makdisi argued that the Scholastic movement and method could be seen in earlier Islamic legal developments. Most instructive for Makdisi was the fact that the technique of al-khilaf, what he referred to as the “sic-et-non method,” was central to the Islamic process for determining orthodoxy. In his view, Islam had to depend on consensus (ijma) to define orthodoxy because it had no councils or synods; al-khilaf provided the technique for assessing consensus. As he put it, “the development of this method [viz., sic et non] in Christianity could very well not have happened at all, whereas without it, Islam could not have remained Islamic.” Leaving aside the formal discrepancies between the techniques employed by Ibn ‘Aqil, the eleventh-century legal scholar in whose works Makdisi found the use of alkhilaf, and the scholastic works of *Thomas Aquinas (c. 1224–1274), this characterization misconstrues the Latin connections between Scholastic culture and synodical or conciliar declarations. For it was almost always the case that doctrinal positions were promulgated by synods and councils after protracted and often intense debate and disagreement in the very Scholastic documents and procedures that Makdisi considered incidental to Christian culture. Seen from this perspective, however much transmission may have occurred, the incentives for scholastic techniques seem to have been equally present in both Islamic and Christian cultures.

The Nature of Scholasticism

At its core, Scholasticism refers to the pedagogical technique of the schools. Indeed, the term itself is derived from the magister scholasticus, the schoolmaster or head of instruction in the studia of monasteries, religious houses, or cathedrals. The central focus of scholastic education was the authoritative text, whether legal, philosophical, medical or theological. The prominence of the text can be seen in each of the two main pedagogical techniques of medieval education, the lecture and the disputation.

Unlike its modern namesake, the medieval lecture (lectura, literally a reading) was a sequential introduction to the text that defined the course. Within the university setting, lectures were distinguished by both the content and the time of day in which they were given. In the morning, fully qualified masters gave their detailed and comprehensive “ordinary” lectures on the core texts of the curriculum. These were followed in the afternoon by “extraordinary” or “cursory” lectures delivered by bachelors—that is, apprentice scholars whose lectures were part of their training for the degree—over the same books (essentially providing the medieval equivalent to the modern review session) or over secondary books in the curriculum. The lecture itself followed a formal pattern. First, the act of reading the base text sometimes provided a copy of the work itself; the frequent complaints of students that the reading proceeded too quickly and the countervailing injunctions of university authorities against reading too slowly suggest that transmission of the text viva voce did occur. Second, the lecturer “established the text,” that is, provided corrections to errors within circulating copies, thereby ensuring that all students in the class were using the same text. Third, he noted the hierarchical divisions of the text, which in surviving student copies often appear as gibbet-like symbols. Fourth, the master explained linguistic, terminological difficulties, as well as the positions adopted by previous authoritative commentators on the text, both as preliminaries to his own more extended analysis. Finally, important questions or issues within the section of text under discussion that day were analyzed in greater detail.

In short, the lecture provided a relatively economical technique for the transmission of an authoritative textual tradition, one that emphasized both order and recollection of detail. By contrast, the second pedagogical technique, the disputation, assumed the assimilation of this tradition and encouraged the creative juxtaposition of elements from the texts to resolve problems. The centrality of this exercise can be seen in its presence throughout the scholar’s life: part of the bachelor’s training involved attendance at his master’s disputations, and in time he was obliged to “respond” (responsiones) in a private mock dispute with his master or other students; magisterial careers included the expectation of engaging regularly in disputations, either the ordinary kind, in which positions were carefully proposed and prepared in advance, or de quolibet, in which the master would debate any question with any person. Such an exercise was an academic tour de force, in which students and masters alike could display their intellectual prowess, but they also were a means of expanding and extending the tradition of the text.

Although the lecture predated the disputation in the pedagogical development of the early university, one can also see how the disputed question evolved from the lecture. As masters prepared their lectures, certain parts of the text proved problematic and necessitated prolonged resolution. In the prologue to his Sic et non, Abelard articulated several possible explanations for apparent contradictions within the text, including the variability of language and meaning, false attributions of authorship, corruptions in the text itself, and retractions within the writings of authorities. In response, Abelard noted that “consistent or frequent questioning is defined as the first key to wisdom,” and then immediately observed that “Aristotle, the most clear-sighted of all philosophers, urges us to grasp this wholeheartedly.” By themselves, these questions raised within the context of the lecture did not constitute disputations, but it appears that by the time of Simon de Tournai (c. 1130–c. 1203), that is, by the opening years of the thirteenth century, a repertoire of such questions had been detached from the lecture and formed autonomous exercises in their own right. This process was aided by the masters’ growing recognition that education involved active engagement of the text, the creation of several compendia of “sentences”—the opinions of authoritative authors—and the growing assimilation of the new logic of Aristotle, especially the two Analytics, the Topics, and the Sophistical Refutations.

While the precise formulation of the disputed question both varied across European universities and evolved through the High Middle Ages, a central format can be seen within the genre. First, the question, appropriately formulated and answerable either in the affirmative or the negative, is enunciated. Following this, in support of one response—generally the one that is ultimately rejected—the author presents several “principal arguments.” In the Sed contra, the author observes the contrary position, generally supported by an authoritative quotation. Following this, the author presents his extended discussion of the issue (the responsio) in a format that displayed considerable variation throughout the Middle Ages. By the fourteenth century, for example, it was not uncommon for authors to present multiple opinions expressed by previous scholars and arguments against those opinions as well as subsidiary conclusions and doubts that serve as preliminaries to the author’s ultimate resolution of the question. Finally, the author returns to the “principal arguments” and replies to each, often drawing on the distinctions and conclusions developed in the responsio.

Transcription and Dissemination

Although the lecture and the disputation were oral exercises in the university, both came to be disseminated in written format through reportationes, that is, a transcription prepared during the oral session by someone else, a reportator. Beyond these “live” sessions, works that were originally delivered orally and transcribed were also revised by master himself and “published” as ordinationes. As a result, scholastic materials survive in a complex array of formats, from occasional notes used by masters in the oral sessions, to private student notes, more authoritative reportationes and subsequently ordinationes, and finally derivatives of these materials, often abbreviations that permitted rapid scanning of results without the more tendentious details.

Other forms of scholastic literature often reflect the techniques developed in the lecture and disputation. The systematic and comprehensive Summae, in which both law and theology were organized with rigor and precision, reflect in their constituent parts the questions that lay at the heart of the disputation. The scholastic commentary on authoritative texts adopted techniques from both the lecture and the disputation, depending on whether the commentary was structured as a literal exposition or a topical series of questions. But beyond these products of lecture and disputation, a collection of ancillary literatures grew up to help scholastic authors in the preparation of their works. Chief among these was the florilegium, a collection of extracts taken from authoritative authors. Florilegia that focused on the bible or the Fathers were extremely popular among sermon writers and theologians, but philosophical florilegia, such as the Auctoritates Aristotelis or the Propositiones Aristotelis, were mined for the commentary literature, both in the arts and theology. Union lists of books and catalogues of libraries, arranged alphabetically and thematically, appeared in the thirteenth century and proved to be enormously valuable in the search for materials on which to base lectures and commentaries. Handbooks of logical technique, such as *William of Heytesbury’s Rules for solving sophisms, were aimed at the undergraduate market as guides in training young scholars in the art of disputation. And finally, in the service of those preparing for examinations, compendia of questions and responses such as those found in Barcelona, Archivio de la Corona de Aragón, Ripoll 109, served as convenient (if frequently misleading) study aids to overburdened students of the scholastic curriculum.

See also Aristotelianism; Cathedral schools; Encyclopedias; Universities; Vocabulary

Bibliography

Baldwin, John W. The Scholastic Culture of the Middle Ages, 1000–1300. Lexington: Heath, 1971.

Bazàn, Bernardo C. Les Questions disputées et les questions quodlibétiques dans les facultés de théologie, de droit et de médecine. Turnhout: Brepols, 1985.

Del Punta, Francesco. “The Genre of Commentaries in the Middle Ages and its Relation to the Nature and Originality of Medieval Thought.” In Was ist Philosophie im Mittelalter? [Miscellanea mediaevalia 26] Edited by Jan A. Aertsen, Andreas Speer. Berlin: W. de Gruyter, 1998, pp. 138–151.

Endres, Joseph Anton. Über des Ursprung und die Entwicklung der scholastischen Lehrmethode. Philosophisches Jahrbuch (1889) 2: 52–59.

L’enseignement des disciplines à la Faculté des arts, Paris et Oxford, XIIIe-XVe siècles: actes du colloque international. Edited by Olga Weijers and Louis Holtz. Turnhout: Brepols, 1997.

Les Genres littéraires dans les sources théologiques et philosophiques médiévales: définition, critique et exploitation. Actes du Colloque international de Louvain-la-Neuve, 25-27 mai 1981. Louvain-la-Neuve: Université catholique de Louvain, 1982.

Giusberti, Franco. Materials for a Study on Twelfth Century Scholasticism. Napoli: Bibliopolis, 1982.

Grabmann, Martin. Die Geschichte der scholastischen Methode nach den gedruckten und ungedruckten Quellen. 2 vols. Freiburg im Breisgau: Herdersche Verlagshandlung, 1909–1911.

Hamesse, Jacqueline. “The Scholastic Model of Reading.” In A History of Reading in the West. Edited by Guglielmo Cavallo, Roger Chartier, Lydia G Cochrane. Amherst: University of Massachusetts Press, 1999, pp. 103–119.

Lawn, Brian. The Rise and Decline of the Scholastic ‘Quaestio Disputata’ With Special Emphasis on its Use in the Teaching of Medicine and Science. Leiden: E.J. Brill, 1993.

Makdisi, George. The Scholastic Method in Medieval Education: An Inquiry into its Origins in Law and Theology. Speculum (1974) 49: 640–661 Medieval Literary Theory and Criticism, c. 1100-c. 1375: the commentary-tradition. Edited by A. J. Minnis and A. B. Scott. Oxford: Clarendon Press, 1988.

Panofsky, Erwin. Gothic Architecture and Scholasticism. New York: Meridian Books, 1957.

Radding, Charles and William W. Clark. Medieval Architecture, Medieval Learning: Builders and Masters in the Age of Romanesque and Gothic. New Haven: Yale University Press, 1992.

Weijers, Olga. La ‘disputatio’ dans les Facultés des arts au moyen âge. Turnhout: Brepols, 2002.

STEVEN J. LIVESEY

Scientia

Despite the etymological connections, scientia in the Middle Ages designated an intellectual condition or state that was both broader and narrower than the modern term derived from it. While a full treatment of the subject goes well beyond the limitations of this entry, the goal here will be to provide some measure of the complexity of scientia and its applications in the Latin Middle Ages.

From its beginnings, Christianity displayed an ambivalent and cautious attitude toward scientia. It was, after all, the tree of the knowledge of good and evil (lignum scientiae boni et mali) that occasioned the fall of humanity from its pristine state, but also necessitated the incarnation and redemption of Christ. In a widely-cited passage, Saint Paul observed in 1 Corinthians 8:1 that “knowledge puffs up, but love builds up” (scientia inflat, charitas vero aedificat). Yet four chapters later (12:8), in his discussion of the gifts of the Spirit, Paul noted that some within the body of Christ are given the “word of knowledge” (sermo scientiae) by the Spirit. Through these and other passages, readers were warned that the value of scientia depended on both its source and purpose.

Like the scriptures on which they based their positions, the Fathers offered a broad spectrum of positions about the value of scientia. As has often been observed, Tertullian (c. 155–c. 230) and others of his persuasion considered secular philosophy at best irrelevant, and possibly distracting or corrupting influences in the Christian life. Far more accommodating were members of the Alexandrian school, such as Clement (d. 211–215), whose typological interpretation of the story of Abraham and his sons born of Sarah and Haggar came to prefigure the proper Christian use of secular knowledge: the useful parts of philosophy were to be employed to the advantage of the spiritual, as a handmaid (ancilla) of theology. In a particularly telling passage of City of God, Augustine (d. 430) sought to link the authority of scripture with the authority of secular knowledge: “As in the case of visible objects which we have not seen, we trust those who have (and likewise with all sensible objects), so in the case of things which are perceived by the mind and spirit, i.e. which are remote from our own interior sense, it behooves us to trust those who have seen them set in that incorporeal light…” (De civ. Dei xi.3). Both faith and scientia depend ultimately on the same indirect first principles that must be accepted, not proved, a perspective that had a long trajectory in Latin medieval intellectual circles.

The other principal influence on medieval understanding of scientia was the classical tradition, and the positions of Aristotle in particular, according to which scientia was strictly distinguished from belief or opinion. Scientia begins with experience, the repeated applications of which produce intuition or insight into the universal condition. As a result, this side of Aristotle’s method resembles an inductive process; but Aristotle was also emphatic that real scientia is not produced until it is rigorously demonstrated through a deductive process beginning with first principles and definitions. According to Aristotle, the demonstrated propositions must satisfy three criteria: they must be universally true; they must contain terms that are essential to one another, thereby ensuring the necessity of the propositions; and they must be formed in such a way that the predicate is true of the subject strictly speaking, and not by virtue of some wider domain. Particularly in view of this third criterion, Aristotle considered scientific disciplines largely autonomous entities, each with its own subject domain, principles, and propositions. As a result, the invocation of principles from one discipline in the demonstrations of another, which Aristotle referred to as metabasis, was strictly forbidden, because such boundary infractions could introduce ambiguities, or worse still, errors into the demonstrative process. The only exception admitted by Aristotle belonged to a relatively small class of disciplines, known as the subalternated sciences, in which the principles of one science depend on the propositions of another, as for example, the principles of geometrical optics rely on the results of geometry.

Closely related to these issues was the distinction between scientia quia (that is, knowledge of the fact) and scientia propter quid (that is, knowledge through the cause). In a purely formal sense, scientia for Aristotle was the search for the middle terms of syllogisms. As he observed in the Posterior Analytics, one can demonstrate that the Moon is spherical by observing that the shadow cast on the Moon is circular, but such demonstrations do not arise from the cause of sphericity, but merely the observed effect of sphericity. By changing the middle term of the syllogism—making sphericity the cause through which the Moon’s waxing and waning arises—one obtains a qualitatively stronger result: because, as Aristotle asserted in the opening chapter of the Physics, we truly know things when we know their causes, the more conclusive form of demonstration (which the Middle Ages came to call demonstratio potissima) is that which is based on the ultimate principles of things, their causes. This, and only this, produces scientia propter quid.

Because the medieval understandings of scientia rested in large measure on the transmission of Aristotle’s works, the early Middle Ages came to view scientia as a matter of textual analysis, drawing on *Boethius’s translations of the Categories, De interpretatione, and Porphyry’s Isagoge. In the sacred sphere, this fit conveniently into the prevailing emphasis on theology as exegesis, in which Augustine’s discussions of method combined with the remnants of classical culture to tease meaning from the scripture. At the same time, several early medieval scholars, including Boethius, Cassiodorus (c. 480–c. 575), *Martianus Capella (fl. 410–439?), *Isidore of Seville (c. 560–636), and *Bede (d. 735) continued the ancient handbook tradition that preserved a remnant of classical scientific work. Often two or three times removed from the original sources, their goal was to summarize the details of those sources without the substantiating arguments, in the process obscuring or misconstruing the systematic structure of the material. Thus, for example, their treatments of mathematics are little more than statements of definitions and theorems without proofs, and Isidore of Seville’s discussion of matter theory in Book XIII of the Etymologies places Aristotle’s hylomorphic theory adjacent to the atomist theory, without discussing or even observing their incompatibility.

Under these conditions, theoretical discussions of scientia consisted largely of perfunctory classifications of the sciences, themselves resting on handbook restatements of the Aristotelian tripartite division of theoretical philosophy into metaphysics, mathematics, and physics, or the Stoic division of philosophy into ethics, logic, and physics, without further discussion of the incompatibility of these classifications or the methodological issues on which they rested. In particular, disciplines were distinguished primarily by the objects on which they focused, not always the methods that they employed. Physics, for example, focuses on the forms of bodies as they exist in matter; mathematics the forms of those bodies as they exist apart from matter; and metaphysics being that can exist of itself and apart from matter. While this was accompanied by some reference to the intellectual processes by which each discipline operates, it did not investigate the logical or syllogistic intricacies of scientia.

Medieval Developments

All of this began to change in the course of the twelfth century, when though a variety of channels classical materials and materials from the Islamic tradition entered western Europe. Now in possession of the so-called New Logic (the Prior and Posterior Analytics, the Topics, and the Sophistical Refutations), European scholars became acquainted with Aristotle’s more elaborate discussions of scientia, demonstration, subalternation, and metabasis. As Aristotle’s other works—especially Physica, De anima, De caelo, Ethica Nicomachea, Metaphysica—and the works of Islamic scholars filtered into Europe, Latin scholars possessed the content necessary to both complete the theoretical discussions of scientia and augment the simple classifications of the sciences carried over from the early Middle Ages. All of these new works were assimilated within a receptive new institution, the university. The product of this assimilation was a reconceptualization of the scientiae in Western culture.

A singularly important influence in this process was the introduction of Aristotle with his Islamic commentators. Largely because of the way that Aristotle had been received into Islamic culture, as an encyclopedic corpus of natural knowledge with the methodological prescriptions of the Posterior Analytics, there was a related perspective that became known as both Aristotle and his commentators were brought into Western Europe. This is perhaps most pronounced in the work of Averroes (*Ibn Rushd), the Commentator as he was known in Latin circles, but it can already be seen in the influence of Avicenna (*Ibn Sina) a century earlier. Avicenna’s Qanun (Canon) enjoyed a special place within the medical community of the Western Middle Ages, and because the medical community seems to have had a central role in the early introduction of Aristotle in the twelfth century, Avicenna’s readings of Aristotle and their application to medicine were especially formative. Antiquity in general and Aristotle in particular had viewed medicine in very distinct senses, as both an art and a science, a practice that depended on both the empirical observations of patients by doctors and the traditions learned at the hands of senior practitioners, and a theoretical discipline that had its own principles, just like natural philosophy. Avicenna’s emphasis was placed on the latter sense of medicine as the consideration of the human body insofar as it is healthy or sick, and therefore in his view, the physician must know the causes of health and sickness, including both symptoms and the principles of being.

In some quarters, medicine was considered a science subordinate to psychology, the basic text of which was Aristotle’s De anima. As a result, introductory lectures and formal prologues to De anima—and to the basic texts of medical faculties at universities—focused on three issues: whether medicine was a science, the most appropriate method of teaching medicine, and the particular subject matter of medicine. Many if not most of these long and detailed introductions adopted the Aristotelian perspective, augmented by Avicenna, of the nature of scientia and discussed the relationship between empirical medicine and scientific medicine in much the same way that Aristotle had delineated scientia quia and scientia propter quid.

A second influential development arose from a Latin source, the comments of *Robert Grosseteste (c. 1168–1253). As a translator of the Nicomachean Ethics and one of the earliest commentators on the Physics and the Posterior Analytics, Grosseteste’s positions were cited repeatedly by subsequent readers of Aristotle’s works. Especially in the area of the subalternate sciences and the interrelationship of disciplines, his comments added two crucial elements to the medieval position. First, in his commentary on the Physics, Grosseteste argued that in subalternate sciences such as astronomy, natural accidents were added over and above (superadditur) the subjects of pure mathematics, thereby making a composite subject of the new discipline. In his commentary on the Posterior Analytics, while agreeing with Aristotle that the subalternate, inferior discipline provides scientia quia and the subalternating, superior discipline scientia propter quid, Grosseteste observes that in astronomy or optics, neither geometry nor natural philosophy as subalternating sciences can provide the complete cause of phenomena: geometry provides the formal cause, natural philosophy the efficient and material cause. As a result, complete propter quid demonstrations must include both, and so astronomy and optics are partially subalternated to two (or more) disciplines.

Much the same kind of development can be seen in another important application of scientia, namely in the scholastic discussions of theology as a science. Over the course of the twelfth century, the older descriptive and exegetical senses of theology came to be augmented and in some quarters replaced by an analytic, systematic theology. Once again, as in the case of medicine, the introductory lectures on or prologues to theological texts began to explore the scientific nature of theology, drawing on Clement’s imagery of the ancilla. While more conservative commentators emphasized that ancilla must be taken in the sense of famulatus (that is, a servant), more philosophically astute writers drew the parallel of the ancillary relationship of philosophy and theology and Aristotle’s discussion of subalternation. Their discussions followed two paths. Some, such as *Thomas Aquinas (c. 1224–1274), asked whether Aristotle’s account of scientia and the first principles on which it was based shed light on the foundations of theology: is theology scientific because it proceeds from principles known in a superior scientia, viz. the knowledge of God and the blessed? In other words, as subsequent readers of Thomas rendered his position, “our theology is a subalternated science to the science of the blessed” (Summa Theologiae I, 1, 2; John of Reading [1989] 102). The other path focused instead on the relationship between theology and the human sciences; as Henry of Ghent (d. 1293) argued, theology subordinates other sciences to itself because scripture speaks propter quid, through causes, about those things that the human sciences speak only quia and by experience.

While these kinds of speculations about the relationships between theology and the human sciences had a residual effect beyond the Middle Ages—consider, for example, Galileo’s arguments in his Letter to Christina about the proper understanding of the preeminence of theology—for a variety of reasons such discussions seem to have been eclipsed by the third or fourth decade of the fourteenth century. First, prologues to commentaries on the Sentences (the chief locus for such speculations) diminished in size and all but disappeared by 1340. More to the point, scholars seem to have exhausted the traditional questions of the scientific status of theology and moved on to epistemological questions about the sources and certainty of scientia.

The strands of those developments are numerous, complex, and not always disentangled. One focused on the psychological states by which scientia was acquired and retained. Drawing on an account in Aristotle’s Categories (VIII 8b28–34), scholastic authors considered scientia a mental state, or habitus, that was permanent or at least difficult to change. Beginning in the late thirteenth century and extending through the next century, scholars debated the relationship between those mental states and the particular elements of scientific knowledge humans possess. Some, including Peter Aureol (d. 1322), argued that there was a single overarching habitus that governed each discipline, conferring an essential unity recognizable in the discipline’s content and method. *William of Ockham (c. 1285–1347) and others argued that this did not suffice to explain how humans acquired discrete parts of disciplinary understanding, and so proposed that each discipline was governed by multiple mental habits, each corresponding to a proposition or even a part of a proposition within the discipline. Essential unity of scientific disciplines was therefore sacrificed for a conventional unity that permitted more flexible alterations of their contents.

Another important element of this development concerned the sufficiency of the criteria for scientia. Although the standard criteria involved the evidence of both reason and experience, increasingly in the fourteenth century there were doubts about the possibility of one or the other, or in some cases, both. Many of the novel positions of fourteenth-century natural philosophy were developed secundum imaginationem, that is, hypothetically and not categorically. Thus, in a famous passage from his Livre du ciel et du monde, *Nicole Oresme argued that neither experience nor rational proof was capable of establishing the cause for diurnal phenomena. His objective in the discussion was to provide a “means of refuting and checking those who would like to impugn our faith by argument.” By the end of the fourteenth century, scholars at the new university in Vienna expressed doubts about the sufficiency of Aristotelian syllogistic in proving or even expressing core theological positions like the Trinity. There are perhaps several interrelated developments that were responsible for these shifts. First, the condemnations at Paris and elsewhere in the late thirteenth century, combined with an emphasis on voluntarist theology at the same time, encouraged subsequent scholars to include possible divine interventions in the natural world, and consequently all demonstrative or inductive proofs were subject to cancellation by divine omnipotence. Second, while Aristotle had distinguished sharply between dialectical and demonstrative proofs, later medieval scholars came to blur the distinctions between these modes of argument. Third, many of the natural speculations of the late Middle Ages arose in quaestiones disputatae, and especially quaestiones de sophismatibus, in which the goal of the participant in debate was not demonstration of universal truth, but agility in the disputation. And finally, Joel Kaye has argued that hypothetical currents of the fourteenth century arose from the economic theories of money and value that emphasized relative rather than absolute measures.

On occasion, these currents merged in the late Middle Ages. In 1342/1343, the Augustinian Hermit Gregory of Rimini (d. 1358) argued in his commentary on the Sentences that God could preserve the habit of perspective in the intellect, while not preserving the habit of geometry. In such an intellect, perspective would be a subalternate science, even though it would have no understanding of its own principles, but rather only faith. In this hypothetical example, fueled by the emphasis on divine omnipotence, only those parts of perspective that were acquired before the loss of geometric knowledge would retain their scientific status; conclusions derived subsequently would fail to be scientific. Subsequent commentators, such as the Cistercian James of Eltville (d. 1393), even argued that evidence is not necessary for scientia: a collection of propositions would be scientific by virtue of the fact that it conforms to the rules of consequentiae, even though by divine omnipotence it has no subjective referent. Extreme though these examples may be, they suggest the extensive deviations between late medieval understandings of scientia and the Aristotelian sources on which they were grounded.

See also Condemnation of 1277; Logic; Medicine, theoretical; Reason; Religion and science; Universities

Bibliography

Brown, Stephen F. “Late Thirteenth Century Theology. ‘Scientia’ pushed to its Limits.” In ‘Scientia’ und ‘Disciplina.’ Wissenstheorie und Wissenschaftspraxis im 12. und 13. Jahrhundert. Edited by Rainer Berndt, Matthias Lutz-Bachmann, Ralf M. W. Stammberger. Berlin: Akademie Verlag, 2002, pp. 249–260.

Chenu, M.-D. La Théologie comme science au XIIIe siècle. Paris: J. Vrin, 1969.

Crombie, Alistair. Styles of Scientific Thinking in the European Tradition: The History of Argument and Explanation Especially in the Mathematical and Biomedical Sciences and Arts. 3 vols. London: Duckworth, 1994.

Funkenstein, Amos. Theology and the Scientific Imagination from the Middle Ages to the Seventeenth Century. Princeton: Princeton University Press, 1986.

Hintikka, Jaakko. On the Ingredients of an Aristotelian Science. Nous (1972) 6: 55–69.

Kaye, Joel. Economy and Nature in the Fourteenth Century: Money, Market Exchange, and the Emergence of Scientific Thought. New York: Cambridge University Press, 1998.

Livesey, Steven J. “Scientific Writing in the Latin Middle Ages.” In Scientific Books, Libraries and Collectors. Edited by Andrew Hunter. 4th edition. Aldershot: Ashgate, 2000, pp. 72–98.

———. Theology and Science in the Fourteenth Century: Three Questions on the Unity and Subalternation of the Sciences from John of Reading’s Commentary on the Sentences, edition and critical commentary. Leiden: E. J. Brill, 1989.

McKirahan, Richard D., Jr. Aristotle’s Subordinate Sciences. British Journal for the History of Science (1978) 11: 197–220.

Murdoch, John. “The Analytic Character of Late Medieval Learning: Natural Philosophy without Nature.” In Approaches to Nature in the Middle Ages. Edited by Lawrence Roberts. Binghamton, NY: Center for Medieval & Early Renaissance Studies, 1984, pp. 171–213.

———. “From Social into Intellectual Factors: An Aspect of the Unitary Character of Late Medieval Learning.” The Cultural Context of Medieval Learning. Edited by John Murdoch and Edith Sylla. Dordrecht, Holland: D. Reidel Publishing Co., 1975, pp. 271–348.

Oresme, Nicole. Le Livre du ciel et du monde. Edited by A. D. Menut and A. J. Denomy. Madison, Wisconsin: University of Wisconsin Press, 1968.

Scientia und ars im Hoch- und Spätmittelalter. Edited by Ingrid Craemer-Ruegenberg and Andreas Speer. [Miscellanea mediaevalia 22/1-2] Berlin: Walter de Gruyter, 1994.

Weisheipl, James A. Classifications of the Sciences in Medieval Thought. Mediaeval Studies (1965) 27: 54–90.

STEVEN J. LIVESEY

Shipbuilding

Early medieval Europeans received from their predecessors two broad ranges of wooden shipbuilding traditions, one in the Mediterranean and the other in the northern seas. At the same time Chinese shipwrights had already developed the central features of the design of the junk. Its watertight compartments, adjustable keel, and highly flexible number of masts each carrying a lug sail with battens, made the junk a highly versatile and reliable seagoing ship. Junks by the year 1000 were much larger than any ships in Europe or in the great oceanic area where a Malaysian shipbuilding tradition predominated. There, ocean-going rafts with outriggers or twin hulls and rigged with, at first, bipole masts ranged much more widely than vessels from any other part of the world carrying the designs and building practices across the Indian Ocean to Madagascar and around the Pacific Ocean to the islands of Polynesia. Along the shores of the Arabian Sea shipbuilders constructed dhows, relatively shallow cargo vessels rigged with a single triangular or lateen sail. The planks of the hulls were typically sewn together with pieces of rope, a loose system which made the hull flexible, and so able to handle rough seas, but not very watertight. There were also serious limitations on how big such hulls could be built, unlike junks where vessels of one thousand tons and more seem to have been feasible.

Mediterranean Practice

Roman shipbuilders followed Greek practices in building their hulls with mortise and tenon joints. Wedges or tenons were placed in cavities or mortises gouged out of the planks and held in place by wooden nails passed through the hull planks and the tenons. In the Roman Empire the methods of fastening predominated on all parts of ships, including the decks, and the tenons were very close to each other. The resulting hull was extremely strong, heavy, and sturdy so the internal framing was minimal. The hull was also very watertight but even so the surface was often covered with wax or even copper sheathing to protect it from attack by shipworm (Teredo navalis). Propulsion came from a single square sail stepped near the middle of the ship. Often the mainsail was supplemented with a small square sail slung under the bowsprit. Roman shipbuilders produced vessels of two general categories, round ships with length-to-breadth ratios of about 3:1 propelled entirely by sails, and galleys with length-to-breadth ratios of about 5:1 propelled both by the standard rig and by oars. Although it was possible to have multiple banks of rowers, in the Roman Empire there was typically only one, with each rower handling a single oar. Shipbuilders gave all those vessels at least one but often two side rudders for control.

As the economy declined in the early Middle Ages and the supply of skilled labor was reduced, the quality of shipbuilding deteriorated. The distance between mortise and tenon joints increased, and on the upper parts of hulls such joints disappeared entirely with planks merely pinned to internal frames. The trend led by the end of the first millennium C.E. to a new form of hull construction. Instead of relying on the exterior hull for strength, shipbuilders transferred the task of maintaining the integrity of the vessel to the internal frame. The process of ship construction as a result reversed, with the internal ribs set up first and then the hull planks added. The planks were still fitted end-to-end as with the old method but now to maintain watertightness they needed to be caulked more extensively and more regularly. The internal frames gave shape to the hull so their design became much more important. The designer of those frames in turn took on a significantly higher status, the hewers of the planks a lesser position. The new type of skeleton-first construction made for a lighter and more flexible ship which was easier to build, needed less wood, but required more maintenance. Increasing the scale of the ship or changing the shape of the hull was now easier. Builders used the new kind of construction both on large sailing round ships and oared galleys.

Thirteenth-century Arabic manuscript depiction of a dhow. (Corbis/Arne Hodalic)

In the course of the early Middle Ages Mediterranean vessels went through a change in rigging as well. Triangular lateen sails were in use in classical Greece and Rome for small vessels. As big ships disappeared with the decline of the Roman Empire and economy the lateen sail came to dominate and square sails all but disappeared. Lateen sails had the advantage of making it possible to sail closer to the wind. Lateen sails had the disadvantage that when coming about, that is changing course by something of the order of ninety degrees, the yard from which the sail was hung had to be moved to the other side of the mast. In order to do that the yard had to be carried over the top of the mast, which was a clumsy, complex, and manpower-hungry operation. There was a limitation then on the size of sails and thus on the size of ships. It was possible to add a second mast, which shipbuilders often did both on galleys and on round ships since that was the only way to increase total sail area.

Northern European Practice

Shipbuilders around the Baltic and North Seas in the early Middle Ages produced a variety of different types of vessels which were the ancestors of a range of craft that melded together over the years to create one principal kind of sailing ship. The rowing barge was a simple vessel with overlapping planking. The planks could be held fast by ropes but over time shipbuilders turned to wooden nails or iron rivets for the purpose. That type of lapstrake construction for hulls meant that internal ribs were of little importance in strengthening the hull. At first shipwrights used long planks running from bow to stern but they discovered that by scarfing shorter pieces together not only did they eliminate a constraint on the length of their vessels but they also increased the flexibility of the hulls. At some point, probably in the eighth century, the rowing barge got a real keel and also a single square sail on a single mast stepped in the middle of the ship. The new type, with both ends looking much the same, was an effective open ocean sailor. Scandinavian shipbuilders produced broadly two versions of what can be called the Viking ship after its most famous users. One version was low, and fitted with oars and a mast that could be taken down or put up quickly and with a length-to-breadth ratio of 5:1 or 6:1. The other version had a fixed mast, few if any oars at the bow and stern which were there just to help in difficult circumstances, and a length-to-breadth ratio of around 3:1. Both types had a single side rudder which apparently gave a high degree of control. The Viking ship evolved into a versatile cargo ship which was also effective as a military transport and warship. Often called a keel because of one of the features which allowed it to take to the open ocean, it was produced in variations throughout northern Europe and along the Atlantic front as far south as Iberia.

The other types that came from early medieval northern shipyards were more limited in size and complexity. The hulk had a very simple system of planking which gave way over time to lapstrake construction. The hull had the form of a banana and there was no keel so it proved effective in use on rivers and in estuaries. The hull planks, because of the shape of the hull, met at the bow in a unique way and were often held in place by tying them together. Rigging was a single square sail on a single mast which could be, in the case of vessels designed for river travel, set well forward. The cog had a very different form from the hulk. While the planks on the sides overlapped there was a sharp angle between those side planks and the ones on the bottom. Those bottom planks were placed end-to-end and the floor was virtually flat. With posts at either end almost vertical the hull was somewhat box-like. The type was suited to use on tidal flats where it could rest squarely on the bottom when the tide was out, be unloaded and loaded, and then float off when the tide came in. There was a single square sail on a single mast placed in the middle of the ship. The design certainly had Celtic origins but it was transformed by shipwrights in the High Middle Ages to make it into the dominant cargo and military vessel of the North.

Shipbuilders, possibly in the Low Countries, gave the cog a keel. In doing that they also made changes in the form of the hull, overlapping the bottom planks and modifying the sharp angles between the bottom and side planks. The result was a still box-like hull which had greater carrying capacity per unit length than keels. The cog could also be built higher than its predecessors but that meant passing heavy squared timbers through from one side to the other high in the ship to keep the sides in place. Shipbuilders fitted the hull planks into the heavy posts at the bow and stern and also fixed a rudder to the sternpost which was more stable than a side rudder. In the long run it would prove more efficient as well. Cogs could be and were made much larger than other contemporary vessels. Greater size meant a need for a larger sail and a larger crew to raise it. To get more sail area sailors added a bonnet, an extra rectangular piece of canvas that could be temporarily sewn to the bottom of the sail. That gave the mariners greater flexibility in deploying canvas without increasing manning requirements. Riding higher in the water and able to carry larger numbers of men than other contemporary types cogs became the standard vessels of northern naval forces, doubling as cargo ships in peacetime.

While the two shipbuilding traditions of the Mediterranean and northern Europe remained largely isolated through the early and High Middle Ages, from the late thirteenth century both benefited from extensive contact and borrowing of designs and building methods. Sailors in southern Europe used the cog certainly by the beginning of the fourteenth century and probably earlier. Shipwrights in the Mediterranean appreciated the advantages of greater carrying capacity but they were also conscious of the limitations set by the simple rig. They added a second mast near the stern and fitted it with a lateen sail. They also changed the form of hull construction, going over to skeleton-first building. The result was the carrack, in use by the late fourteenth century. It was easier to build, probably lighter than a cog of the same size, and could be built bigger. Most of all the two masts and the presence of a triangular sail gave mariners greater control over their vessels and made it possible for them to sail closer to the wind. The next logical step, taken sometime around the end of the fourteenth century, was to add a third small mast near the bow to balance the one at the stern. The driving sail and principal source of propulsion was still the mainsail on the mainmast but the combination or full-rig made ships more maneuverable and able to sail in a greater variety of conditions. While older forms of ships, such as the keel or the cog or the lateenrigged cargo ship of the Mediterranean, did not by any means disappear, the full-rigged ship came to dominate exchange over longer distances, especially in the form of the full-rigged carrack travelling between southern and northern Europe. Northern Europeans were slow to adapt to skeleton-first hull construction, in some cases even combining old methods with the new one. By the end of the fifteenth century the full-rigged ship was the preferred vessel for many intra-European trades, in part because of its handling qualities, in part because of its versatility, and in part because its crew size could be reduced per ton of goods carried compared to other types. The greater range also led to its replacing, for example, the simpler, lower, lateen-rigged caravel in Portuguese voyages of exploration along the west coast of Africa. Full-rigged ships in daily use were the choice for voyages of exploration and became in the Renaissance the vehicles for European domination of the ocean seas and for the resulting international trading connections and colonization.

See also Navigation; Travel and exploration

Bibliography

Bass, George, ed. A History of Seafaring Based on Underwater Archaeology. London: Thames and Hudson, 1972.

Friel, Ian. The Good Ship: Ships, Shipbuilding and Technology in England, 1200–1520. London: British Museum Press, 1995.

Gardiner, Robert, ed. The Earliest Ships: the Evolution of Boats into Ships. London: Conway Maritime Press, 1996.

———, ed. Cogs, Caravels and Galleons The Sailing Ship 1000–1650. London: Conway Maritime Press, 1994.

Hattendorf, John B., ed. Maritime History in the Age of Discovery: An Introduction. Malabar, Florida: Krieger, 1995.

Hutchinson, Gillian. Medieval Ships and Shipping. Rutherford: Fairleigh Dickinson University Press, 1994.

Lane, Frederic C. Venetian Ships and Shipbuilders of the Renaissance. Baltimore: Johns Hopkins Press, 1934.

Lewis, Archibald R. and Timothy J. Runyan. European Naval and Maritime History, 300–1500. Bloomington: Indiana University Press, 1985.

McGrail, Seán. Boats of the World from the Stone Age to Medieval Times. Oxford: Oxford University Press, 2001.

Pryor, J. H. Geography, Technology and War: Studies in the Maritime History of the Mediterranean 649–1571. New York: Cambridge University Press, 1988.

Unger, Richard W. The Ship in the Medieval Economy, 600–1600. London: Croom-Helm Ltd., 1980.

RICHARD W. UNGER

South-Central Asian Science

South-central Asia, particularly India, is famous for its rich tradition in religion and philosophy, but less renowned for its scientific culture. However, evidence suggests that scientific activity was extensive in India in the Middle Ages, and the Indian scientific corpus of the period has been estimated at around three million manuscripts, the majority of which remain unexamined by modern historians of science. Among the areas in which scientific activity was carried out were natural science, technology, medicine, architecture, astronomy, and mathematics. This article focuses on an important subset of Indian science, the so-called “exact” sciences, or in Sanskrit jyotihsastra (astral science). Included in jyotihsastra are mathematics, astronomy, and various divinatory procedures.

In the Indian context, where both astronomy and astrology belong to jyotihsastra, no substantial difference was perceived between an astronomer and an astrologer. Mathematical astronomy was a tool for the calculation of planetary positions, and knowledge of planetary positions was necessary for astrological predictions. Many Indian astronomical treatises introduce concepts which have no deeper astronomical purpose, but which play a role in astrology.

The development of jyotihsastra in India during the medieval period was a combination of indigenous activity as well as the importation of foreign scientific ideas, most notably from Greece, and, in the later medieval period, from Islamic Western Asia. Mathematics was, for a large part, a tool utilized and developed by astronomers for their astronomical models and computations, but it also became important in its own right, especially in economics, geometry, conversions of *weights and measures, number theory, *algebra, and trigonometry.

One of the most striking features of medieval Indian scientific works is their format. Like almost all Sanskrit literary works, the jyotihsastra texts were composed in verse. This was partly to aid memorization as the texts were transmitted orally, but also to challenge the students: some authors, it seems, deliberately made their verses obscure in order to test their pupils. This scientific “poetry” greatly contrasted with the written documents that provided the basis of most other sciences in the rest of the world at that time. In order for the material to fit these metrical patterns, a flexible vocabulary was needed, and authors could always make up their own synonyms rather than use a specifically correct term. As a result Indian science always lacked a rigid or standard nomenclature like that of, for example, the ancient Greeks.

The poetic form also entailed a certain degree of obscurity as scientists sought to convey complicated expressions in a restricted space: form influenced the treatment of the subject matter. In order to facilitate the daunting task of memorizing large amounts of technical material, the scientists developed many strategies to make the verses more memorable. A frequent problem was representing long strings of numbers, and several ingenious ways were developed to overcome it. For example, the bhutasankhya system was used extensively, in which common objects associated with an amount through everyday or mythological connections were substituted for the number itself (for example, “nails” represented the number twenty and “Vedas,” the quartet of Hindu sacred books, stood for the number four). Another method was the South Indian katapayadi system, in which each syllable of the Indian script was associated with a different number, and combinations of numbers were ingeniously arranged to spell words representing larger numbers.

In addition, symbols representing numerals in a base ten system were used. *Al-Biruni, a Muslim scholar who accompanied Mahmud of Ghazni during his conquest of India and wrote a famous work on India, observed that Indian scientists did not use letters of their alphabet for numerical notation in the way that their Islamic counterparts used Arabic letters, but rather used numerals in a base ten system.

The obscurity of the verses of the major works was remedied by accompanying commentaries, written for the most part in prose, which sought to elucidate the texts. The commentators did this in many ways, for example by explaining the grammar, paraphrasing the verse, providing synonyms or definitions, or by giving worked examples. The commentaries are often most helpful in deciphering the mathematical rules contained in the verses of the original work. It was not uncommon for authors to write commentaries on their own work.

The Indian Astronomical Model

Indian astronomers used a geocentric astronomical model in which the planets each have two epicycles, one known as manda (Sanskrit: slow), the other as sighra (fast). Both revolve around the deferent, the circular path of the planet in its orbit around the Earth. This concept helps to explain the “wobble” that is sometimes observable in planets. The Sun and the Moon have only one epicycle, the manda, and hence do not appear to oscillate. The true position of the planet is found by calculating the mean of the two epicycles. From the modern heliocentric point of view, one can think of the manda as accounting for the fact that the orbit of a planet around the Earth is not circular, and the sighra for the fact that the Earth is orbiting the Sun. It is certain that the Indian planetary model was based on a Greek prototype which adhered to an Aristotelian idea of concentricity, namely that all complex motion is a product of smaller and simpler circular, uniform motion.

In the Indian conception of time, 4,320,000 years is known as a mahayuga. This period is subdivided into four smaller periods, known as yugas, namely krta, treta, dvapara, and kali. One thousand mahayugas make up one kalpa, and at the end of the kalpa there is a partial destruction of the universe. This conception formed the basis of Indian astronomy. The astronomers would provide the number of revolutions of each planet during the span of a kalpa, or during a mahayuga. From these numbers, together with other parameters (radii of epicycles, positions of apogees and nodes, etc.), as well as knowledge of how much of the kalpa had passed, could be computed the mean position of the planets at any given time. This methodology spread to Islamic Western Asia. In particular, the Arab astrologer Abu Ma‘shar (b. 787) wrote a work entitled Zij al-hazarat in which the mean motions of the planets are calculated in this way, from the number of revolutions in a yuga.

From the time of the introduction of Greek geometrical models of astronomy in India until the adoption of Islamic astronomy in the fifteenth century, the model remained essentially the same. The Indian astronomical milieu was not one of careful observation followed by revisions of the model or the constants utilized in it, but rather one in which changes occured as the mathematical formulae were investigated and refined. Some formulae were simplified for increased ease of practical use; others were elaborated and made theoretically more correct, but they tended to be the ones that had the least practical application.

Other techniques employed by the Indian astronomers were analemmas, two-dimensional planar representations of the celestial sphere, in which calculations concerning arcs and angles on the sphere can be treated as plane triangles, and linked to this, ratios derived from similar triangles, known in Sanskrit as trairasika (the rule of three). In trigonometry, Indians used the sine function as well the versed sine (versine) function. The traditional approach was to tabulate the sine function for certain values of the angle and then compute a given sine using linear interpolation or second-order differences, but algebraic expressions for computing the sine of a given angle were also given. There were many different values used for R (the radius of the circle in which the angle is measured), including 3438, 150, 120, and 60. Observational equipment was never very sophisticated, which is perhaps an indication of the significance of observation to the working astronomer in terms of improving and refining parameters.

The Indian astronomical tradition is divided into a number of schools, the so-called paksas. In terms of fundamental presuppositions the paksas differ little. They share the same basic astronomical model as that outlined above, but employ different values of planetary revolutions per kalpa, radii of epicycles, etc.

The oldest of the paksas is the brahmapaksa, which originated around the beginning of the fifth century, when Greek material was transmitted into India. This school gave the existing material a distinctly Indian form, presenting it as the revelation of the god Brahma. The brahmapaksa flourished in western and northwestern India. In this system, the epoch begins at sunrise at Lanka, an imagined equatorial city on the Indian prime meridian through Ujjain (23º11’N 75º46’E). Other paksas and their chief features are discussed below.

Early cosmological accounts, established in various Indian sacred texts, depict a flat Earth at the center of which is a huge mountain, Meru, whose peak points toward the polestar. Above the Earth, centered on the axis of Meru, is a series of wheels on which the luminaries and the planets, suspended from the tail of a large fish, revolve in the cosmic winds. The order varies, but the most common is: Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn, the naksatras (twenty-seven or twenty-eight constellations in the path of the Moon), and the saptarsis (Ursa Major).

The traditional cosmology was prevalent in society at large as well as among most learned people in medieval India, but with the introduction of foreign scientific ideas, a more theoretically based model was adopted by the astronomers. This was the geometrical model outlined above and based on Greek ideas in which the planets revolve around a centrally placed spherical Earth (the earliest works reflecting this interpretation date from the fifth and sixth centuries C.E.).

Due to its sacred nature and the popular credence attached to it, astronomers could not entirely disregard the older cosmology. In a sense, the attempt to create a synthesis of the two cosmologies is as old in India as the introduction of geometrical models. The astronomers placed Mount Meru at the North Pole (a place suited for this purpose for a number of reasons) and relegated other curiosities of the older cosmology to the southern hemisphere. Later, a whole literary genre evolved to attempt to reconcile the two cosmologies, an enterprise which is, in fact, still going on today.

Relating to this conception of time, Indian astronomical treatises are of several kinds: these include siddhantas, tantras, karanas, kosthakas, and yantras. A siddhanta is a fully fledged treatise, based on the beginning of the kalpa. A tantra simplifies matters by taking the beginning of the present kaliyuga as an epoch, and a karana, which generally contains approximate formulae meant for easy use, utilizes an epoch close to the time of its author. A kosthaka is a text which includes tables and accompanying explanation. A yantra is a text on instruments.

Notable Astronomers and Mathematicians

Aryabhata (born 476 C.E.), who lived in Pataliputra (modern Patna in Bihar), founded two of the astronomical paksas: the aryapaksa, whose system is expounded in his treatise the Aryabhatiya, and the ardharatrikapaksa (in which the epoch begins at midnight, rather than at sunrise) which he expounded in c. 500 C.E. in a now lost work. Aryabhata sought to simplify the astronomical system, not through actual observations of the heavens (as is illustrated by the fact that he does not talk about the stars in the Aryabhatiya and that the position of the ascending nodes of the planets and the Sun at the beginning of the present kaliyuga form an arithmetical progression), but through mathematical manipulation. In his system, a kalpa consists of one thousand eight mahayugas each of which is divided into four equal yugas, and a mean conjunction occurs at the beginning of each mahayuga, a fact that allows him to operate within the shorter span of a mahayuga rather than the longer kalpa. In the mathematical section of the Aryabhatiya, Ayabhata deals with arithmetic, algebra (for example a method of finding integer solutions of the equation ax ± c = by), and trigonometry. He also gives a value of *** correct to eight decimal places:

π = \frac{62832}{20000}

(although in his works, for practical purposes, he uses the traditional approximation p = 10).

Three centuries later another school appeared which sought to apply Aryabhata’s astronomical parameters while adhering to the traditional division of the kalpa and the yugas. This is the so-called saurapaksa. In order to utilize Aryabhata parameters within the framework of the traditional division of the kalpa, the expounders of the saurapaksa postulate a period of 17,064,000 years at the beginning of the creation during which the planets remain motionless. Authors adhering to this pakda include Jnanaraja (fl. 1503).

Almost immediately after Aryabhata, the famous astronomer Brahmagupta (b. 598 C.E.), who was to become Aryabhata’s most outspoken rival, wrote two important astronomical works following the tradition of the brahmapaksa, in which he often adopted a critical attitude towards Aryabhata. The first, the Brahmasphutasiddhanta, was written when Brahmagupta was thirty years old. This work contains material ranging from planetary theory, eclipse theory, mathematics, including rules for cyclic quadrilaterals (although Brahmagupta never mentions the applicability of these quadrilaterals to a circle, there can be no doubt that this is what he intended), and the so-called bija (algebraic) calculations), instruments, and mathematical tables. In this work, Brahmagupta pursues mathematics for the sake of mathematics and not exclusively as an aid to astronomy. His second work, the Khandakhadyaka (with an epoch of Sunday, March 15, 665 C.E.), was a response to Aryabhata’s Ardharatrikapaksa. Both works were known in Sanskrit to al-Biruni, who quotes many passages, especially in his works India and in al-Qanun al-Mas‘udi. The legacy of Aryabhata and Brahmagupta was far-reaching, and many works written thereafter are simply are based on their achievements.

A later astronomer who wrote both important original works and commentaries on older texts is Bhaskara II (b. 1114). Bhaskara II was celebrated for his achievements by his contemporaries: An inscription dating from 1207 records that funding was given to form an educational institution dedicated to the study of the his works. The Siddhantasiromani and the Karanakutuhala (a siddhanta and a karana respectively) and the Bijaganita and the Lilavati (mathematical works) are his most important achievements. To the latter work, the Lilavati, tradition has attached a charming story, found in many variants, of a beautiful young woman named Lilavati, to whom many of the mathematical problems in this work are addressed. According to one, Bhaskara II had calculated that Lilavati, his daughter, had to be married at a certain time to save her future husband from a premature death. To effect this, he constructed a waterclock that would indicate the auspicious time. However, Lilavati had her curiosity aroused and, while looking at the waterclock, a pearl from one of her ornaments fell into it, causing the water to flow at a slower rate. Lilavati thus became a widow as a young woman; to console her, her father taught her mathematics and wrote a mathematical treatise, naming it in her honor. As similar stories exist in other contexts, this is presumably a pre-existing story that got attached to the Lilavati.

Among the mathematical problems studied by Bhaskara II are arithmetic, plane and solid geometry, and the solution of certain indeterminate equations. In particular, following the mathematician Jayadeva (c. 1050 C.E.), he expounds a method for the solution of what is now known as Pell’s equation, i.e., integer solutions to the equation ax² + 1 = y² where a is a given integer, giving solutions to specific examples that were not solved in Europe until centuries later.

Influence from Islamic astronomy can be seen in India as early as the tenth century in the work of Munjala and Sripati, which seem to contain traces of Islamic concepts. However, it is not until the latter half of the fourteenth century that a direct transmission can be confirmed, most notably in the work of the Jain astronomer Mahendra Suri (fl. 1370). He wrote the first Indian treatise on the astrolabe, called the Yantraraja (1370), which contains a Sine table with R = 3,600, an Islamic value for the obliquity of the ecliptic (å = 23.35), and listed the latitudes of various cities, including Mecca, Nishapur, and Samarkand.

Narayana (fl. 1356), one of the most famous Indian mathematicians of the medieval period, wrote the Ganitakaumudi (1356), a work devoted to mathematical operations concerning numbers. Particularly ingenious are his square root approximation, his work on number sequences and series, and magic squares which explore the properties of combinations and permutations.

At around the same time in the south of India, Madhava (c. 1340–1425), founder of the Keralese mathematical school, flourished. Some of his works on astronomy survive, but none of his mathematical works are extant. His mathematical results were, however, preserved in later works in his school. Madhava is most famous for his value of p (p = 3.14159265359), correct to eleven places, as well as his expressions for the series expansions of the sine, cosine, and arc-tangent functions, which were not discovered in Europe until two centuries later.

As seen earlier, one of the consequences of the oral scientific tradition was that preservation of existing information was more important than scientific development. Scientists were much more concerned with borrowing parameters and tinkering with mathematical formulae than with improving parameters through frequent and extended observations. Most Indian astronomers mention the need for agreement between computed and observed phenomena, but they lacked the practical techniques to make observations that were accurate enough for their purposes. In fact, many of the procedures concerning observations mentioned in the texts simply cannot be carried out practically.

It is not until the fourteenth century, with the work of the Keralese astronomer Paramesvara (c. 1380), that a deliberate list of observations is included within a work. These observations, which comprise thirteen eclipses, both solar and lunar, ranging from 1393 until 1432, are recorded in his work the Siddhantadipika. However, despite this conscious inclusion, the extent to which these observations actually affected Paramesvara’s parameters is undetermined.

Paramesvara wrote three other works on eclipse theory of varying length and detail. As well as several other original texts, including the Drgganita (1431) and the Goladipika, he wrote commentaries on astronomical texts that were dominant in Kerala at the time. Most of the works are preserved in Malayalam, a South Indian Dravidian language.

Paramesvara’s style of astronomy, including his emphasis on observation, was passed down, through his son Damodara, to the famous astronomer Nilakantha (b. 1444). Nilakantha developed the efforts begun by Paramesvara for placing more emphasis on observation in astronomy. He not only asserted the importance that astronomy be based on experimentation and observation and that calculations should reflect reality (as many previous astronomers had done), but gave details and examples of how this was to be achieved. Nilakantha declared that eclipse observations were the most convenient and useful means to achieve this. Nilakantha is also an important source of information about Madhava.

Bibliography

Datta, B. and A. N. Singh. History of Hindu Mathematics, A Source Book, Parts 1 and 2 (single volume). Bombay: Asia Publishing House, 1962.

Pingree, D. E. Jyotihsastra: Astral and Mathematical Literature. Wiesbaden: Harrassowitz 1981.

Sarasvati Amma, T. A. Geometry in Ancient and Medieval India. Second revised edition. New Delhi: Motilal Banarsidass, 1999.

Subbarayappa, B. V. and K. V. Sarma. Indian Astronomy: A Source-Book. Bombay: Nehru Centre, 1985.

CLEMENCY WILLIAMS AND TOKE KNUDSEN

Surgery

During the Middle Ages, surgery gained new status within the European healthcare system. There were surgeons in antique Rome and in the Arab world but they were never as well organized or as recognized as surgeons were to become in western Europe during the Middle Ages. Surgeons are mentioned in a variety of sources throughout Europe as early as the eighth century but surgery did not attain a state of institutional stability until the thirteenth century. Several factors made possible this emergence of surgery as a recognized profession at this time. First of all, numerous translations of Arabic medical sources played an essential role in the establishment of European surgery. Meanwhile, the rise of urban living led to the creation of new settings for the transmission of medical knowledge such as the university and the corporation with its accompanying apprenticeship system. Of course, surgery, defined as a manual intervention on the body, was considered a fairly radical medical strategy. Such a strategy fell far behind diet and medication in the scheme of Galenic medicine and was mainly centered on the relief of external ailments such as wounds and apostemes (abscesses) but also on more internal ailments such as cancer.

The rise in the status of surgeons seems to have paralleled that of the barbers with whom they banded together in many European towns. Barbers had traditionally performed bleeding, one of surgery’s most ancient functions, and for that reason they closely associated with the generally more learned surgeons. As surgeons added book learning to their practical training, they positioned themselves halfway between the manual branch and the learned branch of medical practice. Excluded from most of the universities, surgeons managed to acquire academic knowledge through the use of books, first in Latin and later in vernacular languages. The thirteenth-century Parisian surgeon *Henri de Mondeville, who lobbied for the inclusion of surgery in academic curricula, divided the art of surgery into two indispensable branches: magisterium (mastering the theory), and ministerium (mastering the practice). Learned surgeons tended to adopt this model but they were outnumbered by the less learned city surgeons. Nevertheless, by the late Middle Ages, mastering the theory of surgery had been facilitated by the increased availability of a Mediterranean learned tradition of scholastic surgery, consisting of ancient sources and modern authorities.

Ancient Sources

Like other parts of medical theory, surgery is deeply embedded in Hippocratic medicine. Some works of the Hippocratic Corpus (c. 500 B.C.E.) on the subject bear witness to the high level of technical mastery Greek surgery had attained. After that, little is known of surgery before Celsus in the first century but the few surgical passages in his De Medicina show remarkable progress in the field of operative surgery and anatomy. Between these two eras lay the Hellenistic period and the Alexandrian school with its known concern for anatomy represented by doctors such as Herophilus and Eratistratus. *Galen, who attended that school and whose influence on medieval medicine was profound, paid attention to surgery especially through his interest in anatomy. He agreed with *Hippocrates in classifying surgery as a third way of intervention and was basically a generalist, but the position he held as a physician for gladiators in Pergamum had given him considerable expertise in field surgery. In any case, the main contributor to late antique surgery is Paul of Ægina, whose seven-book compilation of known ancient medical writings is set out in such a way that it became a practical manual for doctors. Book Six deals extensively with surgery and treats the surgical ailments one by one from head to toe.

Arabic Sources

While Greco-Roman surgery constituted the primary source of knowledge, ancient surgical writings reached medieval Europe through a very limited number of compilations and fragments. Oribasius, Paul of Ægina, and Aetius of Amida only became known in Western Europe through *al-Zahrawi (Albucasis). It is therefore clear that medieval surgery was born out of Arabic medicine. Aside from Albucasis, *Ibn Sina (Avicenna), *al-Razi, and *Ali ibn al-Abbas al-Majusi (Haly Abbas) were the main external sources of surgical knowledge before the Renaissance.

Albucasis, a Cordoban surgeon of the eleventh century, wrote a surgical treatise entitled Kitab al-Tasrif, a complete encyclopedia of everything needed by surgeons to perform their art, from Hippocratic humoral theory to descriptions of surgical procedures including drawings of some two hundred surgical instruments. This massive work inspired most subsequent medieval surgical writings thanks to its translation into Latin in the late 1100s by *Gerard of Cremona in *Toledo. Translation and assimilation of Arabic and antique science took place not only in Spain but also in Italy, especially in *Salerno, which became an important center of knowledge. *Constantine the African and his assistants made numerous translations from Arabic to Latin, notably of two of the most important texts for the transmission of antique medicine: the Isagoge by *Hunayn ibn Ishaq, and the Pantegni by *Ali Abbas al-Majusi. Both works were practical digests of Galenic lore and served as introductions to humoral theory until more of Galen’s works were made available in Latin and until Avicenna’s convenient synthesis became the preferred source of medical knowledge. In particular, the Pantegni contained a section devoted to surgery that closely followed that of Paul of Aegina. This book was for long the most readily available source of ancient surgical knowledge in the West. The only exclusively surgical text produced in this period is the Bamberg surgery, a rather erratic compilation of existing texts and techniques taken mainly from the Pantegni.

The Salernitan Period

Around 1200, Salerno became a center of learning providing regular courses in medicine: regimen, uroscopy, and therapy were its main themes. Despite the fact that surgery was not an essential part of the cursus at Salerno, that important southern Italian center of learning saw the emergence of a new genre that would determine the path taken by surgery in the next century: the Anatomies, brief treatises based on the dissection of pigs. The first of these works, attributed to Cophon, is devoid of Arabic influence but the second, entitled Second Demonstration of Anatomy, uses the Pantegni extensively.

The school of Salerno played an important role in establishing surgery as an independent part of medicine. This tendency is made clear in *Roger Frugard’s Chirurgia, otherwise known as the Rogerina. One can identify many sources in the Rogerina, which was the predominant Greco-Latin influence on Paul of Aegina and Oribasisus as well as on Arabic sources, mainly those translated by Constantine. This earliest surgical work of the Middle Ages set the standard for scholastic surgical discourse and gave rise to numerous commentaries. The most popular of these was Roland of Parma’s Rolandina, two treatises which, together with the commentaries on Frugard made by the “Four Masters,” constitute the basis of later European surgery.

Surgery in Northern Italy

From Salerno, learned surgery spread to northern Italy, where it acquired adepts in Padua and Bologna. Bruno de Longoburgo composed his Chirurgia magna in Padua around 1252. His work introduced a more systematic use of Albcassis’s surgery, indicating that Spanish translations were becoming more widely available. Ugo de Borgognoni, a veteran of crusades in Syria and a pensioner of the city of Bologna, was another contributor, although his work is known only through his disciple, *Teodorico Borgognoni. The most important contribution to the northern Italian movement came later from Guglielmo of Saliceto with his Treatise on Surgery, the first work to include a chapter on anatomy. The author’s clinical experience is made clear by his reference to autopsies, but his main contribution is his stated conviction—which he shared with other northern Italian surgeons—that surgery cannot be practiced or understood without medical theory. This necessary connection between medicine and surgery gave rise to a new trend of Mediterranean scholastic surgery.

*Taddeo Alderotti was a famous teacher at Bologna and around him gathered several scholars who were interested in anatomy. One of Thaddeo’s disciples, *Mondino de’ Liuzzi, performed the first documented dissection in 1326, and related the deed in his Anatomia. Historians today recognize this event to be quite an arbitrary stepping-stone since dissections had already been performed throughout Italy and southern France, but it is cited as a turning point in the history of medicine. Its impact was felt more in academic teaching than in the practice of surgery. Another student of Taddeo, Dino del Garbo, the son of a Bolognese surgeon, was the author of a commentary on the surgical parts of Avicenna’s Canon.

Surgery in France and England

The spread of surgical knowledge from Italy to France was largely the result of the peregrinations of *Lanfranco of Milan, a disciple of Guglielmo of Saliceto after his exile from Milan in 1290. The prologue of his Chirurgia magna or Practica is a tribute to the city of Paris where he was well received and treated. His sojourn in Paris is believed to have added new vitality to the movement for learned surgery. It follows closely the first statutes on surgery in the provost’s Livre des métiers in 1268. We also know that the king of France pensioned a number of surgeons during this time. One of them was Jean Pitard, who contributed to the establishment of surgery as a Parisian craft. His disciple Henri de Mondeville gave us the first Chirurgia written in France but the work was never finished due to Mondeville’s fragile state of health. Henri de Mondeville gave anatomy lessons at Montpellier in 1304 of which an Occitan account has survived. His work was partly translated in 1314 but did not have a determining effect on the evolution of surgery. Mondeville is cited several times by his successor, *Guy de Chauliac, with regard to his dry treatment of wounds, a procedure that was abandoned by later medieval surgeons and thus initiated a doctrinal controversy in the fourteenth century.

Probably the most learned surgeon of the Middle Ages, Guy de Chauliac studied medicine at Montpellier around 1335 and later became a member of the Pope’s retinue at Avignon. His Inventarium sive collectorium in parte chirurgicali medicinae became a fundamental text for medieval and modern surgery. The Inventarium is an encyclopedia of surgical knowledge that is mainly derived from ancient sources such as Galen—whom he cites eight hundred ninety times—and Avicenna but also uses material from more contemporary authors such as Albucasis, Henri de Mondeville and all the Salernitan scholars and surgeons. The book was used by most medieval surgeons and was translated into Middle French, Middle English, Italian, Catalan, Dutch, and Hebrew before the end of the fourteenth century. Its content was also adapted in excerpts, abridged versions, and questions that are still extent in libraries and archives.

The work of *John of Arderne, a fourteenth-century English surgeon, embodies another kind of medieval surgery. Although he had no formal education in medicine, he played an important role in the promotion of learned surgery. He was self-educated, teaching himself Latin which he avowedly wrote very badly, as well as the elements of learned medicine. His most famous work is the Treatises of the Fistula in Ano, Hemorrhoids, and Clysters, in which he presents some of his techniques for curing such conditions. Since John of Arderne did not have any academic training, it has been widely believed that his career was spent largely on the battlefields. However, a closer look at his writings reveals nothing of the sort, and the first part of the Treatises offers remarkable insights into the practice of surgery in England at the turn of the fourteenth century.

Surgery and Health Care

The evolution of learned surgery bore little relation to the experience of most city surgeons. Most of these practitioners were trained by apprenticeship and never read Latin. Fortunately, most of the surgical literature became available in vernacular languages as early as the beginning of the fourteenth century. Nevertheless, the little we know of the content of the master’s exams, in France for example, seems to suggest that basic knowledge of the veins, anatomy, and some elements of the humoral theory were the only requirements for practice. In Spain, Italy, and the south of France, surgeons were heavily involved in public health care, employed by city councils on a yearly basis as resident doctors or hired specially in times of plague. Some surgeons were also involved in the judicial system, and may have performed the very first autopsies. Their manual skills made them popular with health care practitioners and useful assistants to more theoretically oriented doctors. Their often cheaper rates assured them of regular work, especially in rural communities.

See also Medicine, practical; Medicine, theoretical

Bibliography

D’Arcy Power. John Arderne, Treatises of fistula in ano, Haemorroids and Clysters. London: Kegan Paul, Trench, Trübner & Co., 1910.

Grmek, Mirko D. Mille ans de chirurgie en Occident, Ve–XVe siècles. Paris: Dacosta, 1966.

Jones, Peter Murray. “John Arderne and the Mediterranean Tradition of Scolastic Surgery.” In Practical Medicine from Salerno to the Black Death, edited by Luis Garcia-Ballester et al. New York, Cambridge University Press, 1994.

Kristeller, Paul Oscar: The School of Salerno, its Development and its Contribution to the History of Medicine. Bulletin of the History of Medicine (1945) 17: 138–194. McVaugh, Michael. Guigonis de Caulhiaco: Inventarium sive chirurgia magna, vol. I, text. Leiden: E.J. Brill, 1997.

Nicaise, Edouard. Guy de Chauliac: La grande chirurgie. Paris: Alcan, 1890.

———. Henri de Mondeville: La chirurgie. Paris: Alcan, 1893.

GENEVIÈVE DUMAS

The Nature of Scholasticism

Transcription and Dissemination

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Medieval Developments

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Mediterranean Practice

Northern European Practice

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The Indian Astronomical Model

Notable Astronomers and Mathematicians

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Ancient Sources

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The Salernitan Period

Surgery in Northern Italy

Surgery in France and England

Surgery and Health Care

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South-Central Asian Science

Surgery

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