J

Jabir Ibn Hayyan (Geber)

Traditionally, the Muslim polymath and alchemist Jabir ibn Hayyan (c. 721–815 C.E.) is believed to have been born in the town of Tus, just outside the city of Khurasan (modern-day Mashhad) in northeast Iran. He was soon orphaned after his father, a pharmaceutical chemist from Kufa, was arrested and executed for having advocated the Abbasid usurpation of the Umayyad family during the internal struggle for power. After the Abbasid family seized the Caliphate, in 748 C.E., Jabir is claimed to have befriended the sixth Shi‘ite Imam, Ja‘far al-Sadiq (700–765 C.E.), who exclusively taught him among other things the art of *alchemy, and thereafter became a compiler. However, even though there are numerous instances where Jabir cites the name of Ja‘far al-Sadiq in the invocation wa haqqi sayyidi (“By my Master”), some historians and scholars have maintained that, because there appears to be no mention of a disciple named Jabir in Shi‘ite literature, the relationship between Jabir and Ja‘far al-Sadiq should be dismissed as legend. Moreover, as early as the tenth century, the identity and legitimacy of Jabir appear to have been convoluted.

In the earliest extant biobibliographic reference to Jabir, documented and compiled in 987 C.E. by the Arabic bookseller Ibn al-Nadim (d. 995 C.E.), the Kitab al-Fihrist (Book of the Index) recorded that Shi‘is claimed that Jabir was one of their abwab (spiritual leaders) who was a companion to Ja‘far al-Sadiq. Subsequently, Ibn al-Nadim mentioned a group of philosophers who claimed Jabir was a colleague who wrote on logic and philosophy. In another section of the Fihrist, it states that a group of scholars and warraqun (stationer-copyists) maintained that if Jabir existed, the only writing that can be ascribed to him is Kitab al-Rahmah al-Kabir (The Large Book of Mercy); since all other writings were composed by individuals who intentionally falsified the authorship of their work by ascribing it to Jabir. Whereupon Ibn al-Nadim responded that Jabir was authentic and adamantly refuted the assertion that Jabir never existed; and, thus, concluded by offering a list of various treatises on Shi‘i doctrine, owned by Jabir, as well as numerous treatises on the sciences written by Jabir. In the end, Ibn al-Nadim quoted Jabir, using his kunya (honorific) Abu Musa, as having claimed to have composed over three thousand six hundred books and three hundred leaves on a variety of subjects.

The Jabirian Corpus

The Jabirian corpus is generally presented as having consisted of major theoretical and applicable scientific treatises on alchemy, astrology, medicine, instruments of war, mechanics, etc., and smaller commentaries, paraphrases, supplementary explanations, and refutations that cover such diverse disciplines as languages, philosophy, logic, mathematics, sermons, occultism, cosmology, music, charms, poetry, etc. Due to the sheer magnitude and diversity found in the Jabirian corpus, as well as numerous Greek scientific and philosophical paraphrases, some historians and scholars have maintained that the writings were not solely the work of Jabir. Rather, it has been argued that, beginning in the second half of the ninth century, the Isma‘ili movement emerged from a form of proto-Shi‘i gnosis; and subsequently attempted to influence religious, philosophical, ideological, and political mediums through a propagandistic compilation and presentation of the known sciences. In particular, it has been alleged that it was the Qarmati-Isma‘ili movement that was directly responsible for employing technical terms in most of the these scientific writings; and, sometime between the tenth or early eleventh century, the multi-generational literary endeavor reached its final form in a Corpus Jabirianum. It should be noted, however, that the origins of the Isma‘ili movement are fragmentary until the middle of the ninth century, and ongoing hypotheses continue to be debated by historians and scholars.

The Geber Corpus

It appears from extant manuscripts that during the twelfth and thirteenth century the Latin West was introduced to five alchemic texts by the alchemist “Yeber” or “Gebir filius Hegen ezahufy” (that is, Jabir ibn Hayyan al-Sufi). Subsequent centuries would come to know the alchemist as Ieber, Jeber, Geber Abinhaen or Geber ebn Haen (Jabir ibn Hayyan), Giaber, Gebri Arabis philosophi (“the Arab philosopher Geber”), etc.; until, eventually, the Latin name became standardized as Geber. It should be noted, however, that some historians and scholars who have addressed the “Jabir-Geber problem” do not believe that that the Latin Geber was de facto the ninth century Jabir ibn Hayyan, but rather a twelfth- or thirteenth-century Latin “pseudo-Geber.” The position is maintained, in part, due to the absence of any original extant Arabic works prior to the twelfth or thirteenth century which correspond directly to the Latin Geber corpus. Indeed, according to the thesis, the only extant Arabic work of possible authenticity ascribed to Jabir is the Kitab al-Rahmah al-Kabir. Another proposition that has been asserted, to uphold the claim of a Latin pseudo-Geber, is that the materials and processes mentioned in the Geber corpus (e.g., aqua regia, alumen plumae, alumen roccae, sal petrae, sal tartari, etc.) were only available during the thirteenth and fourteenth centuries. However, it has been suggested that an etymological corruption or mistranslation of these and similar words might account for the historical exclusivity; in addition, it has been asserted that many authentic Arabic-Islamic expressions appear throughout the Geber corpus. Conversely, counterarguments have maintained that not only was the scholastic Latin used in the Geber corpus inadequate to translate such equivalent Arabic texts, but such an etymological corruption has not been conclusively established; furthermore, similar to the practice of forgeries in Greek and Muslim alchemical literature, the imitation and incorporation of authentic Arabic-Islamic phrases was simply used in the Geber corpus to intentionally promote a sense of authentication. Nevertheless, it should be noted that only a mere fraction of Latin alchemical literature, as well early Greek alchemic texts via Syriac and Arabic translations, has been made available in scholarly editions; but it is not unusual for original versions of translated manuscripts to be permanently lost to natural decomposition or human destruction. In short, the authenticity of the Geber corpus remains uncertain and is presently a matter of conjecture.

Single Volume

The Geber corpus was generally presented to the Latin West in a single volume and consisted of five alchemic treatises: Summa perfectionis magisterii (The Sum of Perfection), De investigatione perfectionis (The Investigation of Perfection), De inventione veritatis (The Invention of Verity), Liber fornacum (Book of Furnaces), and Testamentum (Testament). Of the five treatises, Summa perfectionis magisterii is perhaps the most important work. It is divided into two parts. The first discusses (1) The problems involved in the preparation and processes of an elixir; (2) Refutations against the sceptics of the art of alchemy; (3) The natural properties of metals (i.e., gold, silver, lead, tin, copper, and iron) and the division of arsenic, mercury, and sulphur; (4) The method and observation involved in the calcinations, crystallization, distillation, reduction, and sublimation of ores, minerals, solutions, spirits, etc. The second part examines: (1) The importance of understanding the nature of spirits in relation to gold, silver, lead, tin, copper, iron, arsenic, mercury, and metallic sulphide; (2) The properties and preparations for making different medicines; and (3) The laboratory apparatuses and processes involved in the art of alchemy, followed by a summary.

It has been noted by historians and scholars that Jabirian science incorporated the Pythagorean theory of cosmic harmony (a theory derived from qualitative or symbolic properties of numbers). In particular, according to Jabirian science, jawhar (substance) consisted of the four elements harr (hot), bard (cold), balla (moist), and yubs (dry), which could all be arranged in altering proportions of the numbers 1, 3, 5, and 8, but would always result in the universal constant of 17. Thus, when these four elements are perfectly combined with “sulfur” (i.e., a metaphor for active masculinity) and “mercury” (i.e., a metaphor for passive femininity), gold is produced; and the process is generally referred to as the Jabirian “sulfur-mercury theory.” In addition, it has been suggested that the numerical postulate of the action of drugs, ascribed to *Galen, was also incorporated into the framework of Jabirian science. Whereupon each of the four elements (i.e., hot, cold, moist, and dry) used in curing by contraries, was associated with seven grades of intensity, with each grade possessing four degrees of strength, yielding the total number of permutations and combinations in the formula 4 x (7 x 4) = 112. The computation was probably derived from early Arabic translations of Galen carried out by the Nestorian Christian mediator and translator *Hunayn ibn Ishaq al-‘Ibadi (808–873 C.E.). In an epistle of 856 C.E., Hunayn claimed to have translated one hundred four works of Galen (out of a total of one hundred twenty-nine titles) into Syriac and Arabic; and it appears that the Jabirian science not only incorporated parts of these translations in its writings, but also adopted some examples of the proto-Arabic scientific terminology introduced by Hunayn.

Therefore, it appears that Jabirian science attempted to develop a theoretical premise, based on the theory of the reconfiguration of qualities in accordance to their universal position; and, essentially, presented a systematic and rigorous schematic methodology that would be applicable to the transmutation of base metals into gold, the preparation of medicines, and all other processes of the universe. Thus, by the fourteenth and fifteenth century, the Jabir-Geber corpus influenced both scientific and mystical circles; and by the sixteenth and seventeenth centuries, the republication of the collected works seems to have contributed to a revival in alchemy and alchemical medicine.

See also Fihrist; Music theory

Bibliography

Berthelot, Marcellin. Introduction a l’étude de la chimie, des anciens et du Moyen Age. Paris: G. Steinheil, 1889.

Haq, Syed Nomanul. Names, Natures, and Things: The Alchemist Jabir ibn Hayyan and his Kitab al-Ahjir (Book of Stones). Dordrecht and Boston: Kluwer, 1994.

Ibn al-Nadim, Muhammad ibn Ishaq. The Fihrist of Al-Nadim; a Tenth-Century Survey of Muslim Culture. Bayard Dodge, ed. New York: Columbia University Press, 1970.

Kraus, Paul. Jabar ibn Hayyan: Contribution a l’histoire des idées scientifiques dans l’islam. Hildesheim and New York: Georg Olms, 1989.

Newman, William R. The Summa Perfectionis of Pseudo-Geber: A Critical Edition, Translation and Study. Leiden: E.J. Brill, 1991.

Russell, Richard. The Alchemical Works of Geber. York Beach: S. Weiser, 1994.

TOD BRABNER

Jacopo da Forlì

A doctor in the Arts and Medicine and a teacher, Giacomo della Torre is best known as Giacomo (or Jacopo) da Forlì, from the name of his natal town in current Emilia-Romagna. He was born c. 1360 to a wealthy family, and died in Padua on February 12, 1414.

Jacopo da Forlì spent all his life in northern Italy, teaching different branches of the medical and natural sciences in several universities. His career seems to have been turbulent and was characterized by frequent moves, the refusal of a position, and breaches of commitments. He first taught natural philosophy (1383–1385), *astrology and grammar (1384–1385), and medicine and philosophy (1385–1400) at the University of Bologna. In 1388 (while still in Bologna), he was offered a lectureship in natural and moral philosophy in Florence, but declined the offer. In 1400, he moved from Bologna to Padua, at the university of which he taught medicine (1400–1402), as he did also at the universities of Ferrara (1402–1404), and Siena (1404). In the latter, he was offered and accepted a renewal, but he did not respect his commitments. After three years (1407), he resumed teaching at the university of Padua, where he held the chair of ordinary medicine. In 1412, he agreed to lecture at the university of Parma, but again did not fulfill his commitment. He pursued his teaching activity at the university of Padua until the end of his life.

As a university teacher of medicine, Jacopo da Forlì commented on two major works of the post-Salernitan period, the Hippocratic Aphorismi and *Galen, Ars parva (known as Tegni or Microtegni), which were included in the so-called *Articella. To them he added the Canon of Avicenna (*Ibn Sina). The Latin translations of the Greek texts date back to such translators as *Constantine the African (d. after 1085), and to *Gerard of Cremona (c. 1114–c. 1187) for Avicenna. Jacopo da Forlì returned neither to the original Greek text—as *Pietro d’Abano (1257–c. 1315) already had before him—nor to possible new Latin translations made from the Greek. He produced (in chronological order) commentaries on Avicenna’s chapter De generatione embrionis from the Canon (Padua, 1400); the Hippocratic Aphorismi, 2 (Ferrara, 1403); Galen, Ars parva (Padua, 1407), and Avicenna, Canon, 1.1–2 (Padua, 1413–1414). His commentary on Galen became a textbook for the teaching of the third-year course of theoretical medicine in Padua, and replaced the work of *Torregiano de’ Torregiani (c. 1270–c. 1350) used previously. His commentary on Avicenna was widely used later as a university textbook.

The importance of Jacopo da Forlì in medical university teaching during the late Middle Ages is well illustrated by the several manuscripts of his commentaries, and their many printed editions during the late-fifteenth and early-sixteenth centuries: the commentary on Hippocrates was printed as early as 1473 and reprinted several times: 1477 (Padua), before 1480 (Padua), 1495 (Venice), 1501 (Pavia), 1502 and 1508 (Venice), 1512 (Pavia), 1519, and 1520 (Venice); the commentary on Avicenna, De generatione embrionis, was printed in 1479 (Pavia) and reprinted in 1485 (Siena), and 1489 and 1502 (Venice); the Expositio super tres libros Tegni Galieni was first printed in 1475 (Padua) and reprinted c. 1477 (Padua), 1487 (Pavia), 1491 and 1495 (Venice), 1501 (Pavia), 1508 (Venice); the commentary on Avicenna, Canon, was first printed c. 1474 (Milan) and reprinted in 1479 (Venice), 1484–1487 and 1488 (Pavia), 1508, 1518, 1520 (Venice).

Besides such teaching texts, he also wrote a Questio de intensione et remissione formarum (1381–1384), which was printed in Treviso before 1480 and reprinted in Venice in 1496, as well as other works known only in manuscripts, such as Commentarii super Aristotelis Physicorum libris I-IV and discourses. Other works are known only by title.

His commentaries (particularly on Avicenna) rely heavily on previous works, especially the Conciliator of Pietro d’Abano, the commentaries on Avicenna, Canon, by Dino del Garbo (d. 327), and the Anathomia of *Mondino de’ Liuzzi (d. 1326).

Already in his time, Jacopo da Forlì was held in high esteem and considered the most learned and greatest physician of his age. As such he followed Marsiglio de Santa Sofia (d. 1405?) and was followed by *Ugo Benzi (1376–1439), with whom he was in contact. He is credited with a significant contribution to the formation of the Averroist interpretation of Aristotle’s philosophy at the University of Padua. Unquestionably a highly talented teacher, from his turbulent career he seems to have had a similar level of self-esteem.

See also Aristotelianism; Hippocrates; Medicine, theoretical

Bibliography

Lockwood, D.P. Ugo Benzi: Medieval philosopher and Physician, 1376–1439. Chicago: University of Chicago Press, 1951.

Pesenti, Tiziana. Professori e promotori di medicina nello Studio di Padova dal 1405 al 1509. Repertorio Bio-Bibliografico. Padua: Edizioni Lint 1984, pp. 103–112.

Randall, John Herman. The School of Padua and the emergence of modern science. Padua: Editrice Antenore, 1961.

Siraisi Nancy. Avicenna in Renaissance Italy. The Canon and Medical Teaching in Italian Universities after 1500. Princeton: Princeton University Press, 1987.

———. Medicine and the Italian Universities, 1250–1600. Leiden: E.J. Brill, 2001.

ALAIN TOUWAIDE

James of Venice

Although James of Venice (fl. c. 1136–1150) was a prolific translator and commentator of Aristotle, little can be said with any certainty about the details of his life. He referred to himself as “Veneticus Grecus,” which might mean either that he was a Greek born in Venice, a Venetian born and educated in Greece, or an expatriate Venetian who adopted Greece as his second home. There is some circumstantial evidence that John of Salisbury (c. 1115/1120–1180) was acquainted with James, and Minio-Paluello speculated that he might have been the Italo-Greek translator from Sancta Severina in Calabria whom John met in southern Italy about 1148–1153. Whatever the case may be, we know that he was in Constantinople in April 1136, where he heard a theological debate between Anselm of Havelberg (d. 1158) and the archbishop of Nicomedia. In 1148, he provided legal advice to the archbishop of Ravenna and may have been present at the council at Cremona in July of that year. Although referred to as “clericus,” he may never have been ordained a priest.

James’s translations of Aristotle include the so-called “vulgate” version of the Posterior Analytics, the “vetus translatio” of the Physics, the Metaphysica vetustissima, and translations of De anima and large portions of the Parva naturalia (De longitudine et brevitate vitae, De iuventute et senectute, De resperatione, De morte et vita, De memoria et reminiscentia). Fragments of his translation of De sophisticis elenchis survive, as do portions of his translation of a Greek commentary on that work and the Posterior Analytics by “Alexander,” while translations of the Topics and Prior Analytics attributed to him have not been found. In addition to the legal opinion conveyed in the letter to Archbishop Moses of Vercelli, he was also the author of commentaries on De sophisticis elenchis, Topics, and the Prior and Posterior Analytics, produced perhaps about 1130. And if the “Jacobus grecus” mentioned by Cerbano in his Translatio mirifici martyris Ysidori is the translator “Jacobus Veneticus,” it would seem that James had put his hand to writing a historical account of a voyage of the Venetians east to Constantinople.

Both his letter to the archbishop of Ravenna and his surviving translations indicate that James’s preferred translation style was literal, a technique derived not always from linguistic inadequacies but rather the goal of reflecting accurately difficult and unfamiliar material in the twelfth century. His syntax frequently reflects that found in the Greek text which he was translating, and when no exact equivalent can be found in Latin James provides the Greek term first, then a Latin correspondent, which has now acquired a novel definition. As a result, at least in some circles James’s translations were criticized as obscure, although John of Salisbury defended his translation of the Posterior Analytics and attributed the problems encountered by French masters to the difficulty of the work, not the translator’s skill. On the other hand, John also recognized the limitations of James’s linguistic skills, at least in comparison with those of other translators; while he seems to have regarded him as eloquent, his knowledge of Latin was less than perfect.

The success of James’s translations may be measured by the numbers of surviving copies in manuscript. The “vulgate” Posterior Analytics is extant in two hundred and seventy-five manuscripts; the three other translations of the text combined can be found in only eight manuscripts. Likewise, his translations of the Physics and De anima remained the dominant versions until displaced by the newer translations of *William of Moerbeke more than a century later. These early translations were a principal means by which Aristotle’s ideas were assimilated in western Europe.

See also Aristotelianism; Translation movements; Translation, norms and practices; William of Moerbeke

Bibliography

Brams, Josef. “James of Venice, Translator of Aristotle’s Physics.” In Praktika Pagkosmiou Synedriou Aristoteles, Thessalonike, 7–14 Augoustou 1978 = Proceedings of the World Congress on Aristotle, Thessaloniki, August 7–14, 1978. Edited by Ioannes Nikolaou Theodorakopoulos. 4 volumes. Athens: Ekdosis Ypourgeiou Politismou & Epistemon, 1981–1983. vol. 2, pp. 188–191.

Ebbesen, Sten. Jacobus Veneticus on the Posterior Analytics and some early 13th-century Oxford masters. Cahiers de l’Institut du Moyen-âge Grec et Latin (1977) 21: 1–9.

Gutman, Oliver. James of Venice’s Prolegomenon to Aristotle’s Physics: De intelligentia. Medioevo. Rivista di Storia della Filosofia Medievale (2002) 27: 111–140.

Minio-Paluello, Lorenzo. Jacobus Veneticus Grecus: canonist and translator of Aristotle. Traditio (1952) 8: 265–304.

Pertusi, Agostino. “Cultura Greco-Bizantina nel tardo medioevo nelle Venezie e suoi echi in Dante.” In Dante e la cultura Veneta. Atti del Convegno di Studi (Venezia, Padova, Verona, 30 marzo–5 aprile 1966). Edited by Vittore Branca and Giorgio Padoan. Florence: Olschki, 1966, pp. 157–197.

STEVEN J. LIVESEY

Jean de Meurs

Jean de Meurs (Johannes de Muris) was born in Normandy in the diocese of Lisieux in the 1290s; a more accurate birthdate cannot be given. His first writing, a critique of the ecclesiastical computation of the calendar, dates from 1317. A noticeable feature of this treatise of 1317 is that it employs the Tables of Toulouse, not the Alfonsine Tables. In 1321 Jean became a master of arts in Paris and wrote among other things Expositio tabularum Alfonsi regis. In 1323, at the Sorbonne in Paris, he wrote the Musica speculativa secundum boetium, an abbreviation of De musica of *Boethius, and in 1324 the Fractiones magistri J. de Muris, a synoptic table of his Arithmetica speculativa, contained in MS Paris, BnF lat. 16621, fol. 62v–64r. Very probably in this period Jean wrote his Arithmetica speculativa. In the same year (1324) Jean completed a Figura maris aenei Salomonis, i.e., a demonstration of the quantity and figure of the bronze basin in the temple of Salomon. Between 1338 and 1342 he was among the clerks of Philippe III d’Évreux, king of Navarre, and in 1344 he was canon of Mezières-en-Brenne, in the diocese of Bourges. According to the explicit of MS Paris, BnF lat. 14736, Jean completed his Quadripartitum numerorum on November 13, 1343. In a letter dated September 25, 1344, Jean de Meurs was summoned to Avignon by Pope Clement VI for a conference on calendar reform. According to Gushee it may be assumed that Jean left for Avignon shortly after receipt of Pope Clement’s letter, i.e., in October 1344.

In another treatise, which goes by the name De arte mensurandi from the incipit “Quamvis plures de arte mensurandi,” Jean refers to the Quadripartitum numerorum as follows:

(1) Book V, Part 2, Prop. 17: per artem quam in quadripartito numerorum alias explanavi (by the art which I have explained elsewhere in the Quadripartitum numerorum).

(2) Book V, Part 3, Prop. 8: per artem quam in quadripartito numerorum alias ordinavi (by the art which I have set in order elsewhere in the Quadripartitum numerorum).

(3) Book X, Prop. 2: Et hanc artem in quadripartito numerorum alias ordinavi (and this art I have set in order elsewhere in the Quadripartitum numerorum).

From these references we may conclude that Jean wrote De arte mensurandi after the Quadripartitum numerorum, and very likely before his departure to Avignon in 1344.

The epistolary treatise, which Jean and Firminus de Bellavalle composed to transmit their findings and recommendations concerning calendar reform, is dated 1345. No later date for his activity has been established. Besides the works mentioned above Jean wrote a series of tracts on music and astronomy. In the remainder of this entry, we discuss only his mathematical works.

Quadripartitum numerorum

Jean’s main mathematical work, the Quadripartitum numerorum, which takes its name from its division into four books, consists of a metrical and a prose part. According to L’Huillier the text in verse is written at the end of the work before the last tract of Book IV entitled De arte delendi. The prose portion of the Quadripartitum is divided into four books and a semiliber interpolated between books III and IV. Book I, containing a prologue and twenty-four chapters, is devoted to arithmetic and based on the Arithmetica of Boethius and *Euclid’s Elements. In Book II, containing twenty-seven chapters, Jean treats the multiplication and division of integers and introduces fractions. His sources are an unedited arithmetical tract contained in MS Paris, BnF lat. 15461 and Jean de Lignères’s Algorismus minutiarum. Book III, containing twenty chapters and forty-five questions, is devoted to algebra. His source is *al-Khwarizmi’s De iebra et almucabala (Algebra), translated by *Gerard of Cremona. After having written the twenty chapters of Book III, Jean became acquainted with the Liber abaci (Book of the Abacus) of *Leonardo Fibonacci. He has used this work for his Semiliber and the forty-five questions in this order. Book IV is devoted to practical applications of arithmetic and includes five tracts: the first two concern mechanics (De moventibus et motis and De ponderibus et metallis), the third is entitled De monetis, scilicet de arte consolandi, and the fourth, De sonis musicis, is lost or was never written. The last tract, De arte delendi, is an elaboration of the fifth part of Chapter Twelve of Fibonacci’s Liber abaci. Of the thirty-two chapters in Tract I, Grant (1971, 361–377) has published an English translation of chapters 12–14, 21–26, and 28, and Clagett (1978, 7f.) has translated Chapter Thirty-One. As appears from this last chapter, Jean apparently was acquainted with On Spiral Lines of Archimedes. The text of the second tract was translated by Clagett (1959, 113–120). (For an English translation of the definitions and postulates see Moody/Clagett 1960, 41, 43.)

The codex Plimpton 188 of New York’s Columbia University, containing inter alia the Quadripartitum numerorum, belonged to *Regiomontanus (1436–1476). Although not written by him, he abundantly annotated it. L’Huillier (1980) has reported on the contents of his notes. As can be deduced from Regiomontanus’s Tradelist, he intended to publish the work.

The codex New York, Columbia University, Plimpton 173 (a. 1424) contains a work entitled Aggregatorium sive compendium artis arismetrice written by Rolandus Ulysbonensis (Roland l’Ecrivain). Roland plagiarizes here, for his work resembles the Quadripartitum numerorum as contained in the MS Paris, BnF lat. 14736 (Charmasson, 1978).

De arte mensurandi

The subject of De arte mensurandi is practical geometry. One can distinguish two principal parts. Interrupted by death, it seems, the author of the first part did not complete the work. There was a Continuator who took up his work in Chapter V, Part 1, Prop. 9. The identity of the original author of the first part is unknown, but the Continuator was Johannes de Muris. In the proem of the work the original author outlines its scope and objectives. While he intended to complete his work in eleven chapters, in reality the work consists of twelve chapters. Jean utilized the following Archimedean works, translated by *Moerbeke in 1269: On Spiral Lines, On the Measurement of the Circle, On the Sphere and the Cylinder, On Conoids and Spheroids, and Eutocius’ Commentary on the Sphere and the Cylinder. He displays a modest knowledge of Archimedean semiregular polyhedra (Chapter XI) and in Chapter XII, Prop. 30 he says that the volume of a torus is equal to the product of the area of the describing circle and half of the length of the path of its center instead of the length of the path of its center. At the end of Chapter XI, Prop. 5, Jean tells us that a stonecutter has made for him in his presence models of regular and semiregular polyhedra. As far as we know, Jean was the first in the Latin Middle Ages to occupy himself with this subject. Jean inserted the hybrid Circuli quadratura of 1340 in Chapter VIII. It consists of two unequal parts. The first comprises thirteen propositions and seven definitions, all drawn from Moerbeke’s translation of On Spiral Lines. The second part consists of one proposition, the fourteenth, which is taken from the Moerbeke translation of On the Measurement of the Circle. Clagett (1978) has published an English translation and commentary of propositions 1–14. Jean has added a fifteenth proposition: “Given a square to construct a circle equal to the given square.” In addition, Clagett (1978) has published an English translation and commentary of Chapter 6, Prop. 26–29 (pp. 1323–1325, Chapter 7, Prop. 16 (pp. 27–29), Chapter 8, Prop. 1 (pp. 40–43), and Chapter 10 (pp. 105–121).

The autograph Paris, BnF lat. 7380 was in possession of *Nicole Oresme’s nephew, Henri Oresme, and of Oronce Finé (1494–1555), who made use of it in his Protomathesis. The Commensurator, a tract long attributed to Regiomontanus, consists of a collection of propositions (without their proofs) borrowed from De arte mensurandi. In his Underweysung der Messung mit dem zirckel und richtscheyt (Nuremberg, 1525) Albrecht Dürer (1471–1528) translated into German the treatment of the problem of finding two proportional means between two given quantities that appears in the De arte mensurandi, Chapter 7, Prop. 16.

Arithmetica speculativa

The Arithmetica speculativa, an abridgement of the Arithmetica of Boethius, was very popular for a long time, as appears from the thirty-four manuscripts which are known. The work was also printed twice: in Vienna 1515 in a mathematical collection containing Arithmetica communis (of Jean); Proportiones breves; De latitudinibus formarum; Algorithmus M. Georgii Peurbachii in integris; Algorithmus Magistri Joanis de Gmunden de minuciis phicisis. In 1538, it was printed a second time in Mainz under the title of Arithmetica speculativa.

See also Algebra; Archimedes; Arithmetic; Peuerbach, Georg; William of Moerbeke

Bibliography

Boncompagni, Baldassarre. Scritti di Leonardo Pisano, matematico del secolo decimoterzo. 2 volumes. Rome: Tipografia delle scienze matematiche e fisiche, 1857–1862.

Busard, Hubert L.L. Het rekenen met breuken in de middeleeuwen, in het bijzonder bij Johannes de Lineriis. Mededelingen van de koninklijke vlaamse academie voor wetenschappen, letteren en schoone kunsten van belgie. Brussel: Paleis der Academiën, 1968, nr.7.

———. Die “Arithmetica Speculativa” des Johannes de Muris. Scientiarum Historia (1971) 13: 116–132.

———. Johannes de Muris, De arte mensurandi. A Geometrical Handbook of the Fourteenth Century. Stuttgart: Franz Steiner Verlag, 1998.

Charmasson, Thérèse. L’Arithmétique de Roland l’Ecrivain et le Quadripartitum numerorum de Jean de Murs. Revue d’Histoire des Sciences (1978) 31: 173–176.

Clagett, Marshall. The Science of Mechanics in the Middle Ages. Madison: University of Wisconsin Press, 1959.

———. Archimedes in the Middle Ages, Vol. III. Philadelphia: American Philosophical Society, 1978.

Grant, Edward. Nicole Oresme and the Kinematics of Circular Motion. Madison: University of Wisconsin Press, 1971.

Gushee, Lawrence. New Sources for the Biography of Johannes de Muris. Journal of the American Musicological Society (1969) 22: 3–26.

L’Huillier, Ghislaine. Regiomontanus et le Quadripartitum numerorum de Jean de Murs. Revue d’Histoire des Sciences (1980) 33: 193–214.

———. Aspects nouveaux de la biographie de Jean de Murs. Archives d’Histoire Doctrinale et Littéraire du Moyen Age (1981) 47: 272–276.

———. Le Quadripartitum numerorum de Jean de Murs, Introduction et Edition critique. Genève: Librairie Droz, 1990.

Libri, Guillaume. Histoire des sciences mathématiques en Italie. 4 vols. Paris: J. Renouard, 1838–1841. I: 253–297. (Reprint Hildesheim: Georg Olms, 1967).

Moody, Ernest A. and Marshall Clagett. The Medieval Science of Weights. Madison: University of Wisconsin Press, 1960.

Poulle, Emmanuel. Jean de Murs et les Tables alphonsines. Archives d’Histoire Doctrinale et Littéraire du Moyen Age (1981) 47: 241–271.

Saby, Marie-Madeleine. Mathématique et métrologie parisiennes au début du XIVe siècle: Le calcul du volume de la mer d’airain, de Jean de Murs. Archives d’Histoire Doctrinale et Littéraire du Moyen Age (1991) 66: 197–213.

H.L.L. BUSARD

Johannes de Glogovia

Born about 1445, Johannes (John) of Glogovia was one of the most important philosophers and professors at the University of Kraków when Nicholas Copernicus (1473–1543) was there between 1491 and 1495. It is virtually certain that John or some of his students taught Copernicus the liberal arts.

Glogovia is located in Lower Silesia in western Poland about fifty miles (80 km) northwest of Wroclaw. Descended from the Schelling family of merchants, John received his elementary education at local schools, and entered the University of Kraków in the spring of 1462, obtaining a bachelor’s degree in arts in 1465, and a master’s degree in 1468. In the same year he became a lecturer in the faculty of arts, remaining in this capacity except for a brief interruption until his death in 1507. During his long career he taught nearly every subject in the faculty of arts, wrote dozens of commentaries and collections of questions, and published several works that continued to be used by scholars at the university until the 1530s.

John’s most important works are on *logic, natural philosophy, and *metaphysics. As a typical scholastic philosopher, he lectured and wrote his works under the influence of Aristotle, but he also relied on the ideas of *Ibn Rushd (Averroes) and Averroists such as Paul of Venice, John of Jandun, and *Pietro d’Abano. He cited *Giles of Rome, *Thomas Aquinas, *Albertus Magnus, John Versor, and followers of *Johannes Duns Scotus extensively. As these influences suggest, John was an eclectic thinker who summarized opposing arguments, and attempted to reconcile them.

Perhaps his most innovative work was in logic. He commented on the major logical works of Aristotle and on the handbooks of *Petrus Hispanus. He adopted an interpretation of the logic of consequences that Copernicus may have encountered directly or indirectly through John’s students. Although it was not a completely innovative view, John argued forcefully for the idea that in evaluating the logical validity of a conditional proposition or argument, we should consider the relevance of the antecedent to the consequent. In logic, such a criterion leads to rejection of the paradoxes of strict implication, namely, that from an impossible proposition anything follows, and that a necessary proposition follows from anything. John expressed his rejection of the paradoxes clearly and decisively. Perhaps Copernicus had such a criterion in mind in his dedicatory letter to Pope Paul III in De revolutionibus, where he criticized Ptolemaic astronomers for having omitted something essential or having admitted something extraneous and irrelevant as part of their method. Copernicus may have been relying for this criticism on the views of logicians such as John of Glogovia who argued for relevance as a criterion of validity.

In natural philosophy, John tended to reject the nominalistic views of his predecessors at Kraków, and reintroduced the views of thirteenth-century philosophers and their fifteenth-century followers such as John Versor. The mid-century revival of thirteenth-century commentaries and the influence of Thomism was followed in the third quarter of the century by a more historically oriented *Aristotelianism under the influence of Italian humanists. In his Questions on Aristotle’s Physics (c. 1484–1487), John acquainted his students with the interpretations of ancient and medieval Aristotelians as well as with the nominalist and Parisian traditions. Accordingly, late fifteenth-century students learned not only about the doctrines of Aristotle but also how medieval authors had modified Aristotelian doctrines. Such adaptations contributed to a variety of “Aristotelian” interpretations, which in turn led to a variety of non-Aristotelian and even anti-Aristotelian conclusions. Some of the departures from Aristotle’s views were typical of Christian readers, for example, the denial of the eternity of the world, but others were more controversial. Several Kraków natural philosophers argued that extracosmic void space is actually infinite and that it can serve as a receptacle for bodies. Some asserted that celestial matter and terrestrial matter are essentially the same or, at least, belong to the same genus, and some of them adopted the *impetus theory in several forms to account for projectile motion. John of Glogovia did not always share these views, but he reported them to his students in his commentary and attempted to reconcile different opinions. Copernicus’s discussion of natural philosophy, especially the motions of Earth, adapted the Aristotelian principle of natural motion to a heliocentric system, reinterpreting Aristotle’s explicit assertions to the contrary as dialectical exercises and not as decisive arguments against the natural circular motion of the spherical Earth.

John’s work in astronomy and geography exemplifies the extent to which the University of Kraków emphasized mathematics. Even theoreticians such as John learned to use observational instruments, made measurements, constructed tables and astrological calendars, adapted astronomical tables to the Kraków meridian, explained the motions of the Sun, Moon, and planets from a geocentric perspective, and became familiar with the geographical discoveries of the New World. John understood the details of the Ptolemaic models, as demonstrated by his comments about the way that the motions of the planets are linked to the motion of the Sun, a fact that Copernicus thought needed explanation. Teachers such as John trained students in mathematics, and inspired them to undertake serious mathematical studies. It is likely that Copernicus’s teachers in Kraków introduced him to these subjects and stimulated him to make a closer examination of Ptolemaic models. Both Albert of Brudzewo and John of Glogovia emphasized the Averroistic critique of Ptolemaic models and the inadequacy of Ptolemy’s lunar model to account for the observed size of the moon at quadrature. The first observation that Copernicus made as Domenico Maria Novara’s assistant at Bologna in 1496 was of an occultation of the star Aldebaran by the Moon. He used this occurrence to test the adequacy of the Ptolemaic lunar model, and later cited it to confirm the superiority of his lunar model.

Despite the importance of John of Glogovia’s works, many of them remain unedited to this day.

See also Albert of Saxony; Astronomy, Latin; Geography, chorography; John of Sacrobosco; “Latin Averroists”; Marsilius of Inghen; Oresme, Nicole; Planetary tables; Ptolemy; Peuerbach, Georg; Quadrivium; Regiomontanus, Johannes; Theorica planetarum; Universities

Bibliography

Boh, Ivan. “John of Glogovia’s Rejection of Paradoxical Entailment Rules.” In Die Philosophie im 14. und 15. Jahrhundert. Edited by Olaf Pluta. Bochumer Studien zur Philosophie, 10. Amsterdam: B. R. Grüner, 1988, pp. 373–383.

Glogovia, Johannes de. Commentarius in “Metaphysicam” Aristotelis. Edited by Ryszard Tatarzylski. Opera philosophorum medii aevi, 7. Warsaw: Academy of Catholic Theology, 1984.

Goddu, André. Consequences and Conditional Propositions in John of Glogovia’s and Michael of Biestrzykowa’s Commentaries on Peter of Spain and Their Possible Influence on Nicholas Copernicus. Archives d’histoire doctrinale et littéraire du moyen âge (1995) 62: 137–188.

———. The Logic of Copernicus’s Arguments and His Education in Logic at Cracow. Early Science and Medicine (1996) 1: 28–68.

Knoll, Paul W. “The Arts Faculty at the University of Cracow at the End of the Fifteenth Century.” In The Copernican Achievement. Edited by Robert S. Westman. Berkeley: University of California Press, 1975, pp. 137–156.

Zwiercan, Marian. “Jan of Glogów.” In The Cracow Circle of Nicholas Copernicus. Edited by Józef Buszko. Copernicana cracoviensia, 3. Kraków: Jagiellonian University Press, 1973, pp. 95–118.

ANDRÉ GODDU

Johannes de Sancto Paulo

Johannes de Sancto Paulo (John of Saint Paul) was a twelfth- and early thirteenth-century medical writer associated with the famous medical “school” of *Salerno. Little is known about him other than what can be gleaned from his writings. He studied under Romuald, archbishop of Salerno (d. 1181). He was thus a contemporary of three of Salerno’s most accomplished theorists, *Maurus of Salerno, *Gilles de Corbeil, and *Urso of Calabria. Johannes mentions in passing that one Raynerius copied out a draft of his oral teachings, and in at least two of his treatises he makes reference to his socios (students). Johannes thus attained some kind of status as a medical master, even though his work focuses on the practical rather than the theoretical side of medicine. A suggestion that he was a Benedictine monk from the monastery of Saint Paul in Rome (d. 1214–1215) remains to be verified. Since he refers in one of his works to a term that “our Salernitans” (nostri Salernitani) use for a kind of pustule, he seems to acknowledge both his residence in the city and his sense that his own identity lies elsewhere.

Johannes is credited with at least four works: the Breviarium medicine (Breviary of Medicine); De simplicium medicinarum virtutibus (On the Virtues [or Powers] of Simple Medicines), also known as De conferentibus et nocentibus diversis medicinis (On the Beneficial and Harmful Effects of Different Medicines); Flores dietarum (The Flowers of Diets); and a treatise on critical days. Other works are attributed to him, notably a commentary on some pharmaceutical tables (Commentarium Tabulae Richardi) and De carnibus, but these have yet to be confirmed. The treatise on critical days must have been one of Johannes’s earlier works since he cites it in the Breviary; the latter must have also been rather early since it was written while Romuald was still alive (hence, before 1181).

Johannes divides the Breviary, a general medical compendium, into five books: the first on “general” diseases that afflict the whole body (such as swellings, wounds) or its surface (including all skin conditions); the second on the vital organs and respiratory system; the third on the digestive organs; the fourth on the genitalia, joints, hands, and feet; and the fifth on fevers. The Breviary is distinguished from earlier twelfth-century encyclopedic works by Salernitan masters such as those by Copho, Johannes Platearius, and *Bartholomaeus of Salerno by Johannes’s heavy reliance on the Viaticum of Ibn al-Jazzar, one of the Arabic works translated by *Constantine the African in the late eleventh century, and by its more extensive scope. Indeed, the Breviary is the first Salernitan composition to attempt to match the Viaticum’s nosological and therapeutic detail. Johannes’s stated aim is a systematic explanation of the signs and causes as well as the treatments for diseases; in fact, however, he sometimes describes the diseases without offering any cures at all. The work’s ambitious scope and clear exposition of humoral theory led to a wide circulation throughout Europe until it was superseded in the mid-thirteenth-century by the work of *Gilbertus Anglicus, who used Johannes as one of his sources.

Johannes’ works on simples (natural medicinal substances used by themselves without being compounded with other active ingredients) and the medical properties of foodstuffs also enjoyed considerable popularity well into the fifteenth century because they were so straightforward and handy for basic reference. Johannes says that he wrote his work on simples because the major pharmaceutical work then circulating under *Galen’s name had been hopelessly corrupted over the generations by careless scribes. Johannes lists the basic substances used in Salernitan materia medica, dividing them into categories such as herbs, seeds, flowers, gums, etc. The Flowers of Diets is a complementary text, explaining the elemental makeup (i.e., hot, cold, dry, wet) of basic foodstuffs such as grains and beans, and how these foods contribute to dissolving or generating the various humors of the body. It draws heavily on the work on diets by *Isaac Judaeus, whose writings had also been latinized by Constantine the African.

In the context of other Salernitan writings, Johannes’s work would have considerable influence. However, Johannes seems not to have developed any unique concepts in medical theory, therapy, or the organization of medical knowledge. He is rarely cited by subsequent authors—notable exceptions being *Gentile da Foligno and *John of Arderne—possibly because his works often circulated under the names of other writers such as Mesue and *Bernard of Gordon, and aside from two German dissertations in the early twentieth century he has not been studied by modern scholars other than as a source of information on medieval foods.

See also Medicine, practical; Pharmaceutic handbooks

Bibliography

Kroemer, Georg Heinrich, ed. Johanns von Sancto Paulo, “Liber de simplicium medicinarum virtutibus” und ein anderer Salernitaner Traktat, “Quae medicinae pro quibus morbis donandae sunt” nach dem Breslauer Codex herausgegeben. Borna-Leipzig: Druck von Robert Noske, 1920.

Ostermuth, Hermann Johannes, ed. “Flores diaetarum”: eine salernitanische Nahrungsmitteldiätetik aus dem XII. Jahrhundert. Borna-Leipzig: R. Noske, 1919.

MONICA H. GREEN

Illustration of a proctology procedure in a fourteenth-century manuscript of John of Arderne’s Practica. (National Library of Medicine)

John of Arderne

Born in 1307, John of Arderne, an English surgeon who practiced first in the East Midlands town of Newark and then later in London, is best known for authoring an influential Practica on the subject of fistula-in-ano. Written in Latin in the 1370s, the Practica was subsequently translated into several English versions and continued to be copied in both languages up until the end of the sixteenth century.

The surgical practica was a genre generally composed by academic surgeons for the purposes of teaching, but Arderne cannot be shown to have attended any of the great continental schools of surgery. Indeed, Arderne differentiates himself from his predecessors by replacing the head-to-toe order typical of scholastic surgeries with an extended, and highly remarkable, concentration on the anus and its surrounding area. He is also unusual in beginning his Practica with an extensive list of professional anecdotes, some of which refer either by name or by title to such affluent patients as the mayor of Northampton, the treasurer of the Black Prince’s household, and several senior ecclesiastics. The presence in this company of Sir Adam Everingham, a well-regarded knight in the retinue of Henry, Earl of Derby, along with occasional references to Henry’s campaigns in Gascony and Spain, suggests that Arderne might have served in the future Duke of Lancaster’s entourage. This, however, has yet to be proven.

Although Arderne describes his treatment for fistula-inano as a radical improvement over existing operations, he in fact combines two well-established methods, ligature and incision, that derive ultimately from Greco-Roman authorities. The influential Arabic surgeon Albucasis (*al-Zahrawi), influenced by Paul of Ægina, recommends either incision or cautery of the afflicted area, but only if the operator can avoid damage to the sphincter. Alternatively, the surgeon can thread a ligature through the fistula and out the anus and then gradually tighten it, a safer yet more excruciating means to cut the intervening flesh. In the thirteenth century, the Italian surgeons Bruno Longoburgo and *Teodorico Borgognoni, students of Ugo da Lucca, proposed the novel use of ligature as a means to secure the flesh to facilitate the faster and more practical method of cutting with a razor. John of Arderne, for his part, revises this latter operation by employing a peg that allows him to tighten the ligature at will, thereby controlling the speed and intensity of the resulting incision. An impressive program of illustrations accompanies the text and clarifies immensely the highly involved procedure it describes. Some modern practitioners regard Arderne’s innovations as unnecessarily cumbersome. Indeed, his impressive rate of success could well have been the result not of the treatment itself, but of a conservative post-operative strategy that emphasized bed-rest while at the same time downplaying the medieval surgical commonplace that ulcers and other wounds require frequent reopening.

Besides the Practica, John of Arderne is also responsible for a number of shorter treatises on various aspects of medicine that appear together in manuscripts as the Liber medicinalium. This collection includes notes on medicinal herbs, a short treatise on hemorrhoids, and discussions of a number of topics ranging from gynecology to afflictions of the eye. Indeed, his authorship of De cura oculorum in 1377 is the latest record we have of his life; he presumably died not long thereafter.

See also Medicine, practical

Bibliography

McVaugh, Michael. “Therapeutic Strategies: Surgery.” In Western Medical Thought from Antiquity to the Middle Ages, ed. Mirko D. Grmek, trans. Antony Shugaar. Cambridge: Harvard University Press, 1998.

Murray Jones, Peter. “Four Middle English Translations of John Arderne.” In Latin and Vernacular, ed. A.J. Minnis. Cambridge: D.S. Brewer, 1989, pp. 61-89

———. “John of Arderne and the Mediterranean tradition of scholastic surgery.” In Practical Medicine from Salerno to the Black Death, eds. Luis Garcia-Ballester, Roger French, Jon Arrizabalaga, and Andrew Cunningham. New York: Cambridge University Press, 1994, pp. 289–321.

JEREMY CITROME

John of Gaddesden

John (of) Gaddesden (d. 1348/9) is the first prominent English physician to be educated solely in England, and is best known for his medical compendium, the Rosa anglica (English Rose). Originating from Hertfordshire, Gaddesden first appears as a fellow at Merton College, Oxford, in 1305. He would eventually earn master’s degrees in both arts and medicine, and a bachelor’s in theology. He entered royal service in 1332 and remained in service to the king until his death, perhaps from the plague.

According to his own testimony, he compiled the Rosa anglica in his seventh year after incepting as a master of arts, probably c. 1313. As a work of his early career, it is not surprising that it is more a compilation of the teachings of others than an original synthesis. The Rosa is distinguished from the encyclopedic work of his predecessor, *Gilbertus Anglicus (d. c. 1250), by its heavier reliance on Arabic sources: Mesue, Rhazes (*al-Razi), Avicenna (*Ibn Sina), Averroes (*Ibn Rushd), and Serapion. While Gaddesden also makes frequent use of *Constantine the African, he generally eschews Salernitan authorities for Montpellierain masters such as *Bernard de Gordon. His work thus captures the state of scholastic medicine in the early fourteenth century.

Like his model Bernard de Gordon, Gaddesden consistently divides each heading into subsections on causes, symptoms, prognosis, and treatments. Despite his heavy reliance on the work of others, Gaddesden also incorporates his own cures, most famously, a treatment for smallpox that he employed on one of the young princes that involved wrapping the patient in red cloths. Gaddesden also reported a variety of charms and other alternative practices.

Of the nearly twenty extant copies of the Rosa anglica, half are now housed in British libraries. It was heavily employed by later fourteenth- and fifteenth-century medical writers in England, such as John Mirfeld who used it as the basis for his Breviarium Bartholomei, a medical handbook for the hospital of St. Bartholomew in London. It was similarly employed by the author of a lengthy gynecological text that expands on Gaddesden’s several chapters on women’s diseases by fusing them with a variety of excerpts from other texts, including the *Trotula. Portions of the Rosa anglica were translated into English, while a nearly complete Irish translation was made in the late fourteenth or fifteenth century; it was also the basis for a composite health regimen composed in Gaelic by Cormac Mac Duinnshleibhe (fl. c. 1459). More surprising (since there is no evidence that Gaddesden himself ever traveled outside of England) is the Rosa anglica’s popularity on the continent as well. Manuscripts are now found from Germany to Spain, and the first printed edition appeared in Pavia in 1492. The Rosa was reprinted three more times thereafter.

In addition to the Rosa anglica, Gaddesden is credited with authorship of several smaller texts, including a treatise on “the pestilence” which circulated in both Latin and English. This must have been his last work, since he seems to have himself died of the plague.

See also Medicine, practical

Bibliography

Carlin, Martha. “Gaddesden, John (d. 1348/9).” In Oxford Dictionary of National Biography. Oxford: Oxford University Press, 2004.

Cholmeley, H.P. John of Gaddesden and the ‘Rosa medicinae’. Oxford: Clarendon Press, 1912.

John of Gaddesden. Rosa anglica practica medicinae. Pavia: Franciscus Girardengus and Joannes Antonius Birreta, 1492.

Olsan, Lea T. Charms and Prayers in Medieval Medical Theory and Practice. Social History of Medicine (2003) 16:3: 343–366.

Voigts, Linda Ehrsam, and Patricia Deery Kurtz, eds. Scientific and Medical Writings in Old and Middle English: An Electronic Reference. Society for Early English and Norse Electronic Texts. Ann Arbor: University of Michigan Press, 2000. (CD-ROM.)

Wulff, Winifred, ed. Rosa anglica sev Rosa medicinæ Johannis Anglici: An Early Modern Irish Translation of a Section of the Mediaeval Medical Text-book of John of Gaddesden. Irish Texts Society, v. 25. London: Simpkin, Marshall, 1929.

MONICA H. GREEN

John of Gmunden

John of Gmunden was born 1380/1384 in Gmunden am Traunsee, Austria, the son of a tailor, whose presumed family name was Kraft. After matriculating in arts at the University of Vienna in 1400 he became a bachelor in 1402 and a master in 1406. Although his first known lecture in 1406 in Vienna was focused on “Theoricae (planetarum),” during the first phase of his career (1406–1416) his other lectures mainly dealt with nonmathematical subjects. In 1409 he became magister stipendiatus which brought him regular income from the Collegium Ducale. In 1415 he became a bachelor of theology, which obligated him to give two appropriate lectures until 1416. In 1417 he was ordained as priest.

His main scientific activities lay in astronomy, mathematics, and to a lesser degree in theology. From 1416 to 1425 he lectured exclusively on mathematical applications to astronomy, thus becoming the first specialized professor in this field. He was dean of the faculty of arts in 1413 and 1423 and held several administrative positions as well (e.g., treasurer). This was his most productive scientific period: he wrote a booklet on the art of calculating with sexagesimal fractions and produced various tables of proportions and a treatise on the sine-function in relation to arcs and chords, well within the knowledge boundaries of Arabic geometry, showing that he was acquainted with the works of *Jean de Meurs. In astronomy, his collaboration with Johann Andreas Schindel (who had left Prague University) led to the knowledge at Vienna of the writings of Richard of Wallingford concerning the albion, an instrument that calculated planetary positions. His application of this instrument to determination of an eclipse provided a useful tool in the teaching of astronomy at Vienna. His description of the equatorium (which he called instrumentum solempne after *Campanus de Novara) was greatly esteemed by *Peuerbach and subsequently by *Regiomontanus. He gave hints that the torquetum could be used for establishing longitude differences. His main efforts, however, lay in the construction and handling of the astrolabe joined with a star catalogue (1425) as well as the use of the (new) quadrant devised by Robert of England. Construction plans for an ivory quadrant for the German Emperor Frederick III (1438) show his connection to court artisans. While there is no documentation of observation activity by John himself, his pupils were good observers, and his influence on the astronomically interested prior of the monastery of Klosterneuburg (close to Vienna), Georg Müstinger, was especially strong.

In his third period of activity (1425–1431), he withdrew from the Collegium Ducale, became vice-chancellor of the university and canon of the Episcopal church of St.-Stephen. During this period he produced astronomical tables and volvelles (analogue paper computers) and lectured on the astrolabe, obviously dependent on a treatise of Christiannus de Prachatiz.

In his last period (1431–1442), he became plebanus (vicar) of St.-Vitus in Laa (an der Thaya), a rich parish that belonged to the University and provided a handsome income. Besides being renowned for his calendrical calculations, in his will he bequeathed his book collection, together with globes and instruments, to the faculty of arts, materials that provided an intellectual legacy at Vienna. While he certainly was no astrologer, he left astrological books to the library but imposed heavy restrictions on their circulation among students. John of Gmunden died on February 23, 1442, in Vienna and was buried in the crypt of St.-Stephen’s cathedral. A typical scholastic, he did not invent anything personally but prepared many texts in an easily understandable form that established Vienna subsequently as a center of astronomical learning.

See also Astrolabes and quadrants; Astronomy, Latin

Bibliography

Firneis, Maria G. “Johannes von Gmunden—der Astronom.” In Der Weg der Naturwissenschaft von Johannes von Gmunden zu Johannes Kepler. Edited by G. Hamann and H. Grössing. Vienna: Verlag der Österreichischen Akademie der Wissenschaften, 1988, pp. 65–84.

Hadrava, Petr and Alena Hadravová. “John of Gmunden as a Predecessor of Georg of Peuerbach.” In Peuerbach-Symposium 2004. Edited by Franz Pichler. Linz, Austria: Rudolf Trauner, 2004, pp. 1–8.

North, John D. Richard of Wallingford: An edition of his writings. 3 volumes. Oxford: Clarendon Press, 1976.

Vienna, Österreichische Nationalbibliothek, Cod. 2332, 2440, 5268, 5412, 5418.

MARIA G. FIRNEIS

John of Sacrobosco

Not much is known about Sacrobosco apart from his writings. The meaning of his name is unclear. “Sacrobosco” translates the common place-name Holywood. It may well refer to Holywood, in Nithsdale, Scotland (near Dumfries), site of a Premonstratensian abbey, where he may have served for a few years. He probably attended the University of Oxford. About 1221 he went to the University of Paris, where he lectured in the arts faculty on mathematical topics. A cryptic verse added to the end of his Computus refers to 1244 or 1256 as a significant date, most likely the year of his death. His tombstone at the monastery of Saint-Mathurin in Paris was destroyed long ago, but it is known to have been engraved with an astronomical instrument, in honor of his work on astronomy, and an epitaph calling him a computista, that is, a practitioner of the art of *computus or time-reckoning.

Sacrobosco’s significance to the history of science lies in his composition of elementary mathematical and astronomical textbooks. The Algorismus, a textbook on *arithmetic using *Arabic numerals, enjoyed a fair level of popularity and survives in a number of manuscripts and early printed editions. Another work usually ascribed to Sacrobosco, the Tractatus de quadrante, explained the manufacture and use of a kind of quadrant, an astronomical instrument. It is significant as an early set of Latin instructions for this instrument, but the small number of manuscripts (only eighteen have been identified) suggests it was superseded by better texts in the fourteenth century. His most influential works were the Computus and the Tractatus de sphaera.

The Computus contains two main parts corresponding to Sacrobosco’s two divisions of time-reckoning: the motion of the Sun, which determines the civil calendar, and the motion of the Moon, which determines the ecclesiastical calendar. Thus, while an astronomer studies all the celestial objects, the computista is concerned only with the two luminaries. Sacrobosco added nothing significantly new in his textbook on computus, a discipline that had reached maturity centuries earlier. However, he was among the first to publish a proposal for reform of the Julian calendar.

Sacrobosco wrote one of a number of elementary textbooks on astronomy with the title Sphaera; in popularity his surpassed all others. The “sphere” of the title refers to the aetherial sphere of the heavens, itself divided into several planetary spheres; the elementary sphere comprising the four Aristotelian elements; and the armillary sphere, an instrument used to represent the heavens and earth schematically. The book begins with basic Aristotelian *cosmology: the Earth is a sphere resting immobile at the center of the world, surrounded by the celestial sphere which revolves every twenty-four hours. Next comes a discussion of the armillary sphere and the celestial circles it represents. The longest section explains the risings and settings of celestial bodies that result from the daily rotation of the heavens. A brief survey of planetary theories and eclipses concludes the book.

Frontispiece of a fourteenth-century edition of John of Sacrobosco’s Sphaera. (Topham/RHR)

Sacrobosco’s textbooks are characterized by a narrative style laying out the facts of mathematics and astronomy for the reader. They avoid both the demonstrative approach of Ptolemy and the quaestio method of debate then popular at Paris. Numerous classical references and quotations give his works a humanistic air. Yet his frequent citation of al-Farghani illustrates the importance of Arabic sources in the medieval western encounter with *Ptolemy.

The Algorismus, Sphaera, and Computus appear together in a number of manuscripts of the thirteenth and fourteenth centuries, typically with more advanced astronomical texts such as a set of *planetary tables and a *theorica planetarum. Such collections demonstrate that Sacrobosco’s textbooks formed the core of a standard course of reading in mathematics at medieval universities. The situation changed with the advent of printing. Sacrobosco’s Sphaera was among the first scientific works to be printed in the fifteenth century, and it remained in print and readily available into the seventeenth century, but it almost never appears with his other works. Instead, it is found alone—perhaps with a commentary—or else with one or more other astronomical works, frequently a theorica. New commentaries were written. Some, like the commentary of the Jesuit Christopher Clavius, stretched to hundreds of pages in length and dwarfed Sacrobosco’s little book. The total number of printed editions of the Sphaera is in the hundreds. The Computus, on the other hand, only went through about thirty-five editions, nearly half of them from a single city: Wittenberg. The disparity in the fortunes of these two textbooks reflects the contrast between the flourishing of astronomy in the Renaissance and the gradual disappearance of computus.

See also Arithmetic; Astronomy, Latin; Elements and qualities; Quadrivium

Bibliography

Knorr, Wilbur R. Sacrobosco’s Quadrans: Date and Sources. Journal for the History of Astronomy (1997) 28: 187–222.

Lattis, James L. Between Copernicus and Galileo: Christopher Clavius and the Collapse of Ptolemaic Cosmology. Chicago: University of Chicago Press, 1994.

Pedersen, Olaf. In Quest of Sacrobosco. Journal for the History of Astronomy (1985) 16: 175–221.

Thorndike, Lynn. The “Sphere” of Sacrobosco and Its Commentators. Chicago: University of Chicago Press, 1949.

KATHERINE A. TREDWELL

John of Saint-Amand

A French author, physician, and cleric, John of Saint-Amand was one of the three most important medical authors of the late thirteenth century (along with *Taddeo Alderotti and *Arnau de Vilanova) in adapting Arabic and Ancient medical texts and ideas into Latin. He helped to formulate the “New Galen” at the turn of the fourteenth century.

Born c. 1230, probably in Saint-Amand en Pouelle, John’s early life is largely unknown. He undoubtedly studied the liberal arts and medicine at the University of Paris, and was probably also a regent master at the Paris Medical Faculty. Besides his likely academic position, John held more than five ecclesiastical positions, all within nine miles (14 km) of Saint-Amand, including the canonacy of the cathedral of Notre-Dame de Tournai. As a physician, he saw patients, including women and children, and potentates such as Bishop Gautier de Croix. John died between March 14 and May 7, 1303, and was memorialized in Tournai Cathedral.

John’s Latin medical works number more than twenty. His two principal texts are Revocativum, comprised of Concordanciae, Areolae, and Abbreviationes librorum Galeni, and Expositio super Antidotarium Nicolai. The Concordanciae is an alphabetized listing of keywords in the works of *Galen, *Hippocrates, Avicenna (*Ibn Sina) and others; it is also a very early adaptation of the textual device invented in contemporary Paris for biblical interpretation. Abbreviationes summarizes seventeen mostly Galenic and some Hippocratic treatises. Areolae is a consideration of simple medicines as well as brief discursi on compounds and laxatives, and survives in at least thirty-two manuscripts.

The Expositio, a commentary on the Antidotary Nicholai, is John’s most engaging work. He wrote it sometime between 1290 and 1303. The Antidotary was written by an unknown figure in Salerno and circulated widely among apothecaries and physicians. John’s commentary exists in at least forty-six manuscripts in its entirety and at least twenty-four manuscripts in excerpt or fragment, from the thirteenth to the sixteenth centuries; it was printed in editions from 1494 to 1623. In Paris Expositio became the lynchpin for regulation of apothecaries’ stock by the French Crown and the Medical Faculty. Consequently, it was closely kept and corrected by the Faculty.

John was the first Latin academic to comment on the medical work of Avicenna, and one of the earliest to refer to Serapion’s texts. In common with many of his near contemporaries, John wrote scholastic treatises: nine commentaries on medical texts in the stipulated or pending medical curriculum: Quaestiones supra tertiam fen primi Canonis Avicenni; Commentarius in Avicennam, liber quartus; Super Dietas Isaaci; Super Febrium Isaaci; Glosule in Isagogas Iohannitii; Scripta super Librum pulsuum Philareti; Scripta super Librum urinarum Theophili; Commentum super Librum de regimine acutorum; and Additiones Mesue. These commentaries were joined by others on more pharmacological and pharmaceutical texts: Breviarium de Antidotario; Super Dietas Isaaci; and Additiones ad Tacuinum de regimine sanitatis as well as De modis medendi, De remediis; and uncertainly Liber in medicacione cirurgie. Various receptae, excerptae, and marginalia also survive. Two texts linked to his name now appear to be lost: De conservatione sanitatis et tardatione senectutis and De viribus plantarum. Several texts descend to us under separate titles, but are originally parts of his longer works, attesting to their popularity and specific use.

His corpus is relatively standard in its breadth, but unique in its depth of pharmacological examination. Simply put, he represented a second stage in the advancement beyond the Salernitan transmission of *Gilles de Corbeil. His gross interests, pharmacy and medical educational codification, were the same, but his subject and manner of addressing those themes were more elaborate and subtle. From poetry to concordancing, from pharmaceutical listing to pharmaceutical theorizing and standardizing, John advanced over Gilles in codifying Parisian academic medicine. Yet John went beyond mere bridging. His interest in Galen exceeded curricula during his lifetime. His choice of texts fits in more closely with that of Montpellier more than forty years later. However, John’s commentaries also suggest his association with the earlier University of Paris curriculum. Thus John was an innovative figure in the scholastic assimilation of the work of Galen, at once working within the Articellan system of his educational youth and yet anticipating later didactic precepts. Additionally his impact was felt beyond the academy. The elite surgeon Henri de Mondeville used John’s system of citation and phrasing, suggesting he read the work closely.

John’s pharmacologic ideas were also highly integrative and original; simultaneously, they were particularly philosophical compared to the rest of the faculty. John addressed a controversy in pharmacology head-on—how do simple drugs behave when compounded (i.e., is the sum of the parts less than the whole?), suggesting that the measures of the key characteristic (radix) of a drug could be quantified, weight or measured. He also argued that a process of fermentation occurred in the mixing of simples, creating a new formulation in the compound, following along an Avicennan model.

Arguably, until *Jacques Despars in the fifteenth century, John cast the most far-ranging synthetic and theoretical shadow on the University of Paris medical faculty at a time when it was becoming the model for all European universities.

See also Pharmaceutic handbooks; Pharmacology; Universities

Bibliography

Primary Sources

Jean de Saint-Amand. Expositio super Antidotarium Nicholai in Mesue et omnia quae cum eo imprimi… (Venetiis: Iuntas, 1549), fo. 230v–72r.

Pagel, Julius Leopold. Die Areolae des Johannes de Sancto Amando (13.Jahrhundert). Berlin: Georg Reimer, 1893.

———. Die Concordanciae des Johannes de Sancto Amando. Berlin: Georg Reimer, 1894.

Secondary Sources

Arnau de Vilanova. Aphorismi de gradibus. Edited by Michael R. McVaugh, Arnaldi de Villanova Opera Medical Omnia, t. II. Granada and Barcelona: Universidad de Barcelona, 1975.

García Ballester, Luis. “The New Galen: A Challenge to Latin Galenism in Thirteenth-century Montpellier.” In Text and Tradition: Studies in Ancient Medicine and its Transmission: Presented to Jutta Kollesch. Leiden: E.J. Brill, 1998, pp. 55–83.

Jacquart, Danielle. “L’oeuvre de Jean de Saint-Amand et les méthodes d’enseignement à la Faculté de Médecine de Paris à la fin du XIIIe siècle” dans Jacqueline Hamesse, éd., Manuels, programmes de cours et techniques d’enseignement dans les universités médiévales. Louvain-la-Neuve: Université Catholique de Louvain, 1994, pp. 257–275.

Schalick, Walton O. Add One Part Pharmacy to One Part Surgery and One Part Medicine: Jean de Saint-Amand and the Development of Medical Pharmacology in Paris, c. 1230–1303. Johns Hopkins University, Ph.D., 1997. University Microfilms: Ann Arbor, 1997.

WALTON O. SCHALICK, III

John of Saxony

John of Saxony (Jean de Saxe, Iohannes de Saxonia, John Dank, Danco, Danekow) was probably born in Germany, perhaps in Magdeburg. His scholarly work is believed to date from the end of the thirteenth century. However, his presence in Paris can only be proven from 1327 to 1335. John of Saxony is quoted in medieval manuscripts as well as in contemporary literature as the author of various astronomical or astrological treatises, although his authorship is questionable in some of these cases. We shall deal here with three works originating from his hand. A *computus, preserved in manuscript form only and dated to the year 1297, is attributed to John of Saxony. In the manuscript itself, Iohannes Alemanus is given as the author. Also mentioned are the geographical longitudes of Paris and Magdeburg, which is considered to be John of Saxony’s birthplace. These and other facts prove beyond almost any doubt that John of Saxony is the author of this computus. He is certainly the author of the commentary to the astrological treatise Liber introductorius ad magisterium iudiciorum astrorum written by al-Qabisi (Alcabitius), the Arab scholar of the second half of the tenth century. The Alcabitius treatise, which was also known as the Liber isagogicus, was translated into Latin by Iohannes Hispalensis in the twelfth century. The commentary by John of Saxony is preserved in many dozens of manuscripts, several incunabulae and old prints, the latest of which dates from the middle of the sixteenth century.

The most important works by John of Saxony are his Canons on the Alfonsine Tables (Tabule Alfoncii) from 1327. The aim of this treatise was to enable students at the University of Paris to use astronomical tables. In medieval science, such tables were a useful means by which to make astronomical calculations, chiefly of planetary positions. They were used to derive ecliptic longitudes of planets for any chosen time and observer’s position, lunar phases, lunar and solar eclipses, as well as calendar data, etc. The Alfonsine Tables, which are the best known of the preserved tables, became the most widely used astronomical tables in late-medieval Europe. They were completed in the Spanish city of *Toledo around the year 1272 on the order of the Castilian king *Alfonso X the Wise (r. 1252–1284). Like the eleventh-century Toledan Tables from which they were developed, the Alfonsine Tables were based on the geocentric model of the planetary system as described in *Ptolemy’s Almagest. Although the Alfonsine Tables were originally written in Castilian, they were soon disseminated in Latin translation all over Europe. The first printed edition was published in 1483, and further editions followed quickly one after the other. Around 1320, the Alfonsine Tables became known in Paris, where the astronomers Jean de Lignères (Iohannes de Lineriis), his pupil John of Saxony, and later also *Jean de Meurs (Iohannes de Muris) recalculated them and supplemented them with canons, i.e., explanations, instructions, and rules for their use. We do not know how much the original version of the tables in Castilian was changed because this has not been preserved. We do know, however, that the calculation of all mean movements of the planets was consistently transformed into sexagesimal form in Paris. It was supplemented by tables for interpolation into individual days and their parts, while the original tables in Castilian provided the values for the calculation of mean planetary motions in twenty-year periods. Tables were also harmonized with the local Parisian meridian and modified and supplemented in other respects. The Alfonsine Tables were disseminated from Paris to other parts of Europe (in tandem with the establishment of new universities) and were modified in order to conform to the corresponding local meridians. In Central Europe they were commonly used, for example, at the universities of Prague and Kraków, as is evident from the manuscripts preserved there. The so-called Tabulae resolutae (Resolved Tables) usually tabulated planetary positions for certain latitudes and years. John of Saxony’s canons were published in print for the first time by Erhard Ratdolt in Venice in 1483, together with the first edition of the Alfonsine Tables. The canons by John of Lignères and Jean de Meurs have been never published in print.

See also Universities

Bibliography

Primary Source

Les tables alphonsines, avec les canons de Jean de Saxe. Édition, traduction et commentaire par Emmanuel Poulle. Sources d’Histoire Médièvale. Paris: Éditions du Centre national de la Recherche 1984.

Secondary Sources

Chabás, José. The Diffusion of the Alfonsine Tables: The Case of the Tabulae Resolutae. Perspectives on Science (2002) 10: 168–178.

Duhem, Pierre. Le système du monde. Paris: Librairie Scientifique Hermann, 1914–1959. (John of Saxony: IV. Paris 1916, pp. 76–90.)

Porres de Mateo, Beatriz. “Astronomy between Prague and Vienna in the 15th Century: the Case of John Sindel and John of Gmunden.” In Tycho Brahe and Prague: Crossroads of European Science. Edited by J. R. Christianson, A. Hadravová, P. Hadrava, and M. Solc. Acta Historica Astronomiae, vol. 16. Frankfurt am Main: Harri Deutsch Verlag 2002, pp. 248–255.

Porres, Beatriz and José Chabás. John of Murs’s “Tabulae permanentes” for finding true syzygies. Journal for the History of Astronomy 32: 63–72.

Poulle, Emmanuel. Jean de Murs et les tables alphonsines. Archives d’Histoire doctrinale et litteraire du Moyen Age (1980) 47: 241–271.

PETR HADRAVA AND ALENA HADRAVA

John of Seville

There has been much controversy concerning the identity of John of Seville (“Iohannes Hispalensis”), and whether he is a different person from several other “Johns” who were active in the field of Arabic science at approximately the same time. One can isolate a group of texts translated by the same scholar, whose name appears as “Iohannes Hispalensis” (usually with the addition of “et Limiensis/Lunensis”): the regimen of health from *Pseudo-Aristotle; The Secret of Secrets (addressed to Tarasia, the queen of the Portuguese from 1112–1228); Qusta ibn Luqa (Costa ben Luca) On the Difference Between the Spirit and the Soul (a brief treatise giving medical writers’ descriptions of the corporeal spirit and Aristotle’s and Plato’s definitions of the soul, addressed to Raymond de La Sauvetat, archbishop of Toledo 1125–1152); al-Farghani (Alpharganus) Book on the Science of the Stars (an introduction to Ptolemaic astronomy, in thirty chapters, completed in Limia on March 11, 1135); and several works on the branches of astrology: al-Qabisi (Alcabitius), The Introduction to Astrology (possibly 19 March 19, 1135), Umar ibn al-Farrukhan al-Tabari (Omar), On Nativities, *Abu Ma‘shar (Albumasar), The Great Introduction to Astrology (probably translated in 1133), *Masha’allah On Questions and On the Matter of Eclipses, and *Thabit ibn Qurra On Talismans (a text on astrological magic, translated in Limia). In addition, works on the construction and use of the astrolabe are attributed to the same author, which may not be translations. Moreover, manuscript affiliation and similarity of style suggest that three further astrological works by Albumasar, all concerning general and historical astrology, should be included: The Book of Experiments, The Flowers and On the Great Conjunctions. These texts indicate that John of Seville was active in northern Portugal (possibly in Ponte do Lima), in the 1120s and 1130s, and may have moved to *Toledo, if his dedication of a text to the archbishop of that city indicates patronage. He may thus be the “John of Toledo” who translated *al-Majusi’s On Nativities in July 1152 or 1153. It remains to be proved whether he is the “John of Spain” (Iohannes Hispanus) or “magister Iohannes,” who was definitely established in Toledo later in the twelfth century, collaborating with *Domingo Gundisalvo on translating *al-Ghazali’s Aims of the Philosophers and *Ibn Gabirol’s Fount of Life, and writing sophisticated works on astronomical tables (On the Differences between Astronomical Tables, written for two Englishmen, Gauco and William), on Indian arithmetic (The Book of Alchorismi on the Practice of Arithmetic, based on *al-Khwarizmi’s lost book on Indian arithmetic), and possibly on business arithmetic (The Book of Mahameleth). The last two works occur together in a manuscript (Paris, Bibliothèque nationale de France, lat. 15461) whose other work is a calendar written for Toledo in or just after 1159. He also may be different from the “Iohannes Hispalensis” who, in 1142, wrote a work on the four main branches of astrology, prefaced by an introduction (the Ysagoge and Book of the Four Parts, or Epitome of the Whole of Astrology), since the subject matter and terminology of this work are much closer to those of the astrological works of *Abraham ibn Ezra which were written in Tuscany and Béziers in the 1140s. A “John David” was the dedicatee of a text on the astrolabe written in Béziers by Rudolph of Bruges in 1144, and is described as “most skilled in the four disciplines of mathematics… most zealous in the science of the stars—nay rather in every science committed to script,” in a dedication of another text on the astrolabe, translated by Plato of Tivoli in Barcelona. A “master John David of Toledo” achieved legendary status as the originator of a prediction of cataclysmic events resulting from a “great conjunction” of all the planets in Libra in 1229. Identification of “John of Seville” with Avendauth (= “Son of David” in Hebrew) would, however, seem impossible, since Avendauth, another collaborator of Gundisalvo, is more likely to be the Jewish scholar, Abraham ibn Daud, the outlines of whose biography are reasonably clear.

John of Seville’s translation of On the Difference between the Spirit and the Soul was incorporated into the curriculum of natural philosophy in the medieval universities (as occasionally was his translation of the Secret of Secrets), and was frequently glossed and commented on, whilst his astrological translations—especially those of Alcabitius’s Introduction and Albumasar’s Great Introduction and Great Conjunctions—were central texts for the study of astrology and were printed in the Renaissance.

See also Astrolabes and quadrants; Toledo

Bibliography

Primary Sources

Albumasar. Liber introductorii maioris, translated by John of Seville. In Abu Ma‘sar al-Balhi, Liber introductorii maioris ad scientiam judiciorum astrorum. Edited by Richard Lemay, 9 vols. Naples: Istituto universtaria orientale, 1995–1996, vol. V.

———. De magnis coniunctionibus. In Abu Ma‘sar, On Historical Astrology. Ed. Keiji Yamamoto and Charles Burnett, 2 vols. Leiden: E.J. Brill, 2000.

Alcabitius, Introductorius. In Al-Qabisi (Alcabitius): The Introduction to Astrology. Ed. Charles Burnett, Keiji Yamamoto and Michio Yano. London and Turin: Warburg Institute and Nino Aragno, 2004.

Liber Alchorismi de practica aritmetice. In Muaammad ibn Musi al-Khwarizmi, Le Calcul Indien (Algorismus). Ed. André Allard. Paris: Blanchard, 1992, pp. 62–224.

Johannes Hispalensis. Epitome totius astrologiae. Nürnberg: in officina Ioannis Montani et Ulrici Neuber, 1548.

Secondary Sources

Burnett, Charles. “Magister Iohannes Hispalensis et Limiensis” and Qusta ibn Luqa’s De differentia spiritus et animae: a Portuguese Contribution to the Arts Curriculum? Mediaevalia, Textos e Estudos (1995) 7–8: 221–267.

———. John of Seville and John of Spain: a mise au point. Bulletin de philosophie médiévale (2003) 44: 59–78.

D’Alverny, Marie-Thérèse. “Avendauth?” In Homenaje a Millás-Vallicrosa. 2 vols. Barcelona: Consejo Superior de Investigaciones Científicas, 1954–1956, I, pp. 19–43.

Thorndike, Lynn. John of Seville. Speculum (1959) 34: 20–38.

Williams, Steven J. The Secret of Secrets. The Scholarly Career of a Pseudo-Aristotelian Text in the Latin Middle Ages. Ann Arbor: University of Michigan Press, 2003.

CHARLES BURNETT

Jordanus de Nemore

Although little is known of the life of Jordanus de Nemore (fl. c. 1220), twelve treatises are attributed to him in a library catalogue of the works of Richard de Fournival, compiled between 1246 and 1260. It is therefore likely that he lived and wrote during the first half of the thirteenth century. The works ascribed to Jordanus are concerned with mechanics and mathematics. He appears to be the author of at least six works. The name of Jordanus is most intimately associated with the medieval “science of weights” (scientia de ponderibus), or statics, to which he contributed more than any of his contemporaries. As testimony to his stature, commentators on his works on statics sometimes attributed their own contributions to him. However, thus far only one work in statics can be definitively assigned to Jordanus: The Elements of Jordanus on the Demonstration of Weights (Elementa Jordani super demonstrationem ponderum). Another work, The Book of Jordanus de Nemore on the Theory of Weight (Liber Jordani de ratione ponderis), is probably by Jordanus.

Of these two treatises, the Theory of Weight is the more important, but taken together they represent the most significant works in medieval statics. In them, Jordanus introduces into statics the idea of component forces by means of a concept he called gravitas secundum situm (“positional gravity”). Jordanus applied positional gravity to both rectilinear and arcal paths. Although it does not yield correct results when applied to an arcal path, when Jordanus applied it to rectilinear paths he achieved brilliant accuracy. He also presented a proof of the law of the lever by means of the principle of work, which was previously a vague concept. In the Theory of Weight (Book I, Proposition 10), Jordanus again employs the principle of work in a proof of the inclined plane, demonstrating that “If two weights descend along diversely inclined planes, then, if the inclinations are directly proportional to the weights, they will be of equal force in descending.”

Jordanus advanced statics by combining the dynamical and philosophical approach characteristic of Aristotelian physics with the mathematical physics of *Archimedes. He derived rigorous proofs within a mathematical format based on Archimedean statics and Euclidean geometry. Jordanus’s treatises gave rise to an extensive commentary literature from the thirteenth to the sixteenth centuries. With the advent of printing, Jordanus’s ideas were widely disseminated and influenced leading scholars of the sixteenth and seventeenth centuries, including Galileo Galilei.

Jordanus seems to have been as talented in mathematics as in mechanics. Treatises on geometry, proportions, algebra, and theoretical and practical arithmetic are attributed to him. His Liber Philotegni de triangulis (The Book of the Philotechnist on Triangles) was medieval geometry of the highest order. In the fourth book, Jordanus presents the most sophisticated proofs, including the trisection of an angle, as well as a proposition on how to square the circle in which Jordanus gives a proof that differed from that given by Archimedes in his famous treatise, Measurement of the Circle.

Theoretical arithmetic in the Middle Ages was greatly influenced by Jordanus’s Arithmetica (Arithmetic). The work is divided into ten books in which Jordanus presents more than four hundred propositions. These proceed by way of definitions, postulates, and axioms after the arithmetic books of *Euclid’s Elements, and thus depart from the earlier tradition of *Boethius’s Arithmetic, which was rather informal and often philosophical. Many of Jordanus’s propositions had counterparts in Euclid’s Elements, but some did not. One that was independent of Euclid is Book I, Proposition 9, where the enunciation of the proposition reads: “The [total sum or] result of multiplication of any number by however many numbers you please is equal to the result of the multiplication of the same number by the number composed of all the others.” In modern notation, Jordanus proves that if AB = D, and AC = E, then D + E = A (B + C). Jordanus also composed an algorism (Demonstratio Jordani de algorismo) in which he described the basic arithmetic operations and extraction of roots.

Algebraic treatises in the Middle Ages were often practical texts for the instruction of lawyers and merchants. Jordanus, however, proceeds in the manner characteristic of Greek mathematicians of the caliber of Euclid, Diophantus, and Pappus. In his treatise De numeris datis (On Given Numbers), Jordanus made algebra an analytic discipline more than three centuries before François Viète, who wrote his Introduction to the Analytical Art in 1591. Although Jordanus was probably familiar with Arabic works on algebra and perhaps also with the Liber abaci by *Fibonacci, On Given Numbers is nonetheless an original treatise. It was widely used in the fifteenth and sixteenth centuries and *Regiomontanus (1436–1476) planned to publish it, but died before he could do so. Jordanus incorporated three distinct elements into every proposition: (1) Formal enunciation of the proposition; (2) The proof; and (3) A numerical example. Although the treatise is wholly rhetorical, Jordanus did use letters of the alphabet to represent numbers.

Jordanus composed a treatise on the planisphere (De plana spera) in which he sought to represent on a plane surface the points and circles on a sphere—in other words, stereographic projection. Projections of this kind were usually applied to astrolabes, but Jordanus does not mention those instruments in his treatise. Jordanus’s Planisphere was the most important, and most widely disseminated, treatise on stereographic projection in the Middle Ages.

A treatise on treating fractions (Liber de minutiis) has also been attributed to Jordanus, as well as a brief work on proportions (Liber de proportionibus), the propositions of which strongly resemble those in the fifth book of Euclid’s Elements. For the high level and range of his mathematical and mechanical ideas and proofs, Jordanus de Nemore had no equal in the Latin Middle Ages.

See also Algebra; Arithmetic; Weights, science of

Bibliography

Busard, H.L.L., ed. Jordanus de Nemore, De elementis arithmetice artis: a medieval treatise on number theory. Stuttgart: F. Steiner, 1991.

Høyrup, Jens. Jordanus de Nemore, 13th century mathematical innovator: An essay on intellectual context, achievement, and failure. Archive for History of Exact Sciences (1988) 38: 307–363.

Hughes, Barnabas Bernard, ed., and tr. Jordanus de Nemore: “De numeris datis.” A critical edition and translation. Berkeley: University of California Press, 1981.

Moody, Ernest A. and Marshall Clagett, ed and tr. The Medieval Science of Weights (Scientia de ponderibus): Treatises Ascribed to Euclid, Archimedes, Thabit ibn Qurra, Jordanus de Nemore and Blasius of Parma. Edited with Introductions, English Translations, and Notes. Madison: University of Wisconsin Press, 1952, 119–227.

Thomson, Ron B., ed. Jordanus de Nemore: Opera. Medieval Studies (1976) 38: 97–144.

———, ed. Jordanus de Nemore and the mathematics of astrolabes: De plana spera. [Studies and texts, 39] Toronto: Pontifical Institute of Medieval Studies 1978.

EDWARD GRANT