History – Page 2 – Medieval Studies Research Blog: Meet us at the Crossroads of Everything

December 27, 2023January 9, 2024

On St. Nick’s Beard

The development of the appearance of the modern Santa Claus is a fascinating one, evolving from traditional representations in Germany and the Low Countries, a distinctly English Father Christmas, and the Coca-Cola Company’s efforts to sell product. One of the most distinctive features of the modern portrayal, though, predates all of these: the beard, a sine qua non of the modern depiction, dates back centuries, and likely originated with the historical St. Nicholas himself. Unlike some of the other aspects of his appearance, though, the decision of St. Nicholas (probably) to wear a beard, and the decisions of his later iconographers to depict him with one (or not, as the case may be), were generally not socially or theologically neutral. In this post, I’d like to explore some aspects of the meaning conveyed by St. Nick’s beard, focusing mostly on the Middle Ages and as an excuse to bring up my favorite research topic: the differences that arose between Latin and Greek expressions of Christianity during and after the conflict of the mid-eleventh century.

But first, by way of background, what can be said about the appearance of the historical St. Nicholas, the bishop of Myra in Asia Minor in the first half of the fourth century? While the sources for the general practice of the time period are not unanimous, the consensus of the Christian writers of the period, especially in the Eastern part of the Roman Empire, seems to have been in favor of beard-wearing [1]. Clement of Alexandria, writing the century prior, argued, “For God wished the woman to be hairless and smooth, rejoicing in her hair alone, like the horse does its mane, but He decorated man with a beard, just like the lions” [2]. Nor was the sentiment confined to Christian authors. Emperor Julian (“the Apostate” or “the Philosopher” depending on whom you ask), about as un-Christian an author as one could ask for and a reasonably close contemporary of Nicholas, is famous for his written defense of the beard. At the same time, clergy in many parts of the West, and the city of Rome in particular, retained the republican and imperial Roman custom of cleanshavenness.

The preference of the Eastern churchmen has been taken into account for forensic reconstructions done on the basis of the relics in his tomb in Bari, and the resulting depiction is dominated by a sizeable beard ]. This depiction persisted in subsequent centuries of Greek Christian iconography. From the earliest surviving example (seventh or eighth century, available in the Mount Sinai Archives), through to the present day, St. Nicholas, in the Greek tradition, is consistently depicted with a beard. And, given his ubiquity in the medieval and modern Orthodox church setting, it might be fair to say that he became one of the definitive archetypes for how clergy should look.

Apse of the Ferapontov Convent, Russia, By Dionisius, turn of the 16th c.
Public domain, via Wikimedia Commons.

Clerical appearance took on a new significance as conflicts between the Greek and Latin churches began to arise. During the so-called “Photian Schism” in the ninth century, for example, while Photios himself noted the differences between Greek and Latin practices with equanimity, other Greeks were less tolerant [3]. The Roman Pope at the time, Nicholas I, complained to Hincmar of Reims that the Greeks condemned them for being clean shaven [4]. By the time of the legation of 1054, this condemnation had grown into an occasional cause for a break in communion. As Humbert of Silva Candida complained: “maintaining the hair of their head and their beards, they [i.e., the Greeks] do not receive into communion those who tonsure their hair and shave their beards according to the institution of the Roman Church” [5].

The Latins, as mentioned above, were much friendlier to the notion of cleanshavenness as far back as the Patristic period, especially among the clergy, and this permissiveness gradually evolved into a situation in which not having a beard became one of the defining markers of the clerical state. Even within monastic communities, wearing a beard was a sign of the low social standing of lay brothers in religious communities. Monks who were also ordained, in contrast, were usually clean shaven [6]. Defenders of the Latin tradition, therefore, predictably took a very different position from their Greek interlocutors. This expression ranged from the mild-mannered observation of the difference in practice made by the Norman Anonymous, writing around the turn of the twelfth century (“they observe a different custom in tonsure and habit […], for they are bearded”) to the vituperative Leo Tuscus half a century later (“Their priests, in a Jewish manner, permit their beards to grow, which are sodden with the Lord’s blood when it is drunk by them.”) [7].

So what of St. Nicholas? While the Greeks continued to portray him in the traditional manner, Latin artists (or perhaps iconographers?) chose to portray him not as he was, but as they felt he ought to have been. The Nicholas that emerges in the late Middle Ages looks every bit the part of a Latin bishop: in Latin clerical dress, complete with miter and crosier, and without a trace of a beard.

The De Grey Hours (c. 1390), National Library of Wales, CC0, via Wikimedia Commons.

Of course, it is important to note that St. Nicholas was hardly alone in this treatment: it was entirely commonplace to update the saints of antiquity to suit the sartorial standards of the artist. At the same time, precious few saints with so wide a following in the Latin Church were known to be Greek, and the Greek preference for the beard was equally well known, so it’s difficult not to see some degree of deliberate Latinization in the portrayal of the saint.

In the end, East-West polemic shifted to other topics, clearing the way for the restoration of the beard. And, in a sense, in fixing the image of a bearded Santa Claus so firmly in the modern imagination, to the point that a beardless Santa Claus would be near anathema, perhaps the Coca-Cola Company has earned a small debt of gratitude from contemporary iconographers.

Nick Kamas
PhD in Medieval Studies
University of Notre Dame

[1] A. Edward Siecienski, “Holy Hair: Beards in the Patristic Tradition” St Vladimir’s Theological Quarterly 58:1 (2014), 64.

[2] Clement of Alexandria, Paidogogus 3.3. PG 8.580.

[3] Photius of Constantinople, The Mystagogy of the Holy Spirit, trans. Holy Transfiguration Monastery (Long Island City, NY: Studion Publishers, 1983), 45–46. For a discussion of this and many of the following sources, see A. Edward Siecienski, Beards, Azymes, and Purgatory: The Other Issues that Divided East and West (Oxford: Oxford University Press, 2023), 38–78.

[4] PP Nicholas I, Epistola Hincmaro et Ceteris Confratribus Nostris Archiepiscopis et Episcopis in Regno Karoli Gloriosi Regis […], MGH Epistolae VI, 603.

[5] “Excommunicatio qua feriuntur Michael Caerularius atque ejus sectatores.” Acta et Scripta, ed. Cornelius Will (Frankfurt am Main: Minerva GMBH, 1963), 153–154.

[6] Giles Constable, The Reformation of the Twelfth Century (Cambridge: Cambridge University Press, 1996), 195–196.

[7] Norman Anonymous. “De consecratione sacerdotis,” in Die Texte des Normannischen Anonymus, ed. Karl Pellens (Wiesbaden: Franz Steiner Verlag, 1966), 104. Leo Tuscus, Malae consuetudines Graecorum, PG 140.547D.

October 18, 2023October 23, 2023

Why 1054? Dating the Schism for the Church of Constantinople

To the best of my knowledge, no serious historian or theologian working over the last century has been willing to date a definitive schism between the current Catholic and Eastern Orthodox churches to the year 1054. This raises some obvious questions: what marks a schism in the first place? When did such a division occur between these two ecclesial bodies? And the topic partially addressed in this blog post: how did the year 1054 rise to such prominence that it appears in virtually every high school-level world history textbook in the present day?

It might be helpful to clarify what happened during the Latin legation to Constantinople in 1054. After a mutually unsatisfactory meeting and some debates over issues of liturgical and church disciplinary practice, the Latin legates excommunicated the patriarch of Constantinople, Michael Keroularios, but the expressly excluded the Eastern Roman emperor at the time, Constantine X Monomachos, as well as the city in general, from this breach in communion [1]. Patriarch Michael responded by convening a council to excommunicate the legates personally, but he took great pains to avoid condemning the bishop of Rome, on the grounds that the legates were imposters who hadn’t been sent by the pope at all. Still less was the whole of the Latin Church implicated in the Greek conciliar statement. It is abundantly clear from the surviving documents that no general division between the eastern and western halves of Chalcedonian Christianity was intended in the exchange of the excommunications, and there is no evidence from the time of the event itself that any such division was achieved.

This is confirmed by sources and events in the years immediately following 1054. In the immediate aftermath, Patriarch Michael Keroularios dispatched letters to the other eastern patriarchs complaining about the legates and about Latin liturgical and ritual practices, but he does so without any notion of a break in communion with the whole of western Christianity. The encomium of Michael Psellos for Keroularios, who died in 1059, praises the late Patriarch’s resistance to the legates. Psellos, ever philosophically-minded, focused on the question of the filioque, which was, in fact, one of the issues least discussed by the respective parties in 1054 itself (rather, they were concerned with whether bread for the Eucharist should be leavened, whether priests could be married, etc.). While admitting that Old and New Rome were in disagreement, and that the Roman position was “impious,” there is again no indication of a formal split in communion [2]. In another example a few years later, this time primarily from Latin sources concerning the great pilgrimage of Gunther of Bamberg, we are told that the Greeks were excessively proud in their dealings with the pilgrims (not an uncommon complaint), but not that they considered each other to be heretics or schismatics [3].

So, then, why the significance of this date? If not in the first-hand accounts, was any significance ascribed to the year 1054 in the works of later theologians and polemicists? I am preceded in this examination by an especially helpful article by Tia Kolbaba, a Byzantinist working at Rutgers, who examined twelfth-century sources with the expectation that the increased political tension between the Latin kingdoms and the Eastern Empire would evoke the historical example of Michael Keroularios in the theological literature [4]. Her conclusion is surprising: she was able to find no firmly-datable sources that considered the role of Michael Keroularios in the schism at all, and only a handful of short texts plausibly belonging to the twelfth century that mention him in passing. In the latter group, there is an interpolation in the history of Scylitzes, a single text in Vat. grec. 2198, a paragraph attributed to a certain Nicetas the Chartophylax, and a handful of anonymous texts collected by Hergenröther. This last item, edited under the collective title “Opuscula de origine schismatis,” is the most substantial of these, and even these short texts mention the role of Keroularios in conflicting terms and only in passing, at the end of rather confused accounts about the supposed errors of the Church of Rome [5].

In virtually all of these texts, the cause of the schism (which is fully recognized by the twelfth century) is attributed to the Latins’ mistaken Trinitarian theology, and specifically the question of the filioque. Although it does get mentioned, much less attention is given to the question of (un)leavened bread, a complete reversal of the 1054 conflict in which ritual questions were given pride of place. This change of emphasis leads most, if not all, of these later commentators to draw upon source material from an earlier rupture between Rome and Constantinople: the ninth-century Patriarch Photios, although he did eventually restore communion with the See of Rome, left behind substantial writings and a strong tradition of critiquing the Latin position, especially in terms of its Trinitarian theology. And it is primarily to Photios, rather than to Keroularios, that later Greek church historians and polemicists turned.

And finally, it appears that this interpretation persisted into the early modern period, even among Greek clergy sympathetic to the Roman position. John Plousiadenos, a fifteenth-century Cretan Byzantine-rite priest in union with the Church of Rome, appears content to attribute the fundamental basis of the schism to Photios, whom he described as “the very maker and the demiurge of the schism and the division” [6]. Charles Yost, a fellow graduate of the Medieval Institute, pointed out in his 2019 dissertation that the historiography of Plousiadenos concerning the schism, as well as that of other high-profile Greek churchmen of his time, was rather garbled, with different authors presenting conflicting accounts of whether Photios, for example, was ever personally restored to communion with Rome. In nearly all accounts, however, Keroularios is conspicuous by his absence: Plousiadenos says nothing about him at all, and Manuel Kalekas, another unionist, downplays his role [7]. At the end of the Middle Ages, then, the Great Schism, to the extent that the Greeks were willing to date it at all, happened in the ninth century, and the examples of intercommunion in the centuries following were, ultimately, just failed attempts at reunion.

So where does this leave our starting question, and can we trace any part of the modern prominence given to the date 1054 to the Constantinopolitan/Greek historical or theological tradition? I think that the answer is no. None of the Greek sources following the events themselves are willing to date a definitive schism to that year. At most, the actions of Michael Keroularios are a (small) episode in a series of conflicts with the Church of Rome that began at least two centuries earlier. Otherwise, his name and his role are omitted entirely from the discourse of later commentors. I have found nothing akin to the modern celebrity given the 1054 conflict until the writings of the Athonite Kollyvades fathers around the turn of the nineteenth century. Other than that, it only within the Latin medieval tradition that we can possibly find a substantial reception of 1054. And these both are very much topics for separate posts.

Nick Kamas
PhD in Medieval Studies
University of Notre Dame

[1] The best edition for the documents cited here in relation to the 1054 legation remains Cornelius Will, ed., Acta et Scripta quae de controversiis ecclesiae graecae et latinae saeculo undecimo composita extant (Leipzig: N. G. Elwert, 1861).

[2] K. N. Sathas, ed., Μεσαιωνική Βιβλιοθήκη Δ‘ (Athens: Koromela, 1874), 348. “Στασιάζει πρὸς τὴν νεωτέραν Ρώμην ἡ πρεσβυτέρα, οὐ περὶ μικρῶν οὐδὲ παρορᾶσθαι ἀξίων, ἀλλὰ περὶ τοῦ πρώτου λόγου τῆς εὐσεβείας, καὶ τῆς περὶ τῆν ἁγίαν τριάδα θεολογίας […].”

[3] Annales Altahenses maiores, ed. altera, ed. E. L. B. von Oefele, MGH SS Rer. Germ. 4 (Hannover: impensis bibliopolii Hahniani, 1891), 67. “Constantinopolitanos vidimus [Latini episcopi] graece et imperialiter arrogantes.”

[4] Tia Kolbaba, “The Legacy of Humbert and Cerularius: The Tradition of the ‘Schism of 1054’ in Byzantine Texts and Manuscripts of the Twelfth and Thirteenth Centuries,” in Porphyrogenita: Essays on the History and Literature of Byzantium and the Latin East in Honour of Julian Chrysostomides” (Aldershot: Ashgate, 2003), 47-61.

[5] “Opuscula de origine schismatis,” ed. J. Hergenröther in Monumenta graeca ad Photium ejusque historiam pertinentia, (Regensburg: G.J. Manz, 1869). The first of these texts is unusual in reporting (inaccurately) that Michael Keroularios excommunicated the whole of the Latin church (p. 163), but this is corrected by the second text, which follows Keroularios’s own account that Latin legation had been tampered with for political ends (p. 170). The third text does not mention him at all.

[6] Charles Yost, “The Thought and Ministry of a ‘Unionist Priest’ (ἙΝΩΤΙΚῸΣ ἹΕΡΕΎΣ): John Plousiadenos (†1500), the Council of Florence, and the Tradition of Byzantine Unionism” (Ph.D. Diss., University of Notre Dame, 2019), 649, esp. n. 480.

[7] Ibid., pp. 672, 674.

October 4, 2023October 5, 2023

The Quadrivium and the Stakes for Ordering the Mathematical Arts

Fyodor Bronnikov, *Pythagoreans’ Hymn to the Rising Sun*, 1869. Oil on canvas.

Legend has it that Pythagoras sentenced the first person to discover irrational numbers, Hippasus of Metapontum (c.530-450 BC), to death. He was tossed overboard a ship to drown. Why? Pythagoras taught that number was the essence and cause of all things, and for Pythagoras and his followers, numbers meant integers. Hippasus’ discovery of irrational numbers appeared to undermine the very core of Pythagoras’ teachings about the numerical nature of the universe. The secret could not get out. Hippasus had to die.

Imaginary engraving of the philosopher Hippasus of Metapontum. From the 1580 book *Illustrium philosophorum et sapientum effigies ab eorum numistatibus extractae*, by Girolamo Olgiati. Reprinted 1583.

The existence of irrational numbers became a Pythagorean secret. They were called “unutterables” because in Greek, the ratio between two integers was called logos, and so, irrational numbers were called, alogos, which can be translated as either “irrational” or “not spoken.” The worry caused by this secret knowledge was somewhat alleviated by Eudoxus of Cnidos (408-355 BC) when he argued that the basis of reality was a ratio of magnitudes. In effect, Eudoxus made geometry replace arithmetic as the highest mathematical discipline, the foundation of all others. Geometry and arithmetic were hardly even separate disciplines at the time. This change of emphasis allowed Pythagorean teachings about the numeric nature of the universe to continue.

Philosophia et septem artes liberales (Philosophy and the Seven Liberal Arts), as illustrated in the *Hortus deliciarum*. The order of the arts here are: grammar, rhetoric, dialectic, music, arithmetic, geometry, and astronomy. A more detailed study of this image can be found here and here.

The idea that the mathematical disciplines have some orderly relationship between each other is essential for understanding the medieval concept of “quadrivium.” While it is well known that the medieval liberal arts curriculum, at least in its ideal established by Boethius, taught that a student must study both the trivium and quadrivium before progressing to philosophy and theology, the exact nature and rationale for the quadrivium is often less understood. Lists of the arts comprising the quadrivium (arithmetic, geometry, astronomy, and music/harmony) are consistent, but the exact order for these lists can vary. While there is no doubt that sometimes there is truly no rationale for a given order of the mathematical arts, attention to the mathematical art considered the principle or highest can reveal at least three identifiable streams of quadrivial traditions coming from the ancient world (similar to Chenu’s identification of different kinds of Platonism): the Boethian, the Calcidean, and the Capellan. The mathematical art considered “principle” is the one closest to metaphysical reality of the universe and serves as the foundation for all other mathematical disciplines. While the problem of irrational numbers may not have been on the forefront of anyone’s mind in the Middle Ages…it was a closely guarded Pythagorean secret after all…the problem of the principle mathematical art, inherited from Pythagoreanism, was readily available in the source texts.

“Philosophy Presenting the Seven Liberal Arts to Boethius,” about 1460–1470, Coëtivy Master (Henri de Vulcop?), Ms. 42, leaf 2v (91.MS.11.2.verso), Getty Museum Collection.

Boethius (c.480-525) not only established the seven liberal arts as the traditional curriculum for the Middle Ages, but he also wrote treatises on all of the trivium as well as arithmetic, music, and geometry (the latter work is now lost). He, coined the term, “quadrivium” in his attempt to translate the tessares methodoi (four methods) of the Neopythagorean, Nicomachus of Gerasa (c.60-120). Boethius’ own De institutione arithmetica largely draws upon the work of Nicomachus. Modern day history of mathematics textbooks often observe that Nicomachus’ work is one of the first to distinguish arithmetic and geometry as separate disciplines but that the actual quality of the mathematics contains basic errors. Unlike Euclid, Nicomachus doesn’t always give his proofs. Nicomachus presents arithmetic as the principle mathematical art and as a result, so does Boethius. While Boethius was unlikely to have gotten the problem of irrational numbers from Nicomachus because Nicomachus presents arithmetic as the highest mathematical art, Boethius adopts his fourfold division of the mathematical arts along with the belief that arithmetic was the principle mathematical art (De institutio arithmetica 1,1,8).

Image from Boethius’ *De institutione arithmetica* in British Library, Harley MS 549.

In his work on arithmetic, Boethius explains that the order of the quadrivium he offers (music, astronomy, geometry, and arithmetic) both reflects the true nature of the universe and is the proper pedagogical order for the study of mathematics as a preparation for philosophy. Progression through each of the arts trains the mind to move from sense perception to intelligible reality.

Philosophy Instructing Boethius on the Role of God. Coëtivy Master (Henri de Vulcop?), about 1460–1470. Ms. 42, leaf 3 (91.MS.11.3.recto), J. Paul Getty Museum.

This progression of the soul can be seen in the Consolation of Philosophy, where Boethius begins with music and is drawn to philosophy upward by means of astronomy, geometry, and finally arithmetic.

While Boethius’ highly influential order of the quadrivium was adopted by both Cassiodorus and Isidore, Calcidiuswrites very clearly in his commentary on Plato’s Timaeus that geometry is the foundation of all other mathematical arts (Commentum 2.32). His influence throughout the Middle Ages was also extensive. Calcidius’ translation and commentary of Plato’s Timaeus, was one of the only texts of Plato available throughout much of the Middle Ages. Although there were other translations of the Timaeus available, Calcidius’ commentary, as Reydams-Schils has demonstrated, was actually a very good introduction to Platonism as a whole because it was designed to introduce the reader to Platonic doctrine in a pedagogically sequenced way from mathematics to physics and then theology. Throughout the earlier Middle Ages, as Somfai has shown, the commentary was used to teach the quadrivium itself, and earlier versions contained numerous geometrical diagrams. While interest in his geometrical figures appears to fall out of favor in the twelfth century and in newer commentaries on the Timaeus, Nicholas of Cusa in the fourteenth century has both the old Calcidius’ commentaries and the newer commentaries, and geometry clearly plays a major role in his understanding of infinity and kinds of infinity.

Early tenth century manuscript of Calcidius’ Latin translation of Plato’s *Timaeus* from Italy. *Reg. lat. 1308 fols. 21 verso – 22 recto medbio01 NAN.10.*

The third line of quadrivial tradition can be found in Martianus Capella whose Marriage of Philology and Mercury, places music as the highest of the seven liberal arts, the culmination of his entire work. As Michael Masi has observed, this ordering can be found in many visual depictions of the quadrivium, including most famously, the Incarnation Portal at Chartres Cathedral, where arithmetic is paired with geometry as a mathematical study and music with astronomy as a study in harmony. While the complete reasons for this preference are too numerous to identify in a blog, there is a certain kind of Pythagorean logic even here. Music, for Pythagoras and his followers, was thought to be the best evidence for number being at the foundation of the universe. Even the movement of the stars and planets were considered to be one example of many kinds of music in the universe.

Charles Nègre (French, 1820 – 1880), photographer [Chartres Cathedral, Royal Portal (The Incarnation Portal), South Lateral Doorway], 1857. HeliogravureImage: 59.8 × 45.3 cm (23 9/16 × 17 13/16 in.), Sheet: 71.6 × 55.1 cm (28 3/16 × 21 11/16 in.) The J. Paul Getty Museum, Los Angeles, 84.XM.692.4

The stakes for getting the order of the quadrivium right in the Middle Ages may not have risen to the level of murder (although that might make a nice monastic murder mystery written by Umberto Eco, Murder Most Irrational….). And yet, three sources for the quadrivial tradition in the Middle Ages did present the idea that the order of the mathematical arts reflects the most fundamental nature of the universe itself. Furthermore, this fundamental order of the universe has implications for the order of education in the mathematical arts. These stakes, the metaphysical order of the universe and of education, would still have been considered pretty high for most thinkers throughout the Middle Ages.

Lesley-Anne Dyer Williams is a Professor for Memoria College’s Masters of Arts in Great Books program and graduated with her doctorate from the University of Notre Dame’s Medieval Institute in 2012. She was also the founding director Liberal Arts Guild at LeTourneau University. Her research focuses upon twelfth-century Platonism and poetry, especially Thierry of Chartres and Bernard Silvestris.

Lesley-Anne Dyer Williams
Public Humanities Postdoctoral Fellow
Medieval Institute
University of Notre Dame

Further Reading:

Albertson, David. Mathematical Theologies: Nicholas of Cusa and the Legacy of Thierry of Chartres. Oxford University Press, 2014. https://doi.org/10.1093/acprof:oso/9780199989737.001.0001.

Boethius. Boethian Number Theory: A Translation of the “De Institutione Arithmetica” with Introduction and Notes. Translated by Michael Masi. Studies in Classical Antiquity; v. 6. Amsterdam: Rodopi, 1983.

Boethius. The Consolation of Philosophy. Translated by Victor Watts. London: Penguin, 1999.

Burton, David M. The History of Mathematics: An Introduction. Dubuque, Iowa: Wm. C. Brown Publishers, 1988.

Caiazzo, Irene. “Teaching the Quadrivium in the Twelfth-Century Schools.” In A Companion to Twelfth-Century Schools, edited by Cédric Giraud, translated by Ignacio Duran, 88:180–202. Brill’s Companions to the Christian Tradition. Brill, 2019. https://doi.org/10.1163/9789004410138_010.

Calcidius. On Plato’s Timaeus. Dumbarton Oaks Medieval Library 41. Cambridge, Massachusetts; London, England: Harvard University Press, 2016.

Chenu, M. D. Nature, Man, and Society in the Twelfth Century: Essays on New Theological Perspectives in the Latin West. Chicago and London: University of Chicago Press, 1957.

Eco, Umberto. The Name of The Rose. Reprint edition. Boston: HarperVia, 2014.

Evans, Gillian R. “The Influence of Quadrivium Studies in the Eleventh- and Twelfth-Century Schools.” Journal of Medieval History 1, no. 2 (July 1975): 151–64.

Fassler, Margot E. The Virgin of Chartres: Making History through Liturgy and the Arts. Yale University Press, 2010.

Fournier, Michael. “Boethius and the Consolation of the Quadrivium.” Medievalia et Humanistica, no. 34 (2008): 1–21.

Gersh, Stephen. Middle Platonism and Neoplatonism: The Latin Tradition. 2 vols. Notre Dame: University of Notre Dame Press, 1986.

Martianus Capella. Martianus Capella and the Seven Liberal Arts. Translated by William Harris Stahl, Richard Johnson, and E.L. Burge. Vol. II: The Marriage of Philology and Mercury. 2 vols. Records of Western Civilization 84. Columbia University Press, 1992.

Masi, Michael. “Boethius and the Iconography of the Liberal Arts.” Latomus 33, no. 1 (January 1, 1974): 57–75.

Nicholas of Cusa. Nicholas of Cusa on Learned Ignorance: A Translation and an Appraisal of De Docta Ignorantia. Edited by Jasper Hopkins. Minneapolis: The Arthur Banning Press, 1985.

Oosterhoff, Richard. Making Mathematical Culture: University and Print in the Circle of Lefèvre d’Étaples. Oxford-Warburg Studies. Oxford: University Press, 2018. https://doi.org/10.1093/oso/9780198823520.001.0001.

Reydam-Schils, Gretchen. “Meta-Discourse: Plato’s Timaeus According to Calcidius.” Phronesis 52 (2007): 301–27.

Somfai, Anna. “Calcidius’ Commentary on Plato’s Timaeus and Its Place in the Commentary Tradition: The Concept of Analogia in Text and Diagrams.” Bulletin of the Institute of Classical Studies 47, no. Supplement_83_Part_1 (January 1, 2004): 203–20. https://doi.org/10.1111/j.2041-5370.2004.tb02303.x.

Somfai, Anna. “The Eleventh-Century Shift in the Reception of Plato’s Timaeus and Calcidius’ Commentary.” Journal of the Warburg and Courtauld Institutes 65 (2002): 1–21.

Stahl, William H. “The Quadrivium of Martianus Capella: Its Place in the Intellectual History of Western Europe.” In Arts libéraux et philosophie au moyen âge, 959–67. Actes du IVe Congrès internationl de philosophie médiévale. Montreal Paris, 1969.

Stahl, William Harris, Richard Johnson, and E.L. Burge. Martianus Capella and the Seven Liberal Arts. Vol. I: The Quadrivium of Martianus Capella. 2 vols. Records of Civilization, Sources and Studies 84. New York: Columbia University Press, 1971.