A Medieval Rarity: Heaven, Jesus & Geometry, Euclid & the Phaenomena in 13th Century England

An apparently unique commentary of legendary rarity, with no copy of a Euclid manuscript in Latin translation appearing in nearly half a century and the only one we have found with reference to the Phaenomena.

Bringing medieval Europe closer to modern scientific reasoning, this manuscript leaf is at the centre of European intellectual efforts to meld ancient Greek, showing one scholar’s application, likely of Euclid’s Phaenomena (dealing with the circles of the celestial sphere and the implications for observers on earth), to Christ’s humanity and the geometrical shape of Heaven.

Euclid, an ancient Greek philosopher and thinker who lived from approximately 325 – 270 BC, is widely acknowledged for his contributions to mathematics as “the father of geometry,” through his seminal work Elements (Στοιχεῖα), as well as Phaenomena (φαινομενα), in which he examines the geometry of the celestial sphere.

For a while lost to the Medieval West, Euclid’s works were reintroduced to European intellectuals through translation from Arabic into Latin. In the 12th century, due to the Crusades, there was a spike in such translation activity of the Greek philosophers. This new access point gives way in the thirteenth century to new commentaries and thinking through these philosophies.

The ability to read Ancient Greek had been lost to the West, except for in Ireland where it was retained by the learnéd monks. During the nascence of scholasticism, there was a ‘rediscovery’ of the Ancient Greek texts, chiefly the works of Aristotle, with interest in Galen and Euclid as well. The Reconquista of Spain and the Crusades in the 12th century allowed an easier transfer of knowledge between the thinkers (and translators) of the Jewish, Christian, and Arab world, propelling translations of these Greek philosophers into Latin, and taking medieval Europe’s hand and guiding its scholars towards modern thinking, deductive reasoning, and science.

During this period, Euclid and Ptolemy in particular were twin columns of the great Greek scientific learning transmitted to Northern Europe and embedded in medieval education. The knowledge of Euclid’s works remained fragmentary, likely based on the translation of Boethius (477 – 524 AD); however, during the 12th Century Renaissance, an explosive stretch of interest in literature, arts, science, and philosophy and the recovery of Greek works via Arabic translations, Euclid was brought even more to the fore as his works were translated and established in the curriculum as universities began to form in Italy, Spain, France, and England. The translation of Euclid’s Elements from Arabic into Latin by Adelard of Bath (c. 1080-1142/1152?) stands as the oldest surviving copy (now housed in the British Library). Through his translations, Adelard introduced Western Europe to Greek and Arabic works on astrology, astronomy, philosophy, alchemy, mathematics, and the Arabic numeral system. He left England to travel to France, Italy, as well as Greece, the Middle East, and Sicily; upon returning to the West, he promoted the new philosophies he had learned.

The Italian Campanus of Novara (1220-1296), whose compilation of Euclid was penned around 1260 and whose compilation of Euclid was printed in 1482, which became the standard text book until the 16th century, likely used Adelard’s translation of Elements.

The attempt to reconcile the ‘pagan’ philosophy of the Classical world with Christian theology began during the Carolingian period (beginning in the year 800 with the crowning of Charlemagne). Suddenly, with the arrival of this ancient thought, logic was being applied to theology and the big questions of the day revolved around using math and science to prove the existence of God. Rather than repeating theology and the Church Father’s positions on the nature of God and Heaven, scholars like Peter Abelard began to put forward new ideas about the Divine and testing them using Aristotelian logic and Euclidian geometry. This sort of thinking lead to a schism between the traditional monastic and cathedral schools and the new style of education: the university.

Students returning to England from their study at the University of Paris shortly after its foundation in 1150 began to bolster the teaching activity already present in Oxford. Thinkers from around England and the Continent gathered and by 1248 the university in Oxford was granted a royal charter and the way was paved for going towards a scientific world.

The scholars in Oxford were the renegades of their time, trying to marry theology with philosophy and trying to reconcile math and science to prove God. Any affiliation with Oxford and its scholars in this early era is a remarkable rarity.

Further evidence of the strength of Oxford’s role during this period and the enduring impact of Adelard’s can be found among surviving manuscripts. The most important of commentaries on Euclid are found in Oxford, Balliol College 257 (the only complete version of this commentary), Vienna, MS 5304; Paris Bibliothèque national MS Lat. 7292; Vatican Regin. lat. 1268, fol.1-69r; Bonn, MS S 73, and Campanus’ reworking of Elements, which includes contemporary material.

This leaf does not come from any of the known commentaries on Euclid’s works, and may well be the last surviving record of this commentary written by a scholar situated in the middle of this hotbed of innovation and bubbling modernity.

The subject matter represented by the text and illustrations seems to respond to the themes of Phaenomena, which treats circles, spheres, and circumferences of Heaven and presents a diagram using the astrological symbols, on to which our scholar has mapped the Virgin Mary on to the space of Virgo.

The manuscript

Two fragments of the same leaf with unique commentary illustrations on Heavenly geometry citing Euclid.

England, mid-13th c., [Full document: 292×233 mm; Textual area: 254×158 mm], 5 lines in two sections (recto), 13 lines in one section (verso). Long lines in Latin written in black ink in an English secretarial hand between ruling lines laid out for text and image. Three large illustrations of Christ, Virgin Mary, and angels in pen. Three pilcrows open the sections of text. Leaf trimmed by Early Modern book binder and used in later binding.

The product of a scholar’s work marry theology and geometry, and responding with his notes and illustrations; it is not a known text and it is likely a bespoke product for the scholar himself.

The handwriting is typical of England in the mid-thirteenth century, with a looped letter D, and a fork on top of the ascenders of the letters L, H, and T. A catch-all abbreviation of a thick line, suspended over a truncated word was used in English charters, written in the same quickly executed secretarial hand. English manuscripts of this early day are much less common in those of France or other nations on the continent, making this quite a treasure.

The text which remains shows the scholar’s organization and his reckoning with theology, geometry, and the human and divine condition. Our text begins with section two (secundo), which treats the body of Christ comparing the stiff, immovability of his righteousness to the limbs of statue of marble. Christ blessing the Virgin Mary is depicted immediately below this text in a mirrored image, meant to render temporal change (similar to narrative style of panels in a comic book today). Christ, haloed and holding a TO map (a stylistic representation of the three parts of the earth, delineated by the T, housed in the sphere of the globe, the O), holds out his blessing to the Virgin, flanked by an angel and a saint.

The next section— numbered as the fifth (quinto)— discusses Christ’s humanity and the circles and their circumference surrounding him, illustrated immediately below again. In this design, we see Christ seated in the centre of several concentric circles, which are ornamented by circles housing angels and tabled as the place of the angels (locus angelorum); the Virgin, uncircled, sits to the reader’s left of Jesus, with her hand extended towards his blessing. The scholar has instructed the reader to refer to the illustration to clarify his words (sicut hic uides– as you see here).

The verso side of the folio begins, “in the sixth way” (sexto modo), and launches into a geometric understanding of heaven, trying to understand the circumference (…sed in aliquot loco circunfernecie predicti circuli… — but in some place on the circumference of the previously mentioned circle…). From this heavenly sphere “life could be seen by all” (vita ab omnibus videre), and here the scholar defers to the authority of Euclid himself to lend auctoritas to his understanding of the extremity of the diameter in the concave [in exterminate diametri in concavo] of this circumference of Heaven. Another diagram of the angelic circles representing the circumference of the Heavenly Spheres follows.

Note on rarity

Not only is the present text apparently unique, but the text it is glossing is of legendary rarity. Any text by Euclid in manuscript is exceptionally rare on the market, with no copy of a Western manuscript in Latin translation appearing since the Elementa offered in Sotheby’s on 2 May 1979 (lot 1086 in the Honeyman sale), the single short text in a compendium offered in the same sale (as lot 1085, and now in the Getty Museum) and the palimpsest booklet containing the Elementa offered last by H.P. Kraus in 1980 (his cat. 155, no. 5). However, the identification of the text referred to here as the Phaenomena sets this fragment quite apart. The vast Schoenberg database lists no copy of that text or a commentary of it on the market since that sold by H.P. Kraus in 1970 to the Beinecke Library in Yale, and that a Renaissance copy of the mid-sixteenth century. By way of comparison, Quaritch have not offered one since 1938, Maggs not since 1921, and none has appeared in Christie’s since 1898. Thus, in its reference to the Phaenomena here, this fragment would appear to be the sole one of its kind.

Note on Binding

During the Middle Ages, leaves of manuscripts were reused by binders to re-enforce new bindings. This system of recycling carried on as printed books slowly transitioned out manuscripts and our leaf here is a product of that tradition and is likely the reason it survived when the rest may have perished. In the Early Modern period, a binder found they needed to strengthen the spine of a book they were preparing, so this 13th century scholar’s work on the geometry of Heaven and the humanity and divinity of Christ was cut into this crenelated pattern to wrap around the sewing stations (the distinguished looking bumps on the spine of a leather-bound book). The leaf was bound in with another leaf of the same manuscript, and over the centuries that this work was hidden away in a binding, ink from the other leaf bled onto this leaf, leaving a backwards and upside-down imprint of that text.

See also:

Berggren, J.L. and R.S.D. Thomas, Euclid’s Phaenomena: A Translation and Study of a Hellenistic Treatise in Spherical Astronomy, History of Mathematics Sources. Vol. 29. American Mathematical Society, 1996.

Dekker, Elly. Illustrating the Phaenomena: Celestial Cartography in Antiquity and the Middle Ages. Oxford UP, 2012.

Folkert, Menso, “Euclid in Medieval Europe,” Quesito de rerum natura, 1989.

Heath, T.L. trans. Propositions from Euclid’s Element’s of Geometry, Book III.

Murdoch, John E. “Euclides Graeco-Latinus: A Hitherto Unknown Medieval Latin Translation of the Elements Made Directly from the Greek,” Harvard Studies in Classical Philology, Harvard Studies in Classical Philology 1967, Vol. 71 (1967), pp. 249-302