Pachymeres, Georges (or George)

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(b. Nicaea, 1242; d. 1310), history, mathematics).

Of a Constantinopolitan family, Pachymeres was born in 1242 at Nicaea, where the Byzantine court and government had taken refuge under the Latin occupation following on the capture of Constantinople under the Fourth Crusade in 1204. At the time of the restoration in 1261, he returned to Constantinople, where higher education would soon be restored under the direction of George Acropolites. Georges Pachymeres followed his courses and became deacon. He then followed a brilliant career in the hierarchy of the church and palace. He assumed the high offices of Protekdikos (director of the inspectors of churches and monasteries) and of Dikaiophylax (guardian of the seals), and was Didascalos tôn apostolôn (professor of New Testament exegesis) at the Patriarchal School. One supposes that he was responsible for teaching in many fields, such as rhetoric, philosophy, the sciences. His History stopped in 1307. His death occurred around 1310.

Historical Works Pachymeres’s output can be divided into two parts. On the one hand, there are his Historical Accounts in thirteen books, which retraced the reign of Michael Palaeologus (Michael VIII, 1259–1282) and a part of the reign of Andronicus III, from 1282 to 1307. On the other hand, he composed several works devoted to his teaching, both religious and secular: scholia on the Psalms, a paraphrase of the works of Denys the Areopagite, a summary of the Logic of Aristotle, exercises in rhetoric, and a Quadrivium of the sciences. To this were to be added a Treatise on the Holy Spirit devoted to affirming the orthodoxy of doctrine after the Union of the Churches after the Council of Lyon (1274), letters to the patriarch of Alexandria, Athanasius II, and several short poems in a prologue to these works. His handwriting can be identified in several manuscripts, namely those of philosophical texts, and the autograph of his Quadrivium is preserved in the Angelicus gr. 38 (C.3.7).

Quadrivium Treatise The Quadrivium (or Treatise of the Four Sciences) was intended for his teaching of the sciences at the Patriarchal School, restored after the reconquest of Constantinople in 1261. The Patriarchal School was the foundation for advance teaching controlled by the church, and patronized by the emperor, intended for the training of both clerics and seculars. It has been said that the division of scientific teaching into four sciences was due to Western influence, but that is not at all the case. This classification, already mentioned by Nicomachus of Gerasa (second century CE), is regularly found in Byzantine teaching. For example, there exists an anonymous quadrivium, written around 1007 or 1008.

The Quadrivium of Georges Pachymeres began with a short poem presenting the author and his treatise, and with a prologue to the glory of science, impregnated with Platonism, where the author commented on a sentence of Favorinus of Arles (second century CE): science is natural to the human mind and brings it pleasure. Next he defined science, its aims, and divisions drawing heavily on Nicomachus: Arithmetic and Harmony are sciences of the discontinous (to diôrismenon); Geometry and Astronomy, sciences of the continuous (to synekhes). The first of sciences is therefore Arithmetic, to which is devoted Book 1. The Arithmetic of Pachymeres draws mainly on Nicomachus, Diophantus, who was paraphrased in many passages, and Euclid (Elements 7–9). The second book was devoted to Harmony (or Music), and consisted of a compilation from different authors, such as Nicomachus, Ptolemy, and Aristoxenus. The third book, the Geometry(and Stereometry) was based on Euclid, as expected. Finally the fourth book was devoted to Astronomy. This fourth book, very ill-assorted, began with a long account of arithmetic, devoted to sexagesimal operations and to the multiplication and division of ratios. Then followed long explanations of general astronomy (celestial sphere, shape of Earth, dimensions of Earth, the principal circle of the celestial sphere, the Sun, the Moon, the planets, phases of the Moon, eclipses, etc.). They are followed by a description of the constellations, mainly their simultaneous risings and settings. The author returned once again to operations in the sexagesimal system and to the calculation of the table of chords in the Almagest.

Pachymeres gave, in passing, some notions of astrological theories even though he condemns the astrologers who link the destinies of men to such configurations. In his Astronomy, Plato, Aristotle, Archimedes, Hipparchus, Aratus, Theon of Smyrna, Theon of Alexandria, Cleomedes, and Ptolemy were heavily drawn upon. However, he nowhere put Ptolemy’s astronomy into practice to calculate the positions of Sun, Moon, or planets, the syzygies, or eclipses. He never departed from parameters given by Ptolemy or his predecessors, but one does find a brief notice (chapter 21) of the rate of precession of 1o per sixty-six years, in contrast to Ptolemy’s value, 1o per 100 years—but this passage may not be authentic.

The Quadrivium of Georges Pachymeres has been published, but not translated or commentated. According to Paul Tannery, who had prepared its edition, the work of Pachymeres is only a compilation of classical works, but it shows precisely how the Byzantines used the classical heritage for the teaching of mathematics (citation from Stephanou, Quadrivium, p. 6, note 2). It is also astonishing that the work met with so little success in its time— most of the manuscripts indeed are from the sixteenth century. In reality, a number of Byzantine scholars, such as Theodore Metochites or Theodore Meliteniotes, made full use of it, even plagiarized it, for arithmetic. But in line with the custom of Byzantines, who cited only the ancients, and never their contemporaries, the latter never mentioned his name. One does not know the relation between the Harmonic of Georges Pachymeres and the voluminous treatise on the same subject by Manuel Bryennius, his contemporary, but it is likely that the latter also used it.

If he brought nothing new, Pachymeres proved to have a vast erudition, and in this writer’s opinion, his influence on his contemporaries and successors was important. This is a major source regarding the language and practice of arithmetic of Byzantine scholars. One must not forget that it was a teaching manual and that the length of certain explanations was doubtless in proportion to the difficulties met by the students!



Tannery, Paul ed. Quadrivium de Georges Pachymère. Texte révisé et établi par le R. P. E. Stephanou, Studi e Testi94, Città del Vaticano, 1940.


Lampakis, Stylianos. Georgios Pachymeris, Protekdikos and Dikaiophylax: An Introductory Essay. Monograph 5. Athens: National Hellenic Research Foundation, Institute for Byzantine Research, 2004.

Anne Tihon