Argyrus, Isaac

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(b. c. 1300 or 1310, Thrace; d. c. 1375)

astronomy, mathematics, theology.

Born in Thrace around 1300 or 1310, Argyrus lived in Constantinople, where he pursued his scientific activity around 1367 to 1373. As a monk he participated in the religious disputes (Hesychasm), writing anti-Palamite tracts, directed especially against John Cantacuzenus (Emperor John VI, r. 1341–1355). The latter wrote a long tract against Argyrus. His scientific work was in astronomy, arithmetic, and geometry. A scholium presents him as a pupil of Nicephorus Gregoras, but his name is never cited by the latter.

Argyrus wrote two treatises on the New Tables, both based on Ptolemy, with the date of origin 1 September 1367, and for the meridian of Byzantium. The former treatise was an adaptation of Ptolemy’s Handy Tables of the Sun and Moon, arranged in periods of twenty-four years and for the Roman (i.e., Julian) calendar. The cycle of twenty-four years was adopted because it allowed the easy insertion of bissextile (leap year) years. No explanation was given for the choice of the initial year, but one may think that it was intended to begin with a leap year (1368). The difference between the meridians of Alexandria and Byzantium was, according to Ptolemy, 4°50'/15° = 18m, that must be subtracted from the time at Alexandria, but Argyrus erred in adding the values corresponding to the 18m.

The second treatise was based on the tables of syzygies in the Almagest, starting with the conjunction of 23 September 1367. The correction of the 18m was correctly applied. These two treatises concern only the Sun and Moon, and were intended especially to facilitate the calculation of syzygies, of importance for finding the date of Easter. At the end of the first treatise, Argyrus declared that he also adapted the tables of the five planets for the period of twenty-four Julian years and Roman months, but these tables were not preserved.

Another of his works is a Treatise on the Date of Easter. This treatise, which begins with an account of the solar and lunar cycles, was composed in 1372 to 1373 and was dedicated to Andronicus Oinaiotes. This account was followed by explanations about the beginning of the year. He then considered the date of Easter and the correction of the traditional calculation. These three texts have sometimes been considered as separate treatises, but the Paschal method was a continuation from the preceding chapters, at least in the manuscript Marcianus gr. 328 (fifteenth century), that included a collection of the scientific works of Argyrus. As for the traditional fixing of the date of Easter, Argyrus mentioned two sources of error, the lunar cycle of nineteen years and the length of the solar year. The inexactness of the nineteen-year cycle was an argument that goes back to Barlaam (c. 1332) and was based on Ptolemy. Ptolemy’s value (3651/4–1/300) was inexact for the length of the solar year. Alluding to the Persian Tables and using his own observation of the summer solstice, Argyros proposed to replace the fraction 1/300 by “a fraction greater than 1/200” (Migne, 1857, p. 19, col. 1312). He found, as a result, that the spring equinox was “before March 15.” He did not cite Barlaam, but referred explicitly to Nicephorus Gregoras who, he said, proposed this reform in the presence of the emperor; in consequence of which, again according to Argyrus, it was decided to apply this reform. This formally contradicts the account of Nicephorus Gregoras himself, who declared that the emperor decided not to apply this reform for fear of troubles in the church.

The astronomical work of Argyrus also included a Treatise on the Astrolabe, based on that of Nicephorus Gregoras and dated 1367 to 1368. He assumed Ptolemy’s value of precession, 1o in 100 years.

A treatise titled Paradosis ton Persikon Kanonon is sometimes attributed to Argyrus, but this treatise was in fact Book Three of the Tribiblos of Theodore Meliteniotes, which was widely diffused in the manuscripts. It is not impossible that Argyrus inserted some alterations, but this matter is unsettled. According to the Jewish scholar Mordecai Comtino, Argyrus and his students criticized the Persian Tables, but that is not evident from the extant work. The manuscripts have contradictory remarks on this matter.

Argyrus is the author of a Treatise on the Square Root, in which he perfected the method of Hero of Alexandria. He developed a method of approximation that he presented as his own, but which is close to that developed by Nicolas Rhabdas (c. 1340). At the end of the treatise he gave a table of roots of 1 to 102, expressed in the sexagesimal system. We also owe to him a Treatise on Geodesy (also called On the Reduction of Triangles), which is probably the same text as the Letter to Colybas of Mitylene on the same subject. This short treatise corrects the crude errors of the land surveyors. The text was followed in many manuscripts by a note, probably due also to Argyrus, on Bryson’s method of the Squaring of the Circle.

A number of astronomical scholia (on Cleomedes, Theon of Alexandria) and also geographical scholia were attributed to Argyrus, as well as an edition of the Harmonics of Ptolemy. Apart from the theological works mentioned above, and his scientific output, he wrote a treatise on poetic meters, and commentaries on Aristotle.

It is difficult to make a judgment of the work of Argyrus. There exists no critical edition of his astronomical work, and in the manuscripts it is not easy to distinguish original work from revisions or later additions. His works were very extensively used by his immediate successors, but they very much confused the manuscript tradition. Conservative, he remained true to the Ptolemaic tradition, even though one finds a mention of the Persians in his Paschal treatise. The only trace of innovation—if it is not indeed an interpolation—is a correction to the length of the tropical year, but this does not appear in his astronomical tables. Argyrus emerges as the perfect Byzantine savant, trained in all the scientific disciplines of the ancients, as well as theology and philology, editing, and commenting the texts in the manuscripts. However, his interventions have not yet been precisely cataloged.


Allard, André. “Le petit traité d’Isaac Argyre sur la racine carrée.” Centaurus 22 (1978): 1–43. Treatise on the square root. Delatte, Armand. Anecdota Atheniensia et alia: Tome II, Textes grecs relatifs à l’histoire des sciences. Paris: Faculté de Philosophie et Lettres, Liège and Librairie E. Droz, 1939.

Lefort, Jacques, René-Claude Bondoux, Jean-Claude Cheynet, et al., with the collaboration of J.-M. Martin. Géométries du fisc byzantin. Paris: Réalités Byzantines, 1991. On geodesy.

Migne, J.-P. Patrologia graeca, t.19, Paris, n.p., 1857: col.

1279–1316. Reproduction of Denys Petau, Uranologion sive systema variorum authorum, Paris, n.p., 1630, pp. 359–383. Easter treatise.

Petau, Denis. Uranologion sive systema variorum authorum.Paris. 1630, pp. 359–383. A reproduction edited by J. Migne. Patrologia graeca t. 19: col. 1279–1316. city1857.

Pingree, David. “The Astrological School of John Abramius.” Dumbarton Oaks Papers25 (1971): 191–215.

Schissel, Otmar. “Die Österrechnung des Nikolaos Artabasdos Rhabdas.”Byzantinisch-Neugriechische Jahbücher 14 (1937–1938): 43–59.

Tihon, Anne. “L’astronomie byzantine à l’aube de la Renaissance

(de 1352 à la fin du XVe siècle).” Byzantion 64 (1996): 244–280.

Anne Tihon