Leo the Mathematician

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Leo the Mathematician

also known as Leo the Philospher

(b. Constantinople[?], ca. 790; d. Constantinople[?], after 869)

mathematics, astronomy.

Leo, who is often confused both by medieval and modern scholars with Emperor Leo VI the Wise (886-912) and with the patrician Leo Choerosphactes (b. ca. 845-850’ d. after 919), belonged to a prominent Byzantine family, as is indicated by the fact that his cousin, John VII Morocharzianus the Grammarian, had been patriarch (837-843). The rather conflicting sources attest that Leo obtained a rudimentary education in rhetoric, philosophy, and arithmetic from a scholar on the island of Andros but that his more advanced knowledge of these subjects, and of geometry, astronomy, and astrology was gained through his own researches among the manuscripts that he found in monastic libraries.

In the 820’s Leo began to give private instruction at Constantinople; one of the students who had read Euclid’s Elements with him was captured by the Arab army in 830 or 831, and his enthusiastic report of his master’s accomplishments caused the caliph alMa’mûn (813-833) to invite Leo to Baghdad. The Byzantine emperor Theophilus (829-842), learning of this invitation, responded by charging Leo with the task of providing public education at the Church of the Forty Martyrs in Constantinople. While he was in Theophilus’ service, Leo supervised the construction of a series of fire-signal stations between Loulon, located north of Tarsus and close to the Arab border, and the capital. A message could be transmitted over these stations in less than an hour; by establishing theoretically synchronized chronometers at either end, Leo was able to provide for the transmission of twelve different messages depending on the hour at which the first fire was lit.

From the spring of 840 until the spring of 843 Leo served as archbishop of Thessalonica, a post he received presumably because of his political influence rather than his holiness. He was promptly deposed when the iconodule Methodius I succeeded his iconoclast cousin John as patriarch in 843. Leo apparently returned to private teaching in Constantinople until about 855, when he was appointed head of the “Philosophical School” founded by Caesar Bardas (d.866) in the Magnaura Palace, where arithmetic, geometry, and astronomy, as well as grammar and philosophy, were taught. The last notice of him is in a chronicle recording an astrological prediction that he made in Constantinople in 869.

From ninth-century manuscripts Leo is known to have been involved in the process of transcribing texts written in majuscule script into minuscule; this activity may well have included some editorial work, although its nature and extent are uncertain. In any case, he was connected with the transcription of at least some of the Tetralogies of Plato’s works, of the larger part of the corpus of Archimedes’ works, and of Ptolemy’s Almagest; it is likely that he was also concerned with the collection of mathematical and astronomical writings known as the Little Astronomy. Arethas’ copy of Euclid’s Elements contains, at VI.5, a “school note” by Leo on the addition and subtraction of fractions, in which he uses the Greek alphabetical symbols for numbers as the denominators. Finally, from some of his poems preserved in thePalatine Anthology, it is known that he possessed copies of the Mechanics of Cyrinus and Marcellus, theConics of Apollonius, the Introduction of the astrologer Paul of Alexandria, the romance of Achilles Tatius, as well as works of Theon on astronomy and Proclus on geometry.

His own surving scientific works are astrological. His “Scholia on the Hourly Motion,” which claims to correct an error in an example given in Porphyrius’ commentary on Ptolemy’s Apotelesmatics, in fact refers to one in Pancharius’ commentary on Ptolemy III 11, 8-11, as cited by Hephaestio of Thebes, ApotelesmaticsII 11, 39-40 (Pingree, p. 124); his solution is absurdly taken from an entirely different example in the anonymous commentary on Ptolemy III 11, 10 (Wolf, p.114). This proves that his technical mastery of astrology was very shaky indeed. His treatise “On the Solar Eclipse in the Royal Triplicity” is lifted from Lydus’On Omens 9 (Wachsmuth, pp. 19-21) and from Hephaestio I 21, 12-32 (Pingree, pp. 54-62). The short works on political astrology attributed to him in some manuscripts seem to be derived from the eleventh-century Byzantine translation of an Arabic astrological compendium of one Ahmad, in which they are II 123-125. It is at present impossible to judge the authenticity of the other brief tracts on divination by thunder, earthquakes, the lords of the weekdays, and the gospels and psalms that are found in Byzantine manuscripts, but skepticism seems to be called for.

It remains, then, that Leo was important for his role in the transmission of Greek scientific literature and in the restoration of Byzantine learning after a long period of decline. He made few, if any, original contributions to science.


I. Original Works. 1. A homily delivered at Thessalonica on 25 March 842, is in V. Laurent, ed., Mélanges Eugène Tisserant,II (Vatican City, 1964), 281-302.

2. “Scholia on the Hourly Motion,” F. Cumont, ed., in Catalogus codicum astrologorum graecorum (hereafter cited as CCAG), I (Brussels, 1898), p. 139.

3. “On the Solar Eclipse in the Royal Triplicity,” F.C. Hertlein, ed., in Hermes, 8 (1874), 173-176; cf. F. Boll in CCAG, VII (Brussels, 1908), 150-151.

4. Twelve poems in the Palatine Anthology (IX 200-203, 214, 361, and 578-581; XV 12; and XVI [Planudean Anthology] 387 C). IX 1-358 was edited by P. Waltz (Paris, 1957), and XV by F. Buffière (Paris, 1970); the rest may be found in the ed. by F. Dubner, 2 vols. (Paris, 1864-1877).

5. A group of poems was attributed to Leo and edited by J. F. Boissonade, in Anecdota graeca, II (Paris, 1830), 469 ff.; the first, on old age, may indeed be his.

The following are of doubtful authenticity:

6-7. “How to Know the Lengths of the Reigns of Kings and Rulers, and What Happens in Their Reigns” and “On the Appearance of the Ruler,” F. Cumont, ed., in CCAG, IV (Brussels, 1903), 92—93; it has been noted previously that these are taken from Ahmad.

8. “Thunder Divination According to the Course of the Moon,” an unpublished treatise found on fols. 1-2 of A 56 sup. in the Ambrosian Library, Milan. The index to CCAG, III (Brussels, 1901), incorrectly ascribes to Leo that text edited by A. Martini and D. Bassi on pp. 25-29.

9. “Divination From the Holy Gospel and Psalter,” on fols. 28v–30 of Laurentianus graecus 86, 14, Florence.

10. “On a Sick Man,” a treatise on medical astrology preserved on fols. 137v–138 of Vaticanus graecus 952.

11. A work on astrological predictions from the lords of the weekdays, accompanied by a “portrait” of Leo, on fols. 284v–285v of codex 3632 of the University Library, Bologna.

12. “Earthquake Omens,” A. Delatte, ed., CCAG, X (Brussels, 1924), 132-135, is attributed to the Emperor Leo (Leo VI the Wise); but the attribution could possibly be a mistake for Leo the Mathematician.

13. “Gnomic Sayings,” M. A. Šangin, ed., in CCAG, XII (Brussels, 1936), 105.

14. A poem edited by P. Matranga, Anecdota graeca, II (Rome, 1850), 559, is sometimes–and probably erroneously–ascribed to Leo; it follows some pieces by Leo’s student Constantine, attacking him for studying pagan science, ibid., 555-559.

II. Secondary Literature. The best source is now P. Lemerle, Le premier humanisme byzantin (Paris, 1971), pp. 148-176 ; Lemerle gives references to almost all the pp. 148-176 ; Lemerle gives references to almost all the earlier literature and is weak only in his discussion of Leo’s astrological tracts.

David Pingree