# Theon of Alexandria

**Theon of Alexandria** (/ˌθiːən, ^{[1]} scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's *Elements* and wrote commentaries on works by Euclid and Ptolemy. His daughter Hypatia also won fame as a mathematician.

## Contents

## Life

Little is known about the life of Theon. He made predictions and observances of solar and lunar eclipses in 364 which show he was active at that time, and he is said to have lived during the reign of Theodosius I (379–395).^{[2]} The biographical tradition of the tenth century Byzantine *Suda* defines Theon as "the man from the Mouseion";^{[3]} however, both the Library of Alexandria and the original Mouseion were probably destroyed by the fourth century, although there may have been a new Mouseion established on a different site,^{[4]} perhaps at the Serapeum of Alexandria. Theon was the father of the mathematician Hypatia who was killed by a Christian mob in 415 during a period of religious and sectarian conflict.^{[5]} Theon dedicated his commentary on the *Almagest* to a boy named Epiphanius, who may have been his son.^{[6]} Also, in his commentary on the *Almagest* he states that his daughter Hypatia contributed to Book III of the *Almagest* stating "the edition having been prepared by the philosopher, my daughter Hypatia."^{[7]}

A lunar crater, Theon Junior, now bears Theon's name.

## Works

### Edited works

It is known that Theon edited the *Elements* of Euclid. He may also have edited some other works by Euclid and Ptolemy, although here the evidence is less certain. The editions ascribed to Theon are:

*Euclid's Elements*. Theon's edition of the*Elements*was the only known version until Francois Peyrard discovered an older copy of the*Elements*in the Vatican Library in 1808.^{[8]}Comparison of the two versions show that Theon's edition attempts to remove difficulties that might be felt by learners in studying the text.^{[9]}Hence he amplified Euclid's text whenever he thought that an argument was too brief; attempted to standardise the way that Euclid wrote; and he corrected mistakes in the text, although occasionally he introduced his own errors.^{[2]}Thomas Little Heath notes on Theon's edits include, "remarkably close approximations (stated in sexagesimal fractions)".^{[10]}- Ptolemy's
*Handy Tables*. A collection of astronomical tables originally compiled by Ptolemy.^{[11]}It has often been claimed in modern times that Theon edited this text.^{[12]}However, none of the surviving manuscripts mention Theon,^{[13]}and the evidence suggests that the surviving tables must be very similar to the tables Ptolemy provided.^{[11]}^{[12]}It has, however, been thought possible that his daughter Hypatia edited (or verified) the*Handy Tables*, since the*Suda*refers to her work on the "Astronomical Canon".^{[13]} - Euclid's
*Optics*. Euclid's work on optics survives in two versions, and it has been argued that one version may be an edition by Theon.^{[14]}

### Commentaries

Of his commentaries, those which are extant are:

*Commentary on the Data*of Euclid. This work is written at a relatively advanced level as Theon tends to shorten Euclid's proofs rather than amplify them.^{[2]}*Commentary on the Optics*of Euclid. This elementary-level work is believed to consist of lecture notes compiled by a student of Theon.^{[2]}*Commentary on the Almagest*. Originally a commentary on all thirteen books of Ptolemy's*Almagest*, but now missing book 11 and most of book 5. The commentary is a reworking of Theon's own lecture notes, and is useful chiefly for including information from lost works by writers such as Pappus.^{[1]}It is also useful for Theon's account of the Greek method of operating with the sexagesimal system as it was applied to calculations.^{[2]}*Great Commentary*on Ptolemy's*Handy Tables*. This work partially survives. It originally consisted of 5 books, of which books 1–3 and the beginning of book 4 are extant. It describes how to use Ptolemy's tables and gives details on the reasoning behind the calculations.^{[1]}*Little Commentary*on Ptolemy's*Handy Tables*. This work survives complete. It consists of one book and is intended as a primer for students.^{[1]}In this work Theon mentions that certain (unnamed) ancient astrologers believed that the precession of the equinoxes, rather than being a steady unending motion, instead reverses direction every 640 years, and that the last reversal had been in 158 BC.^{[15]}Theon describes but did not endorse this theory. This idea inspired Thābit ibn Qurra in the 9th century to create the theory of trepidation to explain a variation which he (incorrectly) believed was affecting the rate of precession.^{[15]}*Commentary on Aratus*. Some extant*scholia*on the*Phaenomena*of Aratus are attributed doubtfully to Theon.^{[6]}

### Original works

*Treatise on the Astrolabe*. Both the*Suda*and Arabic sources attribute to Theon a work on the astrolabe. This work has not survived, but it may have been the first ever treatise on the astrolabe, and it was important in transmitting Greek knowledge on this instrument to later ages. The extant treatises on the astrolabe by the 6th century Greek scholar John Philoponus and by the 7th century Syriac scholar Severus Sebokht draw heavily on Theon's work.^{[16]}*Catoptrics*. The authorship of this treatise, ascribed to Euclid, is disputed.^{[17]}It has been argued that Theon wrote or compiled it.^{[2]}The*Catoptrics*concerns the reflection of light and the formation of images by mirrors.^{[17]}

Among Theon's lost works, the *Suda* mentions *On Signs and Observation of Birds and the Sound of Crows*; *On the Rising of the Dog[-Star]*; and *On the Inundation of the Nile*.^{[3]}

## See also

## References

- ^
^{a}^{b}^{c}^{d}John M. McMahon, "Theon of Alexandria" entry in Virginia Trimble, Thomas Williams, Katherine Bracher (2007),*Biographical Encyclopedia of Astronomers*, pages 1133-4. Springer - ^
^{a}^{b}^{c}^{d}^{e}^{f}O'Connor, John J.; Robertson, Edmund F., "Theon of Alexandria",*MacTutor History of Mathematics archive*, University of St Andrews. - ^
^{a}^{b}Suda, Theon θ205 **^**Edward Jay Watts, (2008),*City and School in Late Antique Athens and Alexandria*, page 150. University of California Press**^**Edward Jay Watts, (2006),*City and School in Late Antique Athens and Alexandria*. "Hypatia and pagan philosophical culture in the later fourth century", pages 197–198. University of California Press- ^
^{a}^{b}Smith, William;*Dictionary of Greek and Roman Biography and Mythology*, London (1873). "Theon" **^**Rome, Adolphe (1931–1943).*Commentaires de Pappus et de Théon d'Alexandrie sur l'Almageste. Tome III*. Italy: Vatican. p. 807.**^**Frank J. Swetz, (1994),*Learning Activities from the History of Mathematics*, page 18**^**T L Heath, (1921),*A History of Greek Mathematics*, Vol. 1, page 57. Oxford**^**Thomas Little Heath (1921).*A history of Greek mathematics*. Oxford, The Clarendon Press.- ^
^{a}^{b}James Evans, (1998),*The History and Practice of Ancient Astronomy*, page 240 and footnote 35. Oxford University Press. ISBN 0-19-509539-1 - ^
^{a}^{b}Anne Tihon, "Theon of Alexandria and Ptolemy's*Handy Tables*" in Noel M. Swerdlow, (1999),*Ancient Astronomy and Celestial Divination*, page 359. MIT Press. ISBN 0262194228 - ^
^{a}^{b}Alan Cameron, Jacqueline Long, (1993),*Barbarians and Politics at the Court of Arcadius*, page 45. University of California Press. ISBN 0520065506 **^**A. Mark Smith, (1999),*Ptolemy and the Foundations of Ancient Mathematical Optics*, page 16. American Philosophical Society. ISBN 0871698935- ^
^{a}^{b}James Evans, (1998),*The History and Practice of Ancient Astronomy*, page 276. Oxford University Press. ISBN 0-19-509539-1 **^**James Evans, (1998),*The History and Practice of Ancient Astronomy*, page 156. Oxford University Press. ISBN 0-19-509539-1- ^
^{a}^{b}James Evans, (1998),*The History and Practice of Ancient Astronomy*, page 90. Oxford University Press. ISBN 0-19-509539-1

## Further reading

- Tihon, Anne, "Theon of Alexandria and Ptolemy's Handy Tables", in
*Ancient Astronomy and Celestial Divination*. Dibner Institute studies in the history of science and technology. Edited by N.M. Swerdlow. Cambridge, MA: MIT Press, 1999, p. 357. - A Rome,
*Commentaires de Pappus et de Théon d'Alexandrie sur l'Almageste Tome III*. Théon d'Alexandrie (Rome, 1943). - A Tihon (ed.),
*Le 'Petit Commentaire' de Théon d'Alexandrie aux 'Tables faciles' de Ptolémée*(Vatican City, 1978). - A Tihon (ed.),
*Le 'Grand commentaire' de Théon d'Alexandrie aux 'Tables faciles' de Ptolémée Livre I*(Vatican City, 1985). - A Tihon (ed.),
*Le 'Grand commentaire' de Théon d'Alexandrie aux 'Tables faciles' de Ptolémée Livre II, III*(Vatican City, 1991).

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