**Theon of Alexandria** ( /ˌθiːən,-ɒn/ ; Ancient Greek : Θέων ὁ Ἀλεξανδρεύς; c. AD 335 – c. 405) was a Greek ^{ [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.

Little is known about the life of Theon. He made predictions and observations 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 * Suda *, a tenth-century Byzantine encyclopedia, calls Theon a "man of the Mouseion".^{ [3] } However, both the Library of Alexandria and the original Mouseion were destroyed in the first century BC and according to classical historian Edward J. Watts, Theon was probably the head of a school called the "Mouseion", which was named in emulation of the Hellenistic Mouseion that had once included the Library of Alexandria, but which had little other connection to it.^{ [4] } Theon's school was exclusive, highly prestigious, and doctrinally conservative.^{ [4] } Neither Theon nor his daughter Hypatia seems to have had any connections to the militant Iamblichean Neoplatonists who taught in the Serapeum of Alexandria and instead preferred Plotinian Neoplatonism.^{ [4] }

Theon was the father of the mathematician Hypatia, who succeeded him as head of his school^{ [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.

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] }

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] }

*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] }

**Euclid**, sometimes called **Euclid of Alexandria** to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry". He was active in Alexandria during the reign of Ptolemy I. His *Elements* is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics from the time of its publication until the late 19th or early 20th century. In the *Elements*, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigour.

**Hipparchus of Nicaea** was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry but is most famous for his incidental discovery of precession of the equinoxes.

**Claudius Ptolemy** was a mathematician, astronomer, natural philosopher, geographer and astrologer who wrote several scientific treatises, three of which were of importance to later Byzantine, Islamic and Western European science. The first is the astronomical treatise now known as the *Almagest*, although it was originally entitled the *Mathematical Treatise* and then known as *The Great Treatise*. The second is the *Geography*, which is a thorough discussion of the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the *Apotelesmatiká* (Ἀποτελεσματικά) but more commonly known as the *Tetrábiblos* from the Koine Greek (Τετράβιβλος) meaning "Four Books" or by the Latin *Quadripartitum*.

**Hypatia** was a Hellenistic Neoplatonist philosopher, astronomer, and mathematician, who lived in Alexandria, Egypt, then part of the Eastern Roman Empire. She was a prominent thinker of the Neoplatonic school in Alexandria where she taught philosophy and astronomy. Although preceded by Pandrosion, another Alexandrine female mathematician, she is the first female mathematician whose life is reasonably well recorded. Hypatia was renowned in her own lifetime as a great teacher and a wise counselor. She is known to have written a commentary on Diophantus's thirteen-volume *Arithmetica*, which may survive in part, having been interpolated into Diophantus's original text, and another commentary on Apollonius of Perga's treatise on conic sections, which has not survived. Many modern scholars also believe that Hypatia may have edited the surviving text of Ptolemy's *Almagest*, based on the title of her father Theon's commentary on Book III of the *Almagest*.

An **astrolabe** is an ancient astronomical device that equates to a handheld model of the universe. Its various functions also make it an elaborate inclinometer and an analogue calculation device capable of working out several kinds of problems in astronomy. Historically used by astronomers, it is able to measure the altitude above the horizon of a celestial body, day or night; it can be used to identify stars or planets, to determine local latitude given local time, to survey, or to triangulate. It was used in classical antiquity, the Islamic Golden Age, the European Middle Ages and the Age of Discovery for all these purposes.

The * Almagest* is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy. One of the most influential scientific texts of all time, it canonized a geocentric model of the Universe that was accepted for more than 1200 years from its origin in Hellenistic Alexandria, in the medieval Byzantine and Islamic worlds, and in Western Europe through the Middle Ages and early Renaissance until Copernicus. It is also a key source of information about ancient Greek astronomy.

**Timocharis of Alexandria** was a Greek astronomer and philosopher. Likely born in Alexandria, he was a contemporary of Euclid.

**Pappus of Alexandria** was one of the last great Greek mathematicians of antiquity, known for his *Synagoge* (Συναγωγή) or *Collection*, and for Pappus's hexagon theorem in projective geometry. Nothing is known of his life, other than what can be found in his own writings: that he had a son named Hermodorus, and was a teacher in Alexandria.

**Greek mathematics** refers to mathematics texts written during and ideas stemming from the Archaic through the Hellenistic periods, extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by Greek culture and the Greek language. The word "mathematics" itself derives from the Ancient Greek: μάθημα, romanized: *máthēma*Attic Greek: [má.tʰɛː.ma]Koine Greek: [ˈma.θi.ma], meaning "subject of instruction". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is an important difference between Greek mathematics and those of preceding civilizations.

**Theon of Smyrna** was a Greek philosopher and mathematician, whose works were strongly influenced by the Pythagorean school of thought. His surviving *On Mathematics Useful for the Understanding of Plato* is an introductory survey of Greek mathematics.

**Catoptrics** deals with the phenomena of reflected light and image-forming optical systems using mirrors. A catoptric system is also called a *catopter* (*catoptre*).

**Trepidation**, in now-obsolete medieval theories of astronomy, refers to hypothetical oscillation in the precession of the equinoxes. The theory was popular from the 9th to the 16th centuries.

**Greek astronomy** is astronomy written in the Greek language in classical antiquity. Greek astronomy is understood to include the ancient Greek, Hellenistic, Greco-Roman, and Late Antiquity eras. It is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the language of scholarship throughout the Hellenistic world following the conquests of Alexander. This phase of Greek astronomy is also known as **Hellenistic astronomy**, while the pre-Hellenistic phase is known as **Classical Greek astronomy**. During the Hellenistic and Roman periods, much of the Greek and non-Greek astronomers working in the Greek tradition studied at the Musaeum and the Library of Alexandria in Ptolemaic Egypt.

An **equatorium** is an astronomical calculating instrument. It can be used for finding the positions of the Moon, Sun, and planets without calculation, using a geometrical model to represent the position of a given celestial body.

**Egyptian astronomy** begins in prehistoric times, in the Predynastic Period. In the 5th millennium BCE, the stone circles at Nabta Playa may have made use of astronomical alignments. By the time the historical Dynastic Period began in the 3rd millennium BCE, the 365 day period of the Egyptian calendar was already in use, and the observation of stars was important in determining the annual flooding of the Nile.

* Agora* is a 2009 Spanish English-language historical drama film directed by Alejandro Amenábar and written by Amenábar and Mateo Gil. The biopic stars Rachel Weisz as Hypatia, a mathematician, philosopher and astronomer in late 4th-century Roman Egypt, who investigates the flaws of the geocentric Ptolemaic system and the heliocentric model that challenges it. Surrounded by religious turmoil and social unrest, Hypatia struggles to save the knowledge of classical antiquity from destruction. Max Minghella co-stars as Davus, Hypatia's father's slave, and Oscar Isaac as Hypatia's student, and later prefect of Alexandria, Orestes.

**Gerald James Toomer** is a historian of astronomy and mathematics who has written numerous books and papers on ancient Greek and medieval Islamic astronomy. In particular, he translated Ptolemy's *Almagest* into English.

Ptolemy's * Optics* is a work on geometrical optics, dealing with reflection, refraction, and colour.

**Adolphe Rome** was a Belgian classical philologist and science historian who was particularly concerned with the ancient history of astronomy.

**Anne Tihon** is a Belgian historian of science specializing in the history of astronomy, with works on Theon of Alexandria, Byzantine astronomy, and astronomical tables. She is a professor emerita in the Faculty of Philosophy, Arts and Letters of the Université catholique de Louvain.

- 1 2 3 4 John M. McMahon, "Theon of Alexandria" entry in Virginia Trimble, Thomas Williams, Katherine Bracher (2007),
*Biographical Encyclopedia of Astronomers*, pages 1133-4. Springer - 1 2 3 4 5 6 O'Connor, John J.; Robertson, Edmund F., "Theon of Alexandria",
*MacTutor History of Mathematics archive*, University of St Andrews . - 1 2 Suda, Theon θ205
- 1 2 3 Edward Jay Watts, (2008),
*City and School in Late Antique Athens and Alexandria*, page 191-192. 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 - 1 2 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. - 1 2 James Evans, (1998),
*The History and Practice of Ancient Astronomy*, page 240 and footnote 35. Oxford University Press. ISBN 0-19-509539-1 - 1 2 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 - 1 2 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 - 1 2 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 - 1 2 James Evans, (1998),
*The History and Practice of Ancient Astronomy*, page 90. Oxford University Press. ISBN 0-19-509539-1

- 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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