Theon of Alexandria was one of the most eminent mathematicians and astronomers of late antiquity and the father of Hypatia. His edition of Euclid’s Elements was used by mathematicians for over a thousand years after it supplanted all others, including the original. Theon simplified some of Euclid’s proofs and added new proofs of his own.
Beginnings
Theon of Alexandria was born in the first half of the fourth century, most probably around 335 AD in the Greco-Roman city of Alexandria, Egypt. His name is pronounced Thee-on, the ‘Th’ sound as in ‘thank’ rather than in ‘them.’
Like most educated people in the Eastern Mediterranean in late antiquity, Theon was a Greek speaker.
No details of Theon’s parents or education survive. We do not know what he looked like.
Theon’s Mathematics
Theon was head of the Mouseion, an academy that taught Neoplatonist philosophy. Like other intellectuals of his era, Theon seems to have made no outstanding breakthroughs – he was principally a teacher.
The golden days of Eudoxus, Euclid, Aristarchus, Archimedes, Eratosthenes, Appolonius, and Hipparchus were as distant in time from Theon as Fibonacci and Nicolaus Copernicus are from us.
Lifetimes of Selected Greek Scientists and Philosophers after the Golden Age
Theon’s Edition of Euclid’s Elements
Theon wrote a new ‘student edition’ of Euclid’s Elements that became the go-to version for centuries to come. Editions based on Theon’s were the only ones known until an edition predating his was found in the Vatican Library in 1808. Theon’s edition had reigned for over a thousand years.
Theon corrected hundreds of years of scribal errors – all books then were handwritten copies – and simplified Euclid’s original work to assist his students. For example, if he felt any of Euclid’s proofs were too short he inserted extra lines of reasoning to make it easier for his students to follow Euclid’s logic.
By comparing Theon’s copy with the older Vatican edition we see that Theon went as far as replacing some of Euclid’s proofs with his own proofs. Indeed, in a commentary he wrote on Ptolemy’s Almagest, Theon mentions he added a proof to the Elements:
“But that sectors in equal circles are to one another as the angles on which they stand has been proved by me in my edition of the Elements at the end of the sixth book.”
Euclid’s Elements
Euclid’s Elements is a masterpiece, a work of genius whose importance to the intellectual development of our species is difficult to exaggerate. It inspired ancient Greeks, such as Archimedes; Persians, such as Omar Khayyam; and, following the Renaissance, thousands of individual scientists such as Nicolaus Copernicus, Galileo Galilei, Isaac Newton, James Clerk Maxwell, Albert Einstein, and Thomas Gold.
Working in Alexandria, Euclid compiled mathematical proofs from the Pythagoreans, Eudoxus, and other earlier Greek mathematicians, strengthened the logical rigor anywhere it was weak, added his own proofs, and produced a work of stunning intellectual power.
Euclid was not concerned with solving problems of today in mathematics such as how many tiles you need to cover a roof. His goal was to discover universal truths that would work forever in all situations. The only tools he allowed himself were a straight edge and compass.
Starting with a few self-evident principles, such as that all right-angles are equal, Euclid deduced and proved a large number of ever more sophisticated mathematical theorems placing them in the Elements’ 13 books.
The Elements deals with three fields: geometry in two dimensions; number theory; and geometry in three dimensions.
It includes an extraordinarily beautiful proof that there are infinitely many prime numbers.
It also includes the first ever nontrivial mathematical algorithm, perhaps devised by followers of Pythagoras, which Euclid uses to calculate the greatest common divisor of two numbers.
Greek language papyrus – the Oxyrhynchus papyrus – from about 100 AD – one of the oldest known fragments of Euclid’s Elements.
Following Johannes Gutenberg’s introduction of movable type printing in 1450, Euclid’s Elements – first printed in 1482 – is second only to the Bible in the number of editions released.
Theon’s Astronomy
Eclipses
Theon recorded observations from Alexandria of the solar eclipse on June 16, 364 AD and the lunar eclipse on November 25 of the same year.
Revising the Almagest
Theon remolded Ptolemy’s great astronomical work Almagest to make it more understandable for his students. He carried out his reworking in association with his closest academic colleague, his daughter Hypatia.
The Astrolabe
Theon authored a systematic work on the theory and use of the astrolabe: On the Small Astrolabe. The word astrolabe comes from two Greek words meaning ‘to follow the stars.’
The first astrolabe – a spherical astrolabe, more commonly called an armillary sphere – was invented by Eratosthenes in the third century BC.
An armillary sphere from a painting by Sandro Botticelli in about 1480. The earth is the solid sphere at the center of the device. The ecliptic – the sun’s annual path on the celestial sphere seen from the earth – is shown as the broadest ring, tilted at an angle to the horizontal rings. The ecliptic is the path on which lunar eclipses take place, hence the name. The star constellations lying on the ecliptic make up the zodiac.
Hipparchus, who was one of the greatest of all ancient scientists, realized that by using stereographic projection from three dimensions into two dimensions he could produce a more portable version of the spherical astrolabe. This was the small astrolabe described by Theon.
3D representation of heavens from Earth.
Stereographic projection of 3D to 2D.
A small astrolabe utilizing stereographic projection of heavens from 3D to 2D.
An exploded view of a small astrolabe.
An ancient astronomer uses a very simple small astrolabe to measure a star’s angle above the horizon.
Although Theon’s work on the small astrolabe no longer exists, it was the basis of later works such as that by John Philoponus which carried the knowledge to later astronomers.
In earlier times, the Greeks had built truly awe-inspiring mechanical devices, including astronomical computers. Unfortunately, this remarkable technology was lost to future generations.
Personal Details and The End
We do not know Theon’s wife’s name. Hypatia was his daughter. He may also have had a son, Epiphanius. We know this because Theon made a dedication to him, addressing him as “my dear son” in his commentary to Book IV of Ptolemy’s Almagest. However, Theon uses the word Greek word teknon for son. In addition to meaning a biological son, teknon may also indicate paternal feelings to someone who is not a true son – for example a student at his school in whom he took particular pride.
As a Neoplatonist, Theon believed the ultimate fate of his soul would be a union with the divine.
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Further Reading
Sir Thomas Heath
The Thirteen Books of Euclid’s Elements
Dover Publications, New York, 1956
Morris Kline
Mathematical Thought from Ancient to Modern Times
Oxford University Press, New York, 1972
Otto Neugebauer
A History of Ancient Mathematical Astronomy
Springer Science & Business Media, 2004
Creative Commons
3D representation of heavens from Earth and stereographic projection of 3D to 2D by Michele Invernizzi, DensityDesign Research Lab, under the Creative Commons Attribution-Share Alike 4.0 International license.
Exploded view of small astrolabe by Elrond under the Creative Commons Attribution-Share Alike 4.0 International license.