Euclid's Elements - A 2,500 Year History
Bob Gardner
East Tennessee State University
Department of Mathematics and Statistics
Johnson City, TN 37614
Greek Commentaries on The Elements
Proclus
Image from http://www.athensinfoguide.com/history/t7-1middleages.htm.
Heron of Alexandria (Circa 10 CE to 75 CE)
Image from The MacTutor History of Mathematics archive.
Heron of Alexandria lived around 10 CE to 75 CE. He is known to have written a number of works on geometry and mechanics. Some of these works are known from surviving fragments and others only by reference. Fragments of his commentary on Euclid's Elements survive and is known to have covered at least the first eight books [Saint Andrews biographical webpage].
Eudemus of Rhodes was a pupil of pupil Aristotle. He can be considered the first math historian. He wrote a history of arithmetic, a history of astronomy, and a history of geometry. The history of geometry would have described the state of geometry before Euclid came on the scene - a time when relatively little is known, since the appearance of Euclid's Elements seems to have lead to a level of disinterest in earlier works on geometry and subsequently their loss.
Heath comments that:
"The loss of Eudemus' history is one of the gravest which fate has inflicted upon us, for it cannot be doubted that Eudemus had before him a number of the actual works of earlier geometers, which as before observed, seem to have vanished completely when they were superseded by the treatises of Euclid, Archimedes and Apollonius."
[Heath, page 35]
Image of Proclus from http://www.athensinfoguide.com/history/t7-1middleages.htm.
Proclus lived from 410 to 485 CE. Therefore, his work dates from around 700 years after that of Euclid.
He received his early training in Alexandria and later in Athens where he was the head of the Neo-Platonic school.
He wrote a large number of commentaries, mostly on the dialogues of Plato. "Though he was a competent mathematician, he was evidently much more a philosopher than a mathematician. This is shown even in his commentary on Eucl. I. ... he seizes any opportunity for a philosophical digression." [Heath, pages 29 and 30]
Image of from Amazon.com.
Proclus wrote an extensive commentary on Book I of Euclid's Elements. His commentary is one of the two main sources of information as to the history of Greek geometry which we possess, the other being the Collection of Pappus [Heath, page 29]. In fact, Proclus' commentary on the Elements is still in print today.
Go to the next section: Other Important Geometers.
Last revised November 14, 2009.