The musings of a previously unemployed Jewish Freemason. I write about the job search, about Judaism, and about Freemasonry.

Tuesday, October 16, 2012

Who was Euclid?

Euclid (Εὐκλείδης) of Alexandria (fl. c. 300 BCE), was the author of many books of geometry, the most popular of which is the 13-volume Elements. Most of the biographical information we have about Euclid comes from the geometer Pappus of Alexandria (c. 290 - c. 350 CE), and from the neo-Platonic philosopher Proclus (412 - 485 CE). In the centuries between Euclid's life and the lives of those who wrote about is life, very little practical information survived. We know that much of what they wrote about Euclid of Alexandria came from information about his predecessor, the Socratic philosopher Euclid of Megara (c. 435 - c. 365 BCE), and had nothing to do with Euclid of Alexandria. That makes it rather difficult to discuss the author of the Elements, leaving the text itself as the only true testament.

Euclid taught at the Musaeum, the great learning complex at Alexandria that included the famous Library. We know that he was a big influence on Archimedes of Syracuse (c. 287 - c. 212 BCE), perhaps the greatest mathematician of antiquity, but whether the two of them ever met in unclear. Archimedes comments on Euclid's works, so he had clearly studied them.

Euclid wrote many works of geometry, and also geometric optics, music theory, logic and fallacies, mechanics, and some advanced mathematics as well. His four-volume work on conic sections, which unfortunately does not survive, was a great influence on Apollonius of Perga (c. 262 - c. 190 BCE), whose definitive eight-volume treatment remained definitive through the time of Galileo Galilei, Johannes Kepler and Sir Isaac Newton, and contributed greatly to the invention of analytical physics by these men.

Much of what we know of Euclid comes from Pappus of Alexandria and Proclus. Pappus of Alexandria was a very brilliant geometer and arithmetician who wrote an eight-volume compendium, called the Collection (or Synagoge) of all mathematics known at his time. Pappus is considered to be the last truly great mathematician in the Greek tradition.

Proclus was a neo-Platonic philosopher in the tradition of Plotinus. Recall that it was Plotinus who described how the One emanates into our world: "from a point to a line; from a line to a superfice, and from a superfice to a solid". Proclus left a lucrative law career to become a philosopher, studying at Plato's Academy, and eventually becoming the head of the Academy. He lived in Athens as a vegetarian and a bachelor, leaving from time to time to visit various mystery schools in his attempt to become a "priest of the entire universe," embracing all monotheistic traditions universally. Most of Proclus' writings are commentaries on Plato's dialogues, or works of theology or philosophy of his own. However, because Plato's Academy had a requirement: "let none ignorant of geometry enter here," all beginning students were required to study geometry, and Proclus became the Academy's geometry tutor. From his course notes, he compiled a commentary on the first volume of the Elements, and flavored his commentary with much philosophical speculation and historical anecdotes. It is not clear if Proclus commented on any other books of the Elements.

In a sense, if the Elements are to be true to their elementary nature, it is not necessary to know who the man Euclid was. His great gift to humanity was to take all the knowledge that came before him and systematize it in a pedagogically sound way. It is a tribute to the soundness of his work that he chose to offer his presentation in such a way that the work hides any personal affectation.

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