### The First Book of Euclid's Elements

It is a tragedy of mathematics that what we know of Euclid's life is so meager. It is because of Euclid's work that mathematics was able progress so rapidly in classical times. Euclid's masterpiece The Elements was so popular that it became the most widely read book until the twentieth century (with the exception of The Bible). However, our tragedy lies in what we actually know about Euclid. The sources of Euclid's life are but a few passages from commentators who claim they knew who Euclid was. To this day, there have been only five commentators of Euclid, which are Proclus, Heron, Porphyry, Pappus, and Simplicius (Proclus being the most prominent).1 Pre-twentieth century The Elements was considered the authoritative standard of basic concepts in geometry , number theory, and logic.

It is speculated that Euclid flourished around 300BCE. This has been estimated by one of the passages that Proclus wrote in his Commentary on the First Book of Euclid's Elements. The passage is as follows:

¡§Not much younger than these(sc. Hermotimus of Colophon and Philippus of Medma) is Euclid, who put together the Elements, Collecting many of Eudoxus' theorems, perfecting many of Theaetetus', and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy. For Archimedes, who came immediately after the first (Ptolemy), makes mention of Euclid¡KHe is then younger than the pupils of Plato but older than Eratosthenes and Archimedes; for the latter were contemporary with one another, as Eratosthenes somewhere says.¡¨2

Here Proclus mentions people of which we are more clear of their life span, such as Plato (d. 347/6BCE), Archimedes (d. 212BCE), Eratosthenes (d. 204BCE), and Ptolemy Soter (d. 283BCE). So here we are able to say that Euclid flourished in 300BCE but the exact date of Euclid's birth and death cannot be measured with ...

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