– A rigorous, systematic treatment of mathematics requires the statement of all assumptions and the proof of all propositions by means of uniform methodology.
– All mathematical quantities can be expressed by geometrical figures, either lines, areas, or solids.
– Physical events can be modeled using mathematical expressions.
– Space is infinite in extent, but not infinitely divisible.
Little is known of Euclid’s life except that he taught at Alexandria in Egypt. Most information given on Euclid is not thought to be reliable. Euclid was a very common name around this period, so much of the material that is associated with Euclid of Alexandria is fictitious because there are many references to a man named Euclid. There are three hypotheses surrounding Euclid’s life.
1. Euclid was a historical character who wrote the Elements and the other works attributed to him.
2. Euclid was a member of a group of mathematicians working at Alexandria. Each one contributed to writing the ‘complete works of Euclid’, with the group writing books under Euclid’s name even after his death.
3. Euclid of Megara lived about 100 years before Euclid of Alexandria. Euclid of Alexandria didn’t exist at all. A group of mathematicians wrote The ‘complete works of Euclid and took the name Euclid from Euclid of Megara.
Major Works of Euclid
– The Elements (Stoicheiai)