The Classical Mind
W.T. Jones
1980
Axiomatic Geometry
During the 6th century BC the Greeks began to take what knowledge of Egyptian practical geometry they had and systematize it into a system for the desire of pure knowledge, that is, they didn't study it for any particular utility.
The way axiomatic geometry worked for the Greeks was to start at self-evident principles and then to use logical deductive reasoning to come up with axioms. These axioms were then combined logically to create further axioms and conclusions.
Euclid in 300 BC published Elements. "In Euclid's book, the first theorems are proved by showing that they follow directly from the axioms; then, by judicious combinations of already proved theorems with the axioms, more complex theorems are derived. In this systematic way Euclid was able to 'demonstrate' a large body of geometrical knowledge" (Jones, 20).
The effect that axiomatic geometry had on the Greek thought was far more profound than shaping mathematics. It focused Greek thought so deeply on reasoning that reason became preeminent and far more important than sensory perception.
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