Axiomatic Geometry

(Originally Written August 30, 2006 in History I)

The Classical Mind by W.T. Jones

Axiomatic Geometry:

The Greeks took a basic geometric understanding from the Egyptians and further developed it.

Axiomatic Geometry slowly formed over the 6th and 5th centuries B.C. The earliest complete text is Euclid's Elements written circa 300 B.C.

Axiomatic Geometry starts with self-evident statements (axioms) then uses logical reasoning to produce theorems. Theorems are combined to form more complex theorems and so forth and so on. Euclid had a large demonstrable book by the end of his reasoning.

Axiomatic geometry pushed Greeks to rely on reasoning rather than on sense perception.

Euclid's theorems went unchallenged until the 19th century. Many western philosophers have regarded the Elements as the paradigm of human reasoning.