Chapter 2: The “Big Bang” Of Geometry: Euclid’s Elements

Euclid’s Elements consists of 13 books written by the mathematician Euclid around 300 BCE. Although most of the theorems and constructions included in it had been developed earlier by other Greek mathemati-cians, Euclid’s great achievement was to provide a systematic development in which a small set of axioms were used as a basis for deducing increasingly sophisticated results in plane and solid geometry. Throughout most of its 2,300-year history, Euclid’s Elements was the principal geometry text studied by students in Europe. Between 1482 and 1900, there were more than 1,000 editions printed. In his preface to the first English translation, Billingsley (1570) wrote, “Without the diligent studie of Euclides Elements, it is impossible to attaine unto the perfecte knowledge of Geometrie, and consequently of any of the other Mathematical Sciences” (cited in Hartshorne, 2000, p. 460). In the preface to his 1798 edition, Bonnycastle said: