Thales and Pythagoras

Abstract

The most beautiful discoveries of this period concern relations between lengths (Thales’ intercept theorem), angles (the central angle theorem or Eucl. III.20) and areas (the Pythagorean theorem). A quick look at the index shows that these three theorems are by far the most basic and frequently used results of geometry. The only original documents which have survived from the pre-Euclidean period are some cuneiform Babylonian tablets (from approximately 1900 B.C.), the Egyptian Rhind papyrus and the Moscow papyrus from approximately the same period. The achievements of Thales, Pythagoras and his pupils the Pythagoreans are only documented in commentaries, often contradictory, written many centuries later.

“… la th′eorie des lignes proportionnelles et la proposition de Pythagore, qui sont les bases de la G′eom′etrie … [the theory of proportional lines and the theorem of Pythagoras, which form the basis of geometry]” (J.-V.Poncelet, 1822, p. xxix)

“… the original works of the forerunners of Euclid, Archimedes and Apollonius are lost, having probably been discarded and forgotten almost immediately after the appearance of the masterpieces of that great trio.” (T.L.Heath, 1926, vol. I, p. 29)