Introduction

Abstract

The question of the origins of Greek mathematics has always been considered to be an extremely difficult one. The amazing achievements of ancient Greek mathematicians have been passed down to us almost exclusively via the works of authors such as Autolycus, Archimedes, Euclid, Apollonius, Theodosius, Menelaus, Diophantus, and Pappus, the earliest of whom wrote in the second half of the 4th century BC. Additionally Aristotle’s philosophy of science as put forward in his Analytica posteriora, which was written slightly earlier, shows that at his time mathematical proofs were performed according to methods already close to those applied by Euclid. This is strong evidence that there had been a considerable period before the middle of the 4th century BC during which mathematics had been developed by the Greeks, from their very beginnings, to the state of perfection to which the classical works mentioned testify. But, as has been a continual source of regret ever since, there is an almost total lack of sources concerning the early phases of this process. Moreover Theophrastus of Ephesus and Eudemus of Rhodes seem not to have fared much better when they wrote histories of mathematics in the second half of the 4th century BC. Both have been lost (Waschkies, 1998, p. 368), but the work of Eudemus has left some traces in later works. Proclus refers to it repeatedly, and therefore his so called Survey, which outlines the history of Greek mathematics from its beginnings up to Euclid (Proclus, 1873, pp. 64–68), is often supposed to be from Eudemus, although Proclus does not refer to him by name there. This Survey served as a guide when the exploration of the history of Greek mathematics took a fresh start in 1870 with Carl Anton Bretschneider’s Geometrie und die Geometer vor Eukleides. As it has been customary it seems appropriate to start by quoting some lines from the Survey which refer to the very beginnings of Greek mathematics:

We say, as have most writers of history, that geometry was first discovered among the Egyptians and originated in the remeasuring of their lands. This was necessary for them because the Nile overflows and obliterates the boundary lines between their properties. It is not surprising that the discovery of this and the other sciences had its origin in the necessity, since every thing in the world of generation proceeds from imperfection to perfection. Thus they would naturally pass from sense — perception to calculation and from calculation to reason. Just as among the Phoenicians the necessities of trade and exchange gave the impetus to the accurate study of number, so also among the Egyptians the invention of geometry came about from the cause mentioned.

Thales, who had traveled to Egypt, was the first to introduce this science to Greece. He made many discoveries himself and taught the principles for many others to his successors, attacking some problems in a general way and others more empirically (Proclus, 1970, pp. 51–52).