CHAPTER VI - GREEK GEOMETRY TO EUCLID

Summary

An elaborate history of Greek geometry before Euclid was written by Eudemus, the pupil of Aristotle, who lived about 330 b.c. The book itself is lost but is very frequently cited by later historians and scholiasts, and it may be suspected also that many notices, not directly ascribed to it, were taken from its pages. Proclus, the scholiast to Euclid, who knew the work of Eudemus well, gives a short sketch of the early history of geometry, which seems unquestionably to be founded on the older book. The whole passage, which proceeds from a competent critic, and which determines approximately many dates of which we should otherwise be quite ignorant, may be here inserted verbatim by way of prologue. It will be cited hereafter as “the Eudemian summary.” It runs as follows:

“Geometry is said by many to have been invented among the Egyptians, its origin being due to the measurement of plots of land. This was necessary there because of the rising of the Nile, which obliterated the boundaries appertaining to separate owners. Nor is it marvellous that the discovery of this and the other sciences should have arisen from such an occasion, since everything which moves in development will advance from the imperfect to the perfect. From mere sense-perception to calculation, and from this to reasoning, is a natural transition. Just as among the Phoenicians, through commerce and exchange, an accurate knowledge of numbers was originated, so also among the Egyptians geometry was invented for the reason above stated.