THE BEGINNINGS OF CERTITUDE 59 



and astonishing examples of their powers in the far more diffi- 

 cult analysis of phenomena. Their employment of mathematical 

 methods was constant, its applications were wide. 



One of the earliest was the geometry of light. It must 

 have been recognised far back that light travels in straight 

 lines, and that its reflection has a sharp angle, equal in value 

 to the angle of incidence. These facts were very early utilised 

 in fixing the positions of the heavenly bodies and in effecting 

 the beginnings of our cosmic knowledge. They are still the 

 source of by far the larger part of our information as to the 

 world in which we live. 



By means of the eclipses men were able to understand that 

 the sun lies back of the moon, and to unravel the mystery that 

 lay in the puzzling and apparently inexplicable motions of 

 the planets. It was by means of the eclipses, as we shall see, 

 that a little later the Greeks were able to gather some idea of 

 the relative distances of the moon and sun, some idea of their 

 respective grandeurs as well. 



It must have been very early that attentive minds observed 

 that the light of the sun comes to us in practically parallel 

 lines. On the day of the solstice when the sun seemed to stand 

 still in the heavens, then began its winter retreat, there was a 

 belt of considerable extent, several hundred stadia in width, 

 in which perpendicular objects cast no shadow. This zone lay 

 across the middle reaches of the Nile, just where Egyptian 

 civilisation attained its highest efflorescence. The fact must 

 have been deeply pondered by the observing priests. Its 

 implications could hardly have escaped their wondering minds. 

 A few hundred years later it seems to have been employed 

 by Poseidonius to compute the distance of the sun, with an 

 approximate success that is still amazing. 



When we trace out the history of ideas we find as a rule that 

 their lineage is long. In some of the earliest of Greek manu- 

 scripts that have come down, and again in the pages of Cicero, 

 of Cleomedes, and a dozen others of that later day, we find 

 perfectly correct notions of the earth and its immediate sur- 

 roundings. These conceptions, analogy leads us to believe, 

 must have been very old. 



Inferences of such moment, deductions of such power, imply 

 that far in the ancient time the idea of fixity in phenomena 

 had been deeply impressed upon at least a slender body of 



