8 SCIENCE IN GRECO-ROMAN ANTIQUITY 



sarily supposed the sides of the triangle to be in a cer- 

 tain proportion of whole numbers, 3, 4, 5, for example. 1 

 It may be asked whether the construction of the pyra- 

 mids and temples did not require more advanced 

 theoretical knowledge than that which we attribute 

 to the Egyptians. M. Milhaud has clearly shown 

 that this was not the case. 2 



Whilst the Egyptians were ignorant of the art of 

 calculating an angle, this was the branch of mathe- 

 matics which above all interested the Chaldeans. For 

 them, indeed, the position and movements of the 

 heavenly bodies (especially the planets) had a vital 

 interest, since this movement influenced the destinies 

 both of nations and individuals. So it was necessary 

 to know how to measure exactly, at every instant, the 

 relative positions of the planets and stars, which is 

 impossible without the help of angles and their pro- 

 perties. To measure the magnitude of angles the 

 Chaldeans, as we have seen, conceived the brilliant idea 

 of dividing the circumference into 360 parts. Hence- 

 forward, to estimate the height of a star in the sky, it 

 was sufficient to fix, perpendicularly to a horizontal 

 plane, the quarter of a graduated circumference 

 furnished with a mobile radial arm. In sighting the 

 star by means of this radial arm, an angular displace- 

 ment would be found, which corresponded to the 

 height required. It is a curious fact, that, as we shall 

 see, the Chaldeans had recourse to quite different 

 methods to determine the positions of the stars. The 

 lack of trigonometry did not impel astronomers to the 

 direct measurement of angles. 3 



To sum up, the characteristics which distinguish 

 Egyptian mathematics from Chaldean mathematics 

 correspond to a difference in the practical uses to which 



1 22 Milhaud, Nouvelles Etudes, p. 108. 



2 Ibid., p. 75 et seq. 



3 2 Bigourdan, Astronomic p. 107. 



