BABYLONIA AND EGYPT 29 



about, . . . and a line of thirty cubits did compass it round 

 about." 



There is some evidence of a knowledge of the fact that a triangle 

 of sides 3, 4, and 5 has a right angle, and the trisection of the right 

 angle was accomplished. The circle was divided into 360 degrees. 

 The sun-dial and its division into degrees are very clearly men- 

 tioned in the books of Kings and Isaiah. Parallels, triangles, and 

 quadrilaterals were used. 



We may summarize what we know as to the main features of 

 Babylonian mathematical science as follows : - 



In astronomy, records of observations extending over many cen- 

 turies, the determination of an 18-year eclipse period, the 

 approximate determination of the year as 365 days, a good 

 system of measuring time, the identification of Mercury, 

 Venus, Mars, Jupiter, and Saturn as planets ; 



In arithmetic, a well-developed sexagesimal system, tables of 

 squares and cubes, arithmetic and geometric progressions, 

 the use of large numbers ; 



In geometry, the identification of the right triangle of sides 

 3, 4, and 5, the inscribed hexagon, the division of the circum- 

 ference into 360 degrees, the crude approximation for the ratio 

 of circumference to diameter, TT = 3. 



MATHEMATICAL SCIENCE IN EGYPT. Josephus asserts that 

 the Egyptians learned arithmetic from Abraham, who brought 

 it with astronomy from Chaldea, and that the Egyptians in their 

 turn taught the Greeks. The indebtedness of Greek science to 

 Egyptians must at any rate have been very considerable. The 

 pyramids are monumental evidence of appreciation of geometric 

 form and of a relatively high development of engineering con- 

 struction nearly 4000 years before the Christian era. Their 

 builders must have had precise geometrical and astronomical 

 notions. In nearly all of the pyramids, for example, the slope 

 of the lateral faces is 52, and the direction of their base- 

 edges is nearly uniform. The regular inscribed hexagon was 

 known. After an earlier year of 12 months of 30 days each, the 



