BABYLONIA AND EGYPT 33 



by direct measurement. Arithmetic serves them in domestic 

 affairs and in connection with the theorems of geometry ; it is also 

 of no slight advantage to those who occupy themselves with the 

 stars. For if the position and motions of the stars have been care- 

 fully observed by any people it is by the Egyptians ; they preserve 

 records of particular observations for an incredibly long series of 

 years. . . . The motions and times of revolution and stationary 

 points of the planets, also the influence of each on the development 

 of living things and all their good and evil influences have been 

 very carefully observed by them." 



EGYPTIAN GEOMETRY. In a passage written about 420 B.C., 

 the Greek mathematician, Democritus, boasts that " In construct- 

 ing lines according to given conditions no one has ever surpassed 

 me, not even the so-called rope-stretchers of the Egyptians." 

 The exact orientation of the Egyptian temples required the deter- 

 mination of the meridian and of a right angle. Both processes 

 were naturally an important part of the mathematical lore of the 

 priesthood. The first step was accomplished by observation of 

 the stars. It is believed that the second step was the function of 

 the "rope-stretchers," the name being due to their dependence on a 

 rope of length 12, divided by two knots into sections of 3, 4, and 5. 

 When the two ends of the rope are joined and the three sections 

 drawn taut by the knots, the angle opposite the section 5 is a right 

 angle. The geometrical knowledge thus attributed to the Egyp- 

 tians of a special case of the Pythagorean proposition does not, of 

 course, imply knowledge of the proposition itself, or even the ability 

 to prove the particular case, which was probably known only em- 

 pirically. Egyptian architecture made use of geometrical figures 

 as wall decoration and even employed the principle of propor- 

 tionality, by dividing a blank wall-space into squares before apply- 

 ing the design. The idea of perspective drawing seems, however, 

 not to have been attained. 



The existence of such a problem book as that of Ahmes may be 

 considered as fairly implying also the existence of comparable 

 treatises of a more theoretical character, but other evidence of this 

 is lacking. 



