26 A SHORT HISTORY OF SCIENCE 



the achievements of the older civilizations were marvellous, but for 

 the creation of real science as systematized, organized knowl- 

 edge, containing within itself the seeds of infinite growth, they 

 were quite unequal. 



BABYLONIAN ARITHMETIC. In Babylonian arithmetic whole 

 numbers were expressed in general by only three of the so-called 

 cuneiform or wedge-shaped characters employed on the tablets, 

 1 = Y , 10 = -X, 100 = Y V~, but the numbers known to have 

 been used run into the hundred thousands, this naturally im- 

 plying a highly developed command of the fundamental operations 

 by means of which large numbers are made to depend upon smaller 

 ones. The use of the words for thousand and ten thousand in 

 characterizing an indefinite multitude is illustrated in many 

 scriptural passages, for example : " Saul hath slain his thousands, 

 and David his ten thousands" (1 Sam. xviii. 7); "a thousand 

 thousands ministered unto him, and ten thousand times ten thou- 

 sand stood before him '' (Dan. vii. 10). With such expressions 

 may be compared : " I will make thy seed as the dust of the earth " ; 

 "He telleth the number of the stars; he calleth them all by 

 their names' (Gen. xiii. 16; Ps. cxlvii. 4). The number 40 

 also plays a special role in such expressions as the " forty years 

 in the wilderness," the "forty days and forty nights" of rain 

 which caused the flood. 



Of remarkable interest in the Babylonian inscriptions is the oc- 

 currence, side by side with a decimal system, of a number system 

 based on 60, employed for mathematical and astronomical pur- 

 poses. A table of squares of the natural numbers presents, for 

 example, nothing novel for the first seven numbers, after which 

 follow, however, the equivalent of 



1 4 is the square of 8 



1 21 is the square of 9 



1 40 is the square of 10 



2 1 is the square of 11 



Just as in our notation, for example, 325 means three times the 

 square of ten plus twice ten, plus five, so this table must mean : 



