CHAP. XII. PRIMITIVE NUMBERS. 197 



cessary here to introduce : I shall therefore only 

 observe, that the opinion respecthig the 9 was, 

 that *' there could be no number beyond it, and 

 that it circulates all numbers within itself, as is 

 evident from the regression of numbers. For 

 their natural progression is as far as 9 ; after which 

 their retrogression takes place, 10 becoming once 

 more the monad. Again, 9 being added to each of 

 the numbers 1, 2, 3, 4, and the rest, it will pro- 

 duce 10, 11, 12, 13, 14, &c. : no elementary number 

 can therefore be beyond the ennead ; " whence 

 the Pythagoreans called it " ocean and the hori- 

 zon, all numbers being comprehended by, and 

 revolving wdthin, it ; " but the " decad was called 

 heaven, being the most perfect boundary of 

 number ; " and some characterised numbers as the 

 envelopes of beings. 



That Pythagoras borrowed from Egypt his ideas 

 on this subject, is highly probable : such appears to 

 have been the opinion of the ancients themselves ; 

 and it would be curious to ascertain if our common 

 multii)lication table, for which we are indebted to 

 that philosopher, w^as of Egyptian origin. It is 

 however evident from modern discoveries in tlie 

 language and writing of that people, that the nu- 

 merical system of the Pythagoreans tallies with 

 the formation of the Egyptian numbers, according 

 to that mode of representing them in tlie hieratic 

 character, which is applied to the days of the 

 month, in the sense of the 1st, 2d, 3d, &c., where 

 1, 2, 3, and 4 alone, are perfect numbers ; 5, 6, 

 7, and 8 being composed of 3 + 2, 3 -{- 3y 



o 3 



