THE MYSTIC PROPERTIES OF NUMBERS. 543 



interested in securing due recognition of altruistic rights by his fel- 

 lows. The evils resulting from business frauds afFect the welfare of 

 the community. To quote the illustrative cases cited by Mr. Spencer, 

 *' The larger the number of a shopkeeper's bills left unpaid by some 

 customers, the higher must be the prices which other customers pay ; 

 the more manufacturers lose by defective raw materials or by careless- 

 ness of workmen, the more must they charge for their fabrics to buy- 

 ers. The less trustworthy people are, the higher rises the rate of in- 

 terest, the larger becomes the amount of capital hoarded, the greater 

 are the impediments to industry ; the further traders and people in 

 general go beyond their means, and hypothecate the property of 

 others in speculation, the more serious are those commercial panics 

 which bring disasters on multitudes and injuriously affect all." — 

 Knowledge. 



THE MYSTIC PPwOPERTIES OF OTJMBERS. 



By l^TIENNE DE LA EOCHE (1538). 



ONE of the earliest French mathematical books is the arithmetic 

 of Etienne de la Roche, in which, the title-page states, are given 

 tables of different accounts, with their canons, calculated by Gilles 

 Huguetan, native of Lyons : " in which may easily be found the ac- 

 counts all made, as well of purchases as of sales, of all kinds of mer- 

 chandise. And, principally, of goods which are sold or bought by 

 measure, as by the ell, by the cane, by the toise, by the palm, by the 

 foot, and the like. By weight, as by the pound, by the quintal, by the 

 thousand-weight, by the load, by the half-pound and the ounce, by the 

 piece, by the number, by the dozen, by the gross, by the hundred, and 

 by the thousand. "With two tables of use to booksellers, in selling and 

 buying paper, together with a table of expense, showing, at so much a 

 day, how much one spends by the year and the month, and at so much 

 a month how much it comes to by the year and the day, and at so 

 much a year how much one sj)ends in a month and how much it comes 

 to for each day. 



"Further, tables of the fineness of gold and silver, showing, ac- 

 cording as the coin contains of alloy or fine metal, hoAV much it is 

 worth in the weight of fine gold or of fine silver. 



" Sold at Lyons, at the sign of the Sphere, by Gilles and Jaques 

 Husuetan Brothers, 1.538." 



We give the first chapter of this curious work, which treats of the 

 first twelve numbers, their properties and perfections. Our modern 

 works, while they are less unsophisticated, are certainly far less amus- 

 ing in expounding the "beginnings of arithmetic : 



"Number, according to Euclid, at the beginning of the seventh 



