180 JEROME CARDAN. 



chapter treats of the value of money; the forty-second 

 treats of mirific numbers, that is to say, of remarkable 

 properties of numbers, natural but strange. The next 

 chapter passes on to the supernatural, and treats of the 

 mystic properties of numbers. Then follows a chapter on 

 irrational quantities; and then Jerome comes to the dis- 

 cussion of the rule of three, which he characterises as the 

 key of commerce " clavis mercatorum." The next 

 chapter is upon the rule of six, our double rule of three ; 

 the chapter following compares the two processes. The 

 treatise then passes in the forty-eighth chapter to the first 

 simple rules of algebra, and travels on to higher mathe- 

 matical discussions, closing with chapters upon house- 

 rent, letters of credit and exchange, income, interest, 

 profit and loss, games of chance. It then comes to super- 

 ficial mensuration, and the measuring of solids ; passes on 

 to the practical details of weights and measures, and 

 closes with an exposition of certain errors in the works of 

 Luca de Borgo, and a Long list of cunningly-devised 

 questions in arithmetic and geometry, calculated to put to 

 a severe test the student's practical acquaintance with the 

 rules and reasons laid down in the book. 



While this treatise was at the printer's and nearly a 

 year seems to have been spent in the printing the 

 unhappy author was still struggling against contempt and 

 poverty in Milan. Anxious to work a way out of his 



