The Schoolmaster: Carpentras 



However, all goes well. Quick, let's lock the door 

 again, and hurry back to our own quarters with the 

 pilfered volume. 



A chapter catches my attention in the middle 

 of the volume; it is headed, Newton's Binomial 

 Theorem. The title allures me. What can a 

 binomial theorem be, especially one whose author 

 is Newton, the great English mathematician who 

 weighed the worlds? What has the mechanism of 

 the sky to do with this? Let us read and seek for 

 enlightenment. With my elbows on the table and 

 my thumbs behind my ears, I concentrate all my 

 attention. 



I am seized with astonishment, for I understand! 

 There are a certain number of letters, general sym- 

 bols which are grouped in all manner of ways, 

 taking their places here, there, and elsewhere by 

 turns; there are, as the text tells me, arrangements, 

 permutations, and combinations. Pen in hand, I 

 arrange, permute, and combine. It is a very divert- 

 ing exercise, upon my word, a game in which the 

 test of the written result confirms the anticipations 

 of logic and supplements the shortcomings of one's 

 thinking-apparatus. 



" It will be plain sailing," said I to myself, " if 

 algebra is no more difficult than this." 



I was to recover from the illusion later, when 

 the binomial theorem, that light, crisp biscuit, was 

 followed by heavier and less digestible fare. But, 

 for the moment, I had no foretaste of the future 

 difficulties, of the pitfalls in which one becomes 

 more and more entangled the longer one persists 

 105 



