44 



CHAPTER III. 



GEOMETRICAL RECREATIONS. 



In this chapter and the next one I propose to enumerate 

 certain geometrical questions, puzzles, and games, the discussion 

 of which will not involve necessarily any considerable use of 

 algebra or arithmetic. Most of this chapter is devoted to questions 

 which are of the nature of formal propositions : the next chapter 

 contains a description of various amusements. 



In accordance with the rule I laid down for myself in the 

 preface, I exclude the detailed discussion of theorems which 

 involve advanced mathematics. Moreover (with one or two 

 exceptions) I exclude any mention of the numerous geomet- 

 rical paradoxes which depend merely on the inability of the 

 eye to compare correctly the dimensions of figures when their 

 relative position is changed. This apparent deception does 

 not involve the conscious reasoning powers, but rests on the 

 inaccurate interpretation by the mind of the sensations derived 

 through the eyes, and I do not consider such paradoxes as 

 coming within the domain of mathematics. 



Geometrical Fallacies. Most educated Englishmen are 

 acquainted with the series of logical propositions in geometry 

 associated with the name of Euclid, but it is not known so 

 generally that these propositions were supplemented originally 

 by certain exercises. Of such exercises Euclid issued three 



