VI PREFACE 



of the questions mentioned in the first five chapters are of a 

 somewhat trivial character, and had they been treated in any- 

 standard English work to which I could have referred the reader, 

 I should have left them out: in the absence of such a work, I 

 thought it better to insert them and trust to the judicious reader 

 to omit them altogether or to skim them as he feels inclined. 

 The twelfth chapter is new. I may add that in discussing pro- 

 blems where the complete solutions are long or intricate I have 

 been generally content to indicate memoirs or books in which 

 the methods are set out at length, and to give a few illustrative 

 examples. In some cases I have also stated problems which still 

 await solution. 



I have inserted detailed references, as far as I know them, to 

 the sources of the various questions and solutions given ; also, 

 wherever I have given only the result of a theorem, I have tried 

 to indicate authorities where a proof may be found. In general, 

 unless it is stated otherwise, I have taken the references direct 

 from the original works ; but, in spite of considerable time spent 

 in verifying them, I dare not suppose that they are free from all 

 errors or misprints. I shall be grateful for notices of additions or 

 corrections which may occur to any of my readers. 



W. W. KOUSE BALL. 



Trinity College, Cambridge. 

 April, 1922. 



