PREFACE. Xlll 



y= 17, in which case the problem remains in the 

 same position as before with regard to a solution ; 

 but it is singular that Pell's ingenuity should not 

 have suggested another method of solution in the 

 case which he gives where a = 7, /3 = 7, y = 1 1. In 

 this case we have 



a 2 & 2 = a c - b c = c (a b) 

 or, a + b = c. 



It is unnecessary to pursue this any further, for by 

 substituting this value of c in (3) and (2), and add- 

 ing the two equations together, we obtain 2 (a+&) 2 

 = 18, or c = 3. The values of a and b are 1 and 2 

 respectively, and this is, perhaps, the simplest case 

 which could be selected. 



To return to the contents of our volume. The 

 notes of inventions of Ralph Rabbards at p. 7, may 

 be noticed as somewhat similar to the far-famed 

 " Century of Inventions" of the Marquis of Wor- 

 cester. The number of such proposals is great, and 

 several seem to include discoveries generally consi- 

 dered as belonging to a more modern period*. The 

 letter of Tycho Brahe, at p. 32, may be mentioned 

 as a curious notice of the intercourse between the 

 mathematicians of this and foreign countries. The 

 letters of Thomas Lydyat are more valuable for bio- 



* For instance, Sir Samuel Morland's Tuba Stentorophonica may 

 have been anticipated by Henry Reginald, who, in the year 1603, 

 dedicated a book of inventions to King James, among which was 

 one " to convey the voice for a thousand paces without showing any 

 one near you were talking." MS. Birch, 4384. 



