Xll PREFACE. 



British Museum, printed on narrow slips of paper, 

 and evidently intended to be pasted pro bono publico 

 in conspicuous situations. We have little doubt that 

 the celebrated problem, generally known as Colonel 

 Titus's problem, was originally proposed in this man- 

 ner. We have already intimated that this problem 

 is attributed to the wrong person*, and we have since 

 discovered a note in MS. Birch, 4411, which ex- 

 pressly states that it was " put by Colonel Titus, who 

 had received it from Dr. Pell." The problem in the 

 most general form is as follows : 



a* + bc=a (in 



b 2 + a c = j3 (2) I to find a, b, and c. 



c 2 + a& = 7 (3)J 



Collins has given a solution which occupies four- 

 teen closely written folio pages, and the more modern 

 solutions have not been comprised in a much shorter 

 compass. Wallis's solution is in the same manu- 

 script. Pell, however, criticises Collins's solution 

 very severely, and ridicules him for not observing 

 that the roots will admit both of positive and nega- 

 tive values. 



The problem is generally given with numerical va- 

 lues for a, |3, and y, and the only possible chance of 

 a short solution is a case in which these numbers 

 bear some definite relation to each other, so as to ob- 

 tain an equation independent of the given quantities. 

 For instance, Pell gives one wherein a = 15, |3 = 16, 



* Life of Sir Samuel Morland, p. 28." From No. 4413, fol. 24, 

 it appears that the problem generally ascribed to Colonel Titus was 

 proposed to Pell in 1 649 by William Brereton, who very probably 

 had it from Harriot." 



