TRANSLATOR'S INTRODUCTION. v 



"The encouragement; for it contained a 

 body of knowledge that was really known and 

 could be relied on. 



"The guide; for the aim of every student 

 of every subject was to bring his knowledge 

 of that subject into a form as perfect as that 

 which geometry had attained." 



But Euclid stated his assumptions w4th the 

 most painstaking candor, and would have 

 smiled at the suggestion that he claimed for 

 his conclusions any other truth than perfect 

 deduction from assumed hypotheses. In favor 

 of the external reality or truth of those as- 

 sumptions he said no word. 



Among Euclid's assumptions is one differing 

 from the others in prolixity, whose place fluc- 

 tuates in the manuscripts. 



Peyrard, on the authority of the Vatican MS., 

 puts it among the postulates, and it is often 

 called the parallel-postulate. Heiberg, whose 

 edition of the text is the latest and best (Leip- 

 zig, 1883-1888), gives it as the fifth postulate. 



James Williamson, who published the closest 

 translation of Euclid we have in English, in- 

 dicating, by the use of italics, the words not 

 in the original, gives this assumption as elev- 

 enth among the Common Notions. 



