A MEMOIR ON THE TWENTY-SEVEN LINES UPON 

 A CUBIC SURFACE. 



PART II. 



ARCHIBALD HENDERSON, PH.D. 



CHAPTER II. 



THE CONFIGURATION OF THE DOUBLE-SIX. AUXILIARY 



THEOREMS. 



§5. The Double-Six Notation. 



Let us write down, in Salmon's notation, two systems of 

 non- ; ntersecting- lines 



\, 7 , ef] (ad • cf • eb) x , (ad • cf • eb) 2 . {ad • cf • eb) 3 

 /. eb y ad, (ab • cd • ef) x , (ab • cd • ef)^ (ab ■ cd' - ef)^ 



In this scheme, according- to former postulation (§4), each 

 line of one system does not intersect the line of the other sys- 

 tem, which is written in the same vertical line, but does 

 intersect the five other lines of the second system. 



The configuration was first observed by Schlafli* and was 

 given by him the name it has since borne — a "double-six". 

 The concept of the double-six lies at the very basis of the 

 study of the lines upon a cubic surface and the notation 



*"An attempt to determine the twenty-seven lines npon a surface of the 

 third order, and to divide such surfaces into species in reference to the 

 reality of the lines upon the surface", Quarterly Journal of Math (1858), 

 vol. II, pp. 55-65, 110-120. 



Nov.) 120 



