28 



LES HYPERaUADEtQUES DANS L'ESPACK 



A l'aide de ce tableau on trouve les 



Nombres ti''^ ^ ''' //' r'' d" = ( p q r .y). 



(b()21) = 

 (7121) = 

 (7031) = 

 (0221) = 

 (0131) = 

 (0041) = 

 (5321) = 

 (5231) = 

 (5141) = 

 (5051) = 

 (4421) = 

 (4331) = 

 (4241) = 

 (4151) = 

 (4001) = 

 (3521) = 

 (3431) = 

 (3341) = 

 (3251) = 

 (3101) = 

 (2021) = 

 (2531) = 

 (2441) = 

 (2351) = 

 (2201) = 

 (701 

 (OU 

 (002 



:(S012)=: 35 



:(7112) = 35 



= (7022) = 70 

 :(0212) = 35 

 : (01 22) = 70 

 : (0032) = SO 

 : (53 12) = 35 

 : (5222) = 40 

 :(5132) = SO 

 :(5042)= 50 

 : (4412) = 27 

 : (4322) = 54 

 : (4232) =04 

 :(4142)= 50 

 :(4052)= 15 

 :(3512)= 15 

 : (3422) = 30 

 : (3332) = 30 

 : (3242) = 30 

 :(3152)= 15 

 : (2() 1 2) = 

 :(2522) = 

 :(2432) = 

 : (2342) = 

 :(2252) = 

 3) =35 

 3) = 35 

 3) = 45 



1) 

 10 

 12 

 10 



5 



(5213) 



= 35 



(5123) 



= 45 



(5033) 



= 30 



(4313) 



= 27 



(4223) 



= 37 



(4133) 



= 30 



(4043) 



= 9 



(3413) 



= 1 5 



(3323) 



= 21 



(3233) 



= 18 



(3143) 



= 9 



(2513) 



= 5 



(24^3) 



= 7 



(2333) 



= () 



(2243) 



= 3 



(0014) 



= 10 



(5114) 



= 10 



(5024) 



= 10 



(4214) 



= 10 



(4124) 



= 10 



(4034) 



= 3 



(3314) 



= () 



(3224) 



= 



(3134) 



= 3 



(2414) 



= 2 



(2324) 



= 2 



(2234) 



= 1 



. 



. . {ab(icd)^^. 



Les nombres (a''/j'''(2'''c''d'')i^ se déduisent de ceux de (r//y^("),o au 

 moyen des formules générales 



'III ) 



{a''lf'^'^H;''d )„ = (r/'7y''/3''^r-'-; 

 («'y/''/3''^c'V/-)H = {a"ö''-(i-N-'' 

 (a"b-''(2'''c'-dX = {a"ô"'(d^'H;.a'\, , 



lui ' 



■ P + ^J\ + Ç-i + ^' = 10, 



■ V + <1\ + Il + '■ = ^' 

 . JÖ + ^c, + q-i + V = S, 

 . p^q,-\- q-, + r = 7. 



Donc les nombres {ah^cd)^^ sont coiuius pour s = 1,5—2. Nous 

 avons encore à étudier pour i' = 3 les cas r = 0, r = 1 , y = 2 et pour 



