24 LE3 HYPERQUADUIQUES DANS L'ESPACE 



^'^/3- = /;/3 {n + rf - (/> + /S) (^ + r) {rr + e,.) + (.r + c,f. 

 h'^ = h { (./ + r-)- [5r„ - (« - r)''J - («■' + <■:) {2ac f cj } - 



^*^ = ^/3 (r. + f') [^f„ - {a - c)-'J - /3 {rr + e,) (5«c + c;,), 



^^/3-' = /7/3 (r/ + r-) (5r/r + r;,) - h (r/' + f,) {2ac + cj - /S (0 + e)- («" + c,) + 



W = /j (./ + v) {2ac + r„) [^^/r + r„ - 2 {rr + r,)] - 



{<r + rv) [(.2^/(- + r,J^ -(./ + rf {a' + r,)J, 

 ^^'/3 == />/3 { (r/ + rf [2r, - {a - rf] - {rr + r,) {2nr + r J } - 



(i{a + r){a'^-r:)[2r,.~-{a-rfl 

 h'(d' = /y/3 {a + r)'^ [5r, , ^ {a ^ r)'] - ''^ {^' + r) («^ + r,) [_2r„ - {n ^ c)''] - 



/3 (r/ + r) {a' + r,) (.;?«r- + r,) + (./- + r,.)' (5r/f + r„), 

 /ƒ /3^ = b(i {2ar + r,J^ - {h + /3) (./ + r) {rr + r,) {2rir + r„) + (r/ + cf {a., + O'- 



Par iiiu]tii)]ica.tioii 011 se forme sans ]jeiiie les expressions analo- 

 gnes })onr 



/y'/3, If(^\ //'(2' ; //'(i\ Ô'(2\ ô''(2'' ; /;■/3^ //'iS'' ; /y'/3'\ //^/3' ; ^(^ ; />''/3'\ 



Et (jnand il s'agit d'un nombre fini de figures (^/^/3c'),o on en 

 déduit, /x; re[)résentant encore un ensemble de conditions équivalant 

 à i conditions simples: 



/r(d iJ.T^ô(2{n + r)[j!.-, 



///3 //-,, = /y/3 (.:^</r + rj //,, 



b-'(2'lM- = h(i{r>^rfix,, 



//'/3 /x, = /y/3 (./ ^- r) [5r„ - {a rf] /x,-„ 



/y^'/3V5 = /y/S (^/ + r) {2av + rj /A,, 



/y^'/3 fx, = /y/3 { (./ + rf [2r;, - {a ~ rf] - {rr' + r,.) {2ar + r„) } ^„ 



h'^^'ix, = /y/3 {r, + r)'^ [2r., ^{a- rj^] /.,, 



/5^/3>,, = /y/3(.2«r + rJ>,, 



/y''/3 /x, - -: /y/3 {(i + r) (.2^/r + rj [^r/r + r-„ - 2 {rr + c,)] /«•;5> 



Up IX, = /y/3, (y/ + r) [ {r, + r)^ [2r„ -{a- rf] - (./^ + c,) {2rrr + rj) /Z3, 



/y"/3^V^^. = ''>/3 (^/ + ^0 i2nr + r„) \2r„ - (./ - r)'^] /x„ 



//•/3>, --^ /y^S (yy + rf {2ryr + r;,) [2r,r + r„ ^ 2 {a^ + 6-j] [X,, 



//'(2'!Ji, - /y/3 {2nr + r„) { {r, + rf [2r„ - {n - rf] - {ri' + r;) {2ac + r,f) /x,, 



/y'/3'Vx, = /y/3 {r, + rf [2r;, - {a - cfj fx,, 



/y''/3 Vx I = /y/3 {rr + r) {2rir + c,f \2rir + r„ - 2 [é + rjj ^a,, 



/y^'/3 V, = /y/3 (./ + y) [^6'„ -^ {a - rf] {{a + r)'^ [^r„ - (« - rf] - 



{ri"-^r;) {2ac^r,:)\ jx,, 

 /y''/3* = /y/3 (r/ -H r)' (^r/y + cj [2r„ - {a - rf] [2rir + r„ - 2 {rr + c,)], 

 ^■^/3'^ = /y/3 {(.y + e)-^ [5c-„ -^{a- rf] - (y/'^ + c, .) (i?«c + ej) ^ 



