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1
◦
. (x
1
)
2
+ (x
2
)
2
+ (x
3
)
2
+ (x
4
)
2
= 0 ( )
2
◦
. (x
1
)
2
+ (x
2
)
2
+ (x
3
)
2
−(x
4
)
2
= 0 (
)
3
◦
. (x
1
)
2
+ (x
2
)
2
− (x
3
)
2
− (x
4
)
2
= 0 (
)
4
◦
. (x
1
)
2
+ (x
2
)
2
+ (x
3
)
2
( )
5
◦
. (x
1
)
2
+ (x
2
)
2
− (x
3
)
2
( )
6
◦
. (x
1
)
2
+ (x
2
)
2
= 0 (
x
1
= x
2
= 0)
7
◦
. (x
1
)
2
− (x
2
)
2
= 0 (
)
8
◦
. (x
1
)
2
= 0 ( )
P
2
⊂ P
3
2
◦
A
3
=
P
3
\ P
2
3
◦
5
◦
2
◦
3
◦
5
◦
2
◦
3
◦
5
◦
P
∗
n
P
n
P
∗
n
π ⊂ P
n
p(V
n
(π)) V
n
(π) ⊂ V
n+1
1◦ . (x1 )2 + (x2 )2 + (x3 )2 + (x4 )2 = 0 ( dbadjt gkjobjt egkmfrbghi) 2◦ . (x1 )2 + (x2 )2 + (x3 )2 − (x4 )2 = 0 ( kmqmhikmbbjt gkjobjt egkmfrp bghi) u v n 3◦ . (x1 )2 + (x2 )2 − (x3 )2 − (x4 )2 = 0 ( oabm sjijt gomka bjt egp kmfrbghi) v v 4◦ . (x1 )2 + (x2 )2 + (x3 )2 ( dbadjt gbasmh jt egkmfrbghi) v v 5◦ . (x1 )2 + (x2 )2 − (x3 )2 ( kmqmhikmbbjt gbasmh jt egkmfrbghi) v u v 6◦ . (x1 )2 + (x2 )2 = 0 ( ejfj dbadcr eogh ghim w emfmhm j{qarht eg kmqmhikmbbgu eftdgu x1 = x2 = 0) v 7◦ . (x1 )2 − (x2 )2 = 0 ( ejfj kmqmhikmbbcr emfmhm j{qarht eogh gp v himu) n v u 8◦ . (x1 )2 = 0 ( ejfj hgkej j{qar eogh ghim ) ªZ« µÜ^ -1507* )7- D68 BA+35,,- .-DC-D80: -+35E-: ,*/-+ /7B*,,- .6-/1-/70 P2 ⊂ P3 )5/7> .-B*3C,-/70 2◦ .30,5D6*558 A3 = P3 \ P2 :-*7 -15E57>/8 ¨660./-0D-: DB2.-6-/7,A: 90.*3+-6-0D-: 060 ¨660.70)*/10: .535+-6-0D-: )5/7> .-B*3C,-/70 3◦ F -D,-.-6-/7,A: 90 .*3+-6-0D-: 060 90.*3+-60)*/10: .535+-6-0D-: 5 )5/7> .-B*3C,-/70 5◦ F 1-,2/-: 060 ½060,D3-:< 5 /6*D2*: 30/2,1* .-15E5,- 7-.-6-90)*/1-* /73-*,0* .-B*3C,-/7* 2◦ 3◦ 0 5◦ < 2◦ 3◦ 5◦ Ý^µ £°Y\\Y WXY]\Y WXX\ Pn∗ ^ 5//:-730: :,-*/7B- 90.*3.6-/1-/7* B .3-/735,/7B* Pn < +-E,5)0: ¨7- :,-*/7B- /0:B-6-: Pn∗ < 5D58 90.*3.6-/1-/7> π ⊂ Pn .3*D/75B68*7 /- +- -+35E p(Vn(π)) 9D* Vn(π) ⊂ Vn+1 F .-D.3-/735,/7B- 5//-½003-B5, Ñ©
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