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12 n 86'.(#& = &'!!'(& - / /(%+ / (*"+(0, / A «A est au-dessus de B» B ex. 1 : deux points B A C «B est à gauche de C» «A est au-dessus du milieu de B et de C» «A, B et C sont des points équidistants» ex. 2 : trois points? j.",& A.&(! & 1 / & 1'#("+/ /.'#('1 /3 1' 1'+%, +D /# 4 2%'1(#2 'C * 1D(!'% 0, #'+# 0,D(1 /D'%(# -D,+ & 1'#("+ 1(+2'(& k A? l? 5/ 0, 1D"+.'// 4 -,A -(B! +/("+/3 1 +"!<& -D2+"+*2/ - 1' 1'+%, 0,D(1 7',#.&"-,(&.",& $ -2*&(& ),+ *"+J%,&'#("+ /.'#('1 k(?? 7'(&,+ #&'-,*#("+ (+# &!"-'1 l ',%! +# #&5/ C(# k A? l 0,( /D(+/.(& +# -.62+"!5+ / -. &*.#("+ kl,a -D"!<& # - 1,!(5& 3 '+%1 / -&"(#/ #&'+/7"&!2/ + '+%1 / "<1(0, / 1"&/0,D(1/ + /"+#.'/ -'+/,+.1'+ 7&"+#'13 /,&7'* / -D'&&(5& *'*62 /.'& 1 / /,&7'* / -D'C'+#3 -(!(+,#("+ - 1D'+%1 - C(/("+ 'C * 1'.&"7"+-,& - 1D"<L #???l!'(/ 0,( +.,C +#.'/ &2 11! +# + 11 /B!>! / >#& -(# / +'#,& 11 / j 1 /. &/. *#(C / /"+# <( + - / *"- / - #&'+/*&(.#("+3 # + #'+# 0, # 11 /3 *"!."&# +#,+.'&# - *,1#,&'1(#2 kc"(& 4 * /,L # "1:3 nn3..? l? 1 +D: ' -D'(11,&/.'/ -.&"%&5/ -'+/ 1D6(/#"(& - 1D'&#3 # 1'. &/. *#(C (+C +#2 4,+ 2."0,.,# >#& &!(/ + *',/ 4,+ 2."0,,1#2&(,& k*"!! 1D /# 1'. &/. *#(C %2"!2#&(0, -'+/ 1 /,C& / *,<(/# /l? ' J%,&?n -"++ - / A!.1 / - #&'+/*&(.#("+3 & /. *#(C! +# -'+/ 1D(!'%.1'+ # + 1'+%, 3 - & 1'#("+/ -'+/ 1' -(! +/("+ /.'#('1-1' F GE? D"!<&'% - /. +# /3 /,& 1 / *'&# / " 1D"+ C,# 7'(& J%,& & 1D(!.& //("+ - & 1( 73 /#,+ ',#& A!.1 - &.&2/ +#'#("+ - 1' #&"(/(5! -(! +/("+? 1 &2/,1# 1,( ',//( - *"+C +#("+/ -"+# 1 / 1 *#,&/ /"+# 1.1,/ /",C +# (+*"+/*( +#/? (+/( * 11-1D"&( +#'#("+ - 1D"!<&? &#(+ knm3.? l.&2/ +#,+ *'&# - Z'&(/ # - / / +C(&"+/ " 1D"!<&'% - /. +# / /# &.&2/ +#2 + # +'+# *"!.# -D,+ 2*1'(&'% /,.."/2 C +'+# -, <'/ - 1'.'% j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

13 ? G F G G G EF G GF G G GF G FGFE n A B ex. 1 : perspective cavalière «la face A est la face avant du cube, la face B est la face arrière» A B «la maison A est plus proche de moi que la maison B» ex. 2 : perspective géométrique?nj 1 /. &/. *#(C / /"+# - / *"+C +#("+/ $ %&'!!'#(*'1 / ) - #&'+/*&(.#("+ - 1' #&"(/(5! -(! +/("+ /"+# $ (+C &/2/ ) k*d /#B4B-(& 0, (+ *",1 /,&,+.1'# ',3 0, ""+#!'&#& # 1 ""+#B '12&( + /"+# - / *,C ## /???l3 # * ## (!.& //("+ + / -(//(. 0,D + & #",&+'+# 1 1(C& k',.&(a -D,+ C(/("+ (+6'<(#, 11 - Z'&(/3 'C * + 6',# - 1'.'% l? &#(+ +"# 4 *H#2 j $ + (!'%(+ /"(#,+ 1,!(5& C +'+# -D + 6',# 4 %',*6 3 0,( +",/ /# 7'!(1(5& 3 C&'(/!<1'<1! +# -, 7'(# -D>#& -&"(#( & # - / 6'<(#,- / -D2*1'(&'% 0,( + &2/,1# +#3 /"(#,+ 1,!(5& C +'+# -, 6',# - 1D(!'%? ) k(<(-?l? [\[\[ d h`aigc d +/,(# 3-5/ 0,D(1 /D'%(# - & 1'#("+/ +"+B/.'#('1 /3 1D(!'% / & #&",C 4 2%'1(#2 'C * 1' 1'+%, j 11 -"(# 2#'<1(&,+ G3 *D /#B4B-(&,+ +/!<1 - /*62!'/ /.'#("B/ +/(#(7/ 0,( #&'+/*&(C +# * / & 1'#("+/ /,& /"+.&".&.1'+ - 1D A.& //("+? 11 - C( +# '1"&/ + * 1'3 -'+/ 1 / # &! /. (&*2 +/3,+ -('%&'!! # +"+.1,/,+ (!'% j 11 &.&2/ +# - / "<L #/.'&,+ (/"!"&.6(/! - /#&,*#,& 3 /'+/ 0, 1 / & 1'#("+/ -, /(%+(J'+# # -, &272& +# /"( +# -!>! +'#,& k$ 1 / 6:."(*H+ / 0,( &.&2/ +# +# 1 / & 1'#("+/3.&(+*(.'1! +# -:'-(0, / ", *"+/(-2&2 / *"!! # 11 /3 - /.'&#( / -D,+ *6"/.'& - / & 1'#("+/ '+'1"%, / -'+/ 1,&/.&".& /.'&#( /3 /"+# - / G? ) Z (&* 3 nm 3.? nl? /"!"&.6(/! -"+*3 + I #3!'(/ (/"!"&.6(/! +#(5&! +# *"+C +#("++ 1? *" nm.&"."/ -D'(11,&/ - <( + /2.'& & * # (/"!"&.6(/! - /#&,*#,& - 1' +"#("+ -D(*"+(*(#2? Z& +'+#.",& A!.1 1 / %&'.6 / A(/# +#( 1/ - Z (&* 3 0,( $ (1 /# C&'(??? A6(< +# - / & 1'#("+/ /.'#('1 /3!'(/ * / & 1'#("+/ /.'#('1 / + #( ++ +#.'/ 1(, -D',#& / & 1'#("+/ /.'#('1 / ) k*"3 nm 3.? l3 (1!"+#& 1 *'&'*#5& &@(8?* /0* +0:B9 9* +*. 7:*-7 ),08 A =8:7(+*9*-7 :?,-:/0*. EM

14 n 86'.(#& = &'!!'(& - / /(%+ / (*"+(0, / *"+C +#(" * / -('%&'!! / 0,(3 &2%(/.'&,+ ',#& 7'#"+ -. +/ & 1 / & 1'B #("+/ /(%+(J2 /3.&2/ +# &'( +#,+ *"+J%,&'#("+ /.'#('1 *"!.15#! +# ".."/2? / $ %&'.6 / A(/# +#( 1/ ).&"."/ +# + I # - &.&2/ +# & C(/, 11! +# 1 / & 1'#("+/ /,L # '##&(<,#.'& - / & 1'#("+/ #"."1"%(0, / -D(+*1,/("+? (+/( 1.&2-(*'# $ #",# /'(+# /#,+ 6"!! ) : /# &.&2/ +#2.'& -,A * &*1 / *"+* +#&(0, / j S H & $ * %&'.6 + #&'+/*&(#.'/ 1' +"#("+ *1'//(0, -D(+62& +* -,.&2-(*'# ', /,L #3!'(/ 1' +"#("+!"- &+ -D'..'&# +'+* 4,+ *1'// ) k(<(-?l? %+ ',#& *"+C +#("+ ',&'(# -"+*.,.&2/ +# & * / * &*1 / (!<&(0,2/ -'+/ 1D"&-& (+C &/? ' #&'+/."/(#("+3 /",/ 7"&! - & 1'#("+/ /.'#('1 / -'+/,+.1'+3 - & 1'#("+/ -D,+ ',#& "&-& /# ',L",&-D6,(,#(1(/2 1'&%! +# -'+/ -(C &/ #:. / - &.&2/ +#'#("+/ %&'.6(0, / & 1 C'+# - /2!("#(0, / +#(5&! +# *"+/#&,(# /? D,/'% - * / &.&2/ +B #'#("+/ ' 2#2 #62"&(/2 # (11,/#&2.'& &#(+ nm3 nmm? ' 0, /#("+ - 1D(*"+(*(#2 : /#.'& -2J+(#("+ #"#'1! +# 2C'*,2 j 1 %&'.6(0, / C,# '+'1:#(0, 3 /"+ 1 *#,& /D(+7"&! + "</ &C'+# 1 / &'.."&#/ +#& / /.'&#( /? D $ (!'% ) /# -D'(11,&/3 -'+/ 1 %1"//'(& - &#(+3 1' $ 7"&! C(/, 11 /(%+(J*'#(C. &#, -'+/,+ (+/#'+# -. &*.#("+ k-'+/,+ /,1 *",. -D (1l? 8D /# 1D,+(#2 #!."& &*.#("+ /(%+(B J*'#(C ) k &#(+3 nm3.? l ',#&! +# -(#3 1D(*H+ (+# &C( +# -'+/ 1 %&'.6(0,,+(0,! +# + #'+# 0,!"-'1(#2 (!<&(0,2 k/,& * ## +"#("+3 *7? *6'.? 3.??? l3 # /",/ - / 7"&! / /(!.1(J2 /.,(/0,D 11 /#. &#, $ -'+/,+ /,1 *",. -D (1 )? Z",& -"++ &,+ A!.1 /(!.1 -, #:. - -('%&'!! k', / +/ - Z (&* l 0, &#(+ '.. 11 $ &2/ ', )3 +",/.",C"+/ *(# & 1D"&%'+(%&'!! -D,+ +#&.&(/? D(+B 7"&!'#("+ & 1'#("++ 11 : /# -"++2 /",/ 7"&! - #&'(#/ 1' *"!."/'+# 4 &.&2B / +# & ' 2#2 *"+C +'<1! +# "&-"++2-7'#"+ 4 * 0, 1D,+ - / -(! +/("+/ -.&2/ +#'#("+. &! ## #&5/ /(!.1! +# - C(/,'1(/ & 1' & 1'#("+ -D"&-&,#(1 k1 +(B C ', 6(2&'&*6(0, l +J+ 1 / /,L #/ /"+# (- +#(J2/.'& - / # A# / -D,+!"-'1(#2 (!<&(0,2 k1,&/ +"!/l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

15 ? G F G G G EF G GF G G GF G FGFE n [\[\ a `di` deaecf d `daecf edb i f`dd f a i d edd %+ ',#& #:. - & 1'#("+/ /,/*.#(<1 -D>#& #&'+/*&(# /,&,+ - //(+ + -,A -(! +/("+/ /# * 1,( - / & 1'#("+/ #!."& 11 /? 81'//(0,! +# = -'+/ 1 /.':/ - *,1#,& %&2*"B1'#(+ = 3 1D2*",1! +# -, #!./3 1"&/0, 1D"+ -"(# 1 &.&2/ +# & AB.1(*(#! +# /,&,+ /,.."&# %&'.6(0, 3 /# J%,&2 - %',*6 4 -&"(#? ' J%,&? +!"+#&,+ A!.1 7'!(1( &?? j 1' *215<&.1'+*6 &.&2/ +#'+# 1D2C"1,#("+ - 1D6"!! / 1"+ '& (+3 /",B C +# &.&"-,(# # *'&(*'#,&2? %',*6 4 -&"(# 3 1 / '+#6&".".(#650, / *"+-,(/ +# ',A 6"!! / 1 /.1,/ 2C"1,2/? 8 ## (11,/#&'#("+ /#!.&,+#2 4,+ *6'.(#& (+#(#,12 $ *"+"%&'.6( -D,+.&2L,%2 ) -D,+ ",C&'% + ': ",1- k G G G G G E G G EF? Z'&(/ k*"11? +*,C &# )l3 nn l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