Figure Cabri II Plus vers. MS-Windows (MAC 1.40)

Window center x: -0.29cm y: -2.36cm Window size x: 31.43cm y: 22.86cm
Resolution: 28 ppc

1: Pt, Val: 0 0
invisible, 

2: Axes, Const: 1, cart, Val: 1 0 0 1
invisible, 

3: Pt, Val: -12.1842105263158 -0.973684210526316
invisible, 

4: Line, Const: 3, Val: 0.999999386811355 0.00110741903301368
color:Bl, DS:5 8, COLOR 255 0 0, 
"H"
TP:  -12.5714285714286,  -1.10714285714286, TS:  1.07142857142857,  0.821428571428571
p: 0, Arial, S: 12 C: 15 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red0\green67\blue250;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 H}{50,91,151,266,267}

5: Pt, Val: 1.26315789473684 1.44736842105263
thick, 1x1, 
"u"
TP:  0.75,  1.67857142857143, TS:  1.07142857142857,  0.821428571428571
p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 u}{50,91,152,267,268}

6: Pt, Val: -1.84210526315789 3.07894736842105
thick, 1x1, 
"v"
TP:  -1.85714285714286,  3.71428571428571, TS:  1.07142857142857,  0.821428571428571
p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 v}{50,91,152,267,268}

7: PBiss, Const: 5,  6, 
color:Bl, invisible, COLOR 255 0 0, 

9: Int, Const: 4,  7, int ind:0, 
invisible, 

10: Cir, Const: 9,  6, 
invisible, 

12: Int, Const: 4,  10, int ind:0, 
invisible, 

13: Int, Const: 4,  10, int ind:0x10000, 
invisible, 

14: Arc, Const: 12,  6,  13, 
color:R, COLOR 0 0 255, 

15: Pt/, Const: 14, Val: -5.28901297612799 1.36809616581697
thick, 1x1, 
"w"
TP:  -5.75,  1.92857142857143, TS:  1.07142857142857,  0.821428571428571
p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 w}{50,91,152,267,268}

16: Pt/, Const: 4, Val: -8.6578947368421 -0.969779098910066
"a"
TP:  -8.82142857142857,  -1.10714285714286, TS:  1.07142857142857,  0.821428571428571
p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 a}{50,91,152,267,268}

17: Line, Const: 16,  15, 
color:Bl, invisible, COLOR 255 0 0, 

18: Perp, Const: 15,  17, 
color:Bl, invisible, COLOR 255 0 0, 

20: Int, Const: 4,  18, int ind:0, 
"b'"
TP:  -3.64285714285714,  -1.14285714285714, TS:  1.07142857142857,  0.821428571428571
p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 b'}{50,91,152,267,268}

21: Line, Const: 20,  5, 
color:Bl, invisible, COLOR 255 0 0, 

22: Perp, Const: 5,  21, 
color:Bl, invisible, COLOR 255 0 0, 

24: Int, Const: 4,  22, int ind:0, 
"c"
TP:  2.5,  -1.10714285714286, TS:  1.07142857142857,  0.821428571428571
p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 c}{50,91,152,267,268}

25: Line, Const: 24,  6, 
color:Bl, invisible, COLOR 255 0 0, 

26: Perp, Const: 6,  25, 
color:Bl, invisible, COLOR 255 0 0, 

28: Int, Const: 26,  4, int ind:0, 
"a'"
TP:  -5.64285714285714,  -1.14285714285714, TS:  1.07142857142857,  0.821428571428571
p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 a'}{50,91,152,267,268}

29: Line, Const: 28,  15, 
color:Bl, invisible, COLOR 255 0 0, 

30: Perp, Const: 15,  29, 
color:Bl, invisible, COLOR 255 0 0, 

32: Int, Const: 30,  4, int ind:0, 
"b"
TP:  9.46428571428571,  -1.10714285714286, TS:  1.07142857142857,  0.821428571428571
p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 b}{50,91,152,267,268}

33: Line, Const: 32,  5, 
color:Bl, invisible, COLOR 255 0 0, 

34: Perp, Const: 5,  33, 
color:Bl, invisible, COLOR 255 0 0, 

36: Int, Const: 34,  4, int ind:0, 
"c'"
TP:  0.5,  -1.03571428571429, TS:  1.07142857142857,  0.821428571428571
p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 c'}{50,91,152,267,268}

37: Line, Const: 36,  6, 
color:Bl, invisible, COLOR 255 0 0, 

38: Perp, Const: 6,  37, 
color:Bl, invisible, COLOR 255 0 0, 

39: Arc, Const: 16,  15,  20, 
color:Bl, COLOR 255 0 0, 

40: Arc, Const: 20,  5,  24, 
color:Bl, COLOR 255 0 0, 

41: Arc, Const: 24,  6,  28, 
color:Bl, COLOR 255 0 0, 

42: Arc, Const: 28,  15,  32, 
color:Bl, COLOR 255 0 0, 

43: Arc, Const: 32,  5,  36, 
color:Bl, COLOR 255 0 0, 

44: Arc, Const: 36,  6,  16, 
color:Bl, COLOR 255 0 0, 

45: Text, Val: -238 67 0, nA, nP, 
"Le plan de Poincare est le demi-plan superieur ouvert limite par la droite horizon H.
Les points situes sur l'horizon ne font donc pas partie de la geometrie.
Les droites hyperboliques sont les demi-cercles du plan de Poincare orthogonaux a l'horizon.
Les points u,v ,w sont donc alignes dans le plan de Poincare.
Deux droites du plan de Poincare tangentes a l'horizon sont dites ultraparalleles.
Il existe une infinite d'hexagones hyperboliques dont les cotes successifs sont ultra paralleles
et passent successivement par les points u, v, w.
Tirer sur le point a pour le constater.
Ce theoreme n'est qu'une reformulation du theoreme de Pascal dans le plan de Poincare.

Francois Rideau"
TP:  -8.5,  -2.39285714285714, TS:  21.0714285714286,  5.85714285714286
p: 0, Arial, S: 12 C: 40 Fa: 0rtfd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