Figure CabriII vers. MacOS 1.1.8

Used macro(s):

Centre d'une conique, no name
Icon:
000000FFFFFF00F0
0000FF000000FFF0
000FF00000000FF0
00FF0000000000F0
00FF0000000000F0
0FF0000000000000
0FF0000000000000
0FF0000000000000
0FF0000000000000
0FF0000000000000
0FF0000000000000
00FF000000000000
00FF0000000000F0
000FF00000000FF0
0000FF000000FF00
000000FFFFFF0000
Mth: 0
CN:1, ON:31, FN:1, PO:30
CT:
conic, CS 5, Bl, W, t, DS:1 1, GT:0, V, nSt
Const:
Seg, Mth:0, 0, 0, CN:2, VN:2, Const: 3 2
Par, Mth:0, 0, 0, CN:2, VN:2, Const: 4 7
Line, Mth:1, 0, 0, CN:2, VN:2, Const: 4 1
Line, Mth:1, 0, 0, CN:2, VN:2, Const: 3 5
Int, Mth:0, 0, 0, CN:2, VN:1, Const: 9 10
Line, Mth:1, 0, 0, CN:2, VN:2, Const: 2 1
Par, Mth:0, 0, 0, CN:2, VN:2, Const: 11 8
Int, Mth:0, 0, 0, CN:2, VN:1, Const: 12 13
Line, Mth:1, 0, 0, CN:2, VN:2, Const: 5 14
Int, Mth:0, 0, 0, CN:2, VN:1, Const: 8 15
Seg, Mth:0, 0, 0, CN:2, VN:2, Const: 16 4
Seg, Mth:0, 0, 0, CN:2, VN:2, Const: 2 3
Seg, Mth:0, 0, 0, CN:2, VN:2, Const: 3 5
Par, Mth:0, 0, 0, CN:2, VN:2, Const: 2 19
Line, Mth:1, 0, 0, CN:2, VN:2, Const: 2 1
Line, Mth:1, 0, 0, CN:2, VN:2, Const: 3 4
Int, Mth:0, 0, 0, CN:2, VN:1, Const: 21 22
Line, Mth:1, 0, 0, CN:2, VN:2, Const: 5 1
Par, Mth:0, 0, 0, CN:2, VN:2, Const: 23 20
Int, Mth:0, 0, 0, CN:2, VN:1, Const: 24 25
Line, Mth:1, 0, 0, CN:2, VN:2, Const: 4 26
Int, Mth:0, 0, 0, CN:2, VN:1, Const: 20 27
Seg, Mth:0, 0, 0, CN:2, VN:2, Const: 2 28
Seg, Mth:0, 0, 0, CN:2, VN:2, Const: 3 5
Mid, Mth:1, 0, 0, CN:1, VN:1, Const: 18
Mid, Mth:1, 0, 0, CN:1, VN:1, Const: 17
Mid, Mth:1, 0, 0, CN:1, VN:1, Const: 29
Mid, Mth:1, 0, 0, CN:1, VN:1, Const: 30
Line, Mth:1, 0, 0, CN:2, VN:2, Const: 31 32
Line, Mth:1, 0, 0, CN:2, VN:2, Const: 33 34
Int, Mth:0, 1, 0, CN:2, VN:1, Const: 35 36, R, W, t, DS:1 1, GT:1, V, nSt

Figure description:

Window center x: 2.8 y: 2.33_

1: Pt, 0, CN:0, VN:1
R, W, t, DS:1 1, GT:1, I, nSt
Val: 0 0

2: Axes, 1, CN:1, VN:3
Y, W, t, DS:1 1, GT:0, I, nSt
Const: 1, Val: 1 0, 0 1

"y1", NP: 3, -34, NS: 20, 19
3: Pt, 0, CN:0, VN:1
R, W, t, DS:1 1, GT:1, V, nSt
Val: -0.0190926702896145 1.15093506791008
p: 0, Times, S: 14 C: 6 Fa: 0, p: 1, Times, S: 12 C: 6 Fa: 512

4: Pt, 0, CN:0, VN:1
R, W, t, DS:1 1, GT:1, V, nSt
Val: -1.61274174715419 0.567345265114607

5: Pt, 0, CN:0, VN:1
R, W, t, DS:1 1, GT:1, V, nSt
Val: -2.42078916640947 -2.28326646392484

6: Pt, 0, CN:0, VN:1
R, W, t, DS:1 1, GT:1, V, nSt
Val: 0.182919184524205 -1.69967666112937

7: Pt, 0, CN:0, VN:1
R, W, t, DS:1 1, GT:1, V, nSt
Val: 2.2030377326624 0.297996125362848

8: Con, 1, CN:5, VN:6
Bl, W, t, DS:1 1, GT:0, V, nSt
Const: 3 4 5 6 7

Ma: Centre d'une conique, Const: 8 i: 0
"O", NP: -18, 19, NS: 17, 15
39: Ma R, F No1, VN:1
R, W, t, DS:1 1, GT:1, V, nSt
p: 0, Times, S: 14 C: 6 Fa: 0

"x", NP: -108, -18, NS: 14, 15
40: Pt, 0, CN:0, VN:1
R, W, t, DS:1 1, GT:1, V, nSt
Val: -3.56_ 0.66_
p: 0, Times, S: 14 C: 3 Fa: 0

41: Ray, 0, CN:2, VN:2
lGr, W, t, DS:1 1, GT:0, I, nSt
Const: 39 40

"x1", NP: -69, 0, NS: 20, 19
42: Int, 256, CN:2, VN:1
R, W, t, DS:1 1, GT:1, V, nSt
Const: 41 8
p: 0, Times, S: 14 C: 6 Fa: 0, p: 1, Times, S: 12 C: 6 Fa: 512

43: Seg, 0, CN:2, VN:2
lBl, W, t, DS:1 1, GT:0, V, nSt
Const: 42 3

44: Line, 0, CN:2, VN:2
P, W, t, DS:1 1, GT:0, V, nSt
Const: 39 3

45: Line, 0, CN:2, VN:2
Br, W, t, DS:1 1, GT:0, V, nSt
Const: 39 42

46: Par, 0, CN:2, VN:2
lBl, W, t, DS:1 1, GT:0, V, nSt
Const: 40 43

"x sur (Oy1)", NP: 18, -72, NS: 73, 19
47: Int, 0, CN:2, VN:1
R, W, t, DS:1 1, GT:1, V, nSt
Const: 44 46
p: 0, Times, S: 14 C: 4 Fa: 0, p: 9, Times, S: 12 C: 4 Fa: 512, p: 10, Times, S: 14 C: 4 Fa: 0

48: Seg, 0, CN:2, VN:2
G, W, t, DS:1 1, GT:0, V, nSt
Const: 42 47

49: Par, 0, CN:2, VN:2
G, W, t, DS:1 1, GT:0, V, nSt
Const: 40 48

"q(x) sur (Oy1)", NP: 39, -140, NS: 90, 19
50: Int, 0, CN:2, VN:1
R, W, t, DS:1 1, GT:1, V, nSt
Const: 44 49
p: 0, Times, S: 14 C: 4 Fa: 0, p: 12, Times, S: 12 C: 4 Fa: 512, p: 13, Times, S: 14 C: 4 Fa: 0

51: Par, 0, CN:2, VN:2
lBl, W, t, DS:1 1, GT:0, V, nSt
Const: 50 43

"q(x) sur (Ox)", NP: -161, -55, NS: 84, 15
52: Int, 0, CN:2, VN:1
R, W, t, DS:1 1, GT:1, V, nSt
Const: 45 51
p: 0, Times, S: 14 C: 3 Fa: 0

53: Text, 0, CN:0, VN:1
B, W, BTh:1, DS:1 1, GT:0, V, nSt
Val: -225 -244 0, A, nP, TP: -7.5, 8.13_, TS: 14.16_, -2.16_
"Pour construire q(x) on utilise que q(ax) = a2q(x)
On est donc ramen� � construire le carr� de a dans le rep�re affine (O, x1, y1) o� x1 est le vecteur x/||x|| - donc R+-colin�aire � x - et y1 et un point quelconque de la conique."
p: 0, Times, S: 12 C: 5 Fa: 0, p: 39, Symbol, S: 12 C: 5 Fa: 0, p: 39, Times, S: 12 C: 5 Fa: 0, p: 45, Symbol, S: 10 C: 5 Fa: 256, p: 45, Times, S: 10 C: 5 Fa: 256, p: 46, Times, S: 12 C: 5 Fa: 0, p: 96, Symbol, S: 12 C: 5 Fa: 0, p: 96, Times, S: 12 C: 5 Fa: 0, p: 124, Times, S: 10 C: 5 Fa: 512, p: 125, Times, S: 12 C: 5 Fa: 0, p: 128, Times, S: 10 C: 5 Fa: 512, p: 129, Times, S: 12 C: 5 Fa: 0, p: 135, Times, S: 10 C: 5 Fa: 512, p: 136, Times, S: 12 C: 5 Fa: 0, p: 168, Times, S: 10 C: 5 Fa: 256, p: 169, Times, S: 12 C: 5 Fa: 0, p: 191, Times, S: 10 C: 5 Fa: 512, p: 192, Times, S: 12 C: 5 Fa: 0

54: Text, 0, CN:0, VN:1
B, W, BTh:1, DS:1 1, GT:0, V, nSt
Val: 123 -91 0, A, nP, TP: 4.1, 3.03_, TS: 7.8, -5.13_
"Construction :

La parall�le � (x1y1) passant par x coupe l'axe (Oy1) en un point d'abscisse x sur (Oy1) dans le rep�re (O, y1).

On poursuit par la construction usuelle du carr� sur l'axe (Oy1), par le th�or�me de Thales, et on ram�ne cette valeur sur (Ox1) pour avoir a2 c'est-�-dire q(x) dans le rep�re (O x1)."
p: 0, Times, S: 12 C: 10 Fa: 4, p: 12, Times, S: 12 C: 10 Fa: 0, p: 16, Times, S: 12 C: 11 Fa: 0, p: 33, Times, S: 10 C: 11 Fa: 512, p: 34, Times, S: 12 C: 11 Fa: 0, p: 35, Times, S: 10 C: 11 Fa: 512, p: 36, Times, S: 12 C: 11 Fa: 0, p: 67, Times, S: 10 C: 11 Fa: 512, p: 68, Times, S: 12 C: 11 Fa: 0, p: 102, Times, S: 10 C: 11 Fa: 512, p: 103, Times, S: 12 C: 11 Fa: 0, p: 125, Times, S: 10 C: 11 Fa: 512, p: 126, Times, S: 12 C: 11 Fa: 0, p: 192, Times, S: 10 C: 11 Fa: 512, p: 193, Times, S: 12 C: 11 Fa: 0, p: 256, Times, S: 10 C: 11 Fa: 512, p: 257, Times, S: 12 C: 11 Fa: 0, p: 271, Times, S: 10 C: 11 Fa: 256, p: 272, Times, S: 12 C: 11 Fa: 0, p: 310, Times, S: 10 C: 11 Fa: 512, p: 311, Times, S: 12 C: 11 Fa: 0