FIGURE CabriII vers. MS-Windows 1.0

Window center x: -0.3175 y: 2.54 Window size x: 20.6163333333333 y: 11.4935

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
Gr, W, t, DS:1 1, GT:0, I, nSt
Const: 1, Val: 1 0, 0 1

3: Pt, 0, CN:0, VN:1
R, W, t, DS:1 1, GT:1, I, nSt
Val: -2.921 1.3335

4: Line, 0, CN:1, VN:2
R, W, t, DS:1 1, GT:0, V, nSt
Const: 3, Val: 0.96561575852067 -0.259973473447873

5: Pt, 0, CN:0, VN:1
R, W, t, DS:1 1, GT:1, I, nSt
Val: -2.9845 -3.66183333333333

6: Line, 0, CN:1, VN:2
Bl, W, t, DS:1 1, GT:0, V, nSt
Const: 5, Val: 9.9695 0.4445

"A", NP: -268, -90, NS: 14, 22
7: Pt/, 0, CN:1, VN:3
R, W, t, DS:1 1, GT:1, V, nSt
Const: 4, Val: -5.588 2.05153846153846
p: 0, Verdana, S: 17 C: 3 Fa: 0

"B", NP: -79, -36, NS: 14, 22
8: Pt/, 0, CN:1, VN:3
R, W, t, DS:1 1, GT:1, V, nSt
Const: 4, Val: -1.54516666666667 0.963083333333334
p: 0, Verdana, S: 17 C: 3 Fa: 0

"C", NP: 94, 2, NS: 14, 22
9: Pt/, 0, CN:1, VN:3
R, W, t, DS:1 1, GT:1, V, nSt
Const: 4, Val: 1.9685 0.0170961538461522
p: 0, Verdana, S: 17 C: 3 Fa: 0

"C'", NP: 106, 165, NS: 19, 22
10: Pt/, 0, CN:1, VN:3
R, W, t, DS:1 1, GT:1, V, nSt
Const: 6, Val: 2.25080665304159 -3.42841201759262
p: 0, Verdana, S: 17 C: 3 Fa: 0

"B'", NP: -53, 170, NS: 19, 22
11: Pt/, 0, CN:1, VN:3
R, W, t, DS:1 1, GT:1, V, nSt
Const: 6, Val: -1.16168067950779 -3.58056113433049
p: 0, Verdana, S: 17 C: 3 Fa: 0

"A'", NP: -245, 183, NS: 19, 22
12: Pt/, 0, CN:1, VN:3
R, W, t, DS:1 1, GT:1, V, nSt
Const: 6, Val: -5.18883964338594 -3.76011599259258
p: 0, Verdana, S: 17 C: 3 Fa: 0

13: Line, 0, CN:2, VN:2
V, W, t, DS:1 1, GT:0, I, nSt
Const: 7 11

14: Line, 0, CN:2, VN:2
V, W, t, DS:1 1, GT:0, I, nSt
Const: 7 10

15: Line, 0, CN:2, VN:2
V, W, t, DS:1 1, GT:0, I, nSt
Const: 9 11

16: Line, 0, CN:2, VN:2
V, W, t, DS:1 1, GT:0, I, nSt
Const: 9 12

17: Line, 0, CN:2, VN:2
V, W, t, DS:1 1, GT:0, I, nSt
Const: 8 12

18: Line, 0, CN:2, VN:2
V, W, t, DS:1 1, GT:0, I, nSt
Const: 8 10

"Q", NP: -39, 72, NS: 15, 22
19: Int, 0, CN:2, VN:1
dG, W, t, DS:1 1, GT:1, V, nSt
Const: 16 14
p: 0, Verdana, S: 17 C: 9 Fa: 0

"P", NP: -152, 57, NS: 12, 22
20: Int, 0, CN:2, VN:1
dG, W, t, DS:1 1, GT:1, V, nSt
Const: 17 13
p: 0, Verdana, S: 17 C: 9 Fa: 0

"R", NP: 24, 77, NS: 14, 22
21: Int, 0, CN:2, VN:1
dG, W, t, DS:1 1, GT:1, V, nSt
Const: 18 15
p: 0, Verdana, S: 17 C: 9 Fa: 0

22: Line, 0, CN:2, VN:2
dG, W, t, DS:1 1, GT:0, V, nSt
Const: 20 21

23: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 7 19

24: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 10 7

25: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 7 20

26: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 20 11

27: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 11 7

28: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 8 20

29: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 20 12

30: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 12 8

31: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 9 12

32: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 12 19

33: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 19 9

34: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 9 21

35: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 21 11

36: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 10 21

37: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 21 8

38: Seg, 0, CN:2, VN:0
V, W, t, DS:1 1, GT:0, V, nSt
Const: 8 10

39: Text, 0, CN:0, VN:1
R, W, BTh:2, DS:1 1, GT:0, V, nSt
Val: -162 -279 0, nA, nP, TP: -3.429, 5.9055,TS: 8.27616666666667, -2.58233333333333
"Pappus's Theorem

A, B and C are collinear, as are A' B' and C'.
AB' and A'B meet in P, AC' and A'C in Q, and BC' and B'C in R.
Then P, Q and R are collinear"
p: 0, Verdana, S: 17 C: 3 Fa: 0

40: Text, 0, CN:0, VN:1
dG, W, BTh:2, DS:1 1, GT:0, V, nSt
Val: -160 -158 0, nA, nP, TP: -3.38666666666667, 3.34433333333333,TS: 7.21783333333333, -1.73566666666667
"Move A to see that P, Q and R remain collinear for all choices.
Move the line ABC to see that they are collinear for any pair of lines"
p: 0, Verdana, S: 17 C: 9 Fa: 0

41: Text, 0, CN:0, VN:1
Br, W, BTh:2, DS:1 1, GT:0, V, nSt
Val: 93 -86 0, nA, nP, TP: 1.9685, 1.82033333333333,TS: 5.92666666666667, -1.73566666666667
"You can get degenerate cases by, for example, moving A to lie on top of B (then P coincides with them)."
p: 0, Verdana, S: 17 C: 10 Fa: 0