Le théorème de Newton
On a quatre droites A,B,C,D et une transversale Z
Les conjugués i,j,k de p,q,r par rapport à b,b';c,c';d,d' sont alignés.

b = (-2.718657718120806, -2.889385307346326)
c = (-2.3932885906040275, -1.8822488755622184)
d' = (-1.6813422818791957, -2.889385307346326)
B = Line(b, d')
A = Line(b, c)
C = Line(c, d')
d = Point(A)
b' = Point(C)
D = Line(d, b')
c' = Intersect(B, D)
e = Line(c, c')
f = Line(d', d)
g = Line(b, b')
p = Point(g)
r = Point(f)
Z = Line(p, r)
q = Intersect(e, Z)
E = Intersect(A, Z)
F = Intersect(D, Z)
a = Segment(E, b')
h = Segment(b, F)
G = Intersect(a, h)
i_1 = Line(d, G)
i = Intersect(g, i_1)
H = Intersect(A, Z)
I = Intersect(B, Z)
j_1 = Line(I, c)
k_1 = Line(H, c')
J = Intersect(j_1, k_1)
l = Line(b, J)
j = Intersect(e, l)
m = Line(j, i)
k = Intersect(f, m)
s = Distance(k, d)
Textekd: Name[k] + (Name[d]) + " \, = \, " + s
t = Distance(k, d')
Textekd': Name[k] + (Name[d']) + " \, = \, " + t
u = Distance(r, d)
Texterd: Name[r] + (Name[d]) + " \, = \, " + u
v = Distance(r, d')
Texterd': Name[r] + (Name[d']) + " \, = \, " + v
kd = Distance(k, d)
n: s / t
o: u / v