### 11.17.3 Harmonic division: harmonic_division

Four collinear points A,B,C and D are in harmonic division if
CA/CB = DA/DB . In
this case, D is called the harmonic conjugate of A, B and C.

Four concurrent lines or four parallel lines are in harmonic division
if the intersection of any fifth line with these four lines consists
of four points in harmonic division. The lines are also said to form a harmonic
pencil. The fourth line is called the harmonic conjugate of the first
three.

The harmonic_division command takes as argument three
collinear points or three concurrent lines and a variable name.

harmonic_division returns and draws the three points or
lines along with a fourth so the four objects are in harmonic
division, and assigns the fourth point or line to the variable name.

Input:

harmonic_division(0,2,3/2,D)

Output:

Input:

harmonic_division(point(0),point(2),point(3/2),D)

Output:

Input:

affix(D)

Output:

3