(notes by R. Bigoni)

Let *P* be a point on the ellipse ε and let *F'* and
*F''* be the foci of ε

It can be demonstrated that **the sum of the measures of the segments PF' and
PF'' is equal to the measure of the major semiaxis of ε, that is 2a**.

Let ρ be the measure of the segment *F'P*, *r* that of the segment
*F''P* and 2*c* that of the segment *F'F''*.

Let's consider the triangle *F'F''P*. From the
law of cosines we have

Since *c = a e*

From the polar equation of ε we obtain

and, by substituting this in the (3)

Finally, remembering that

we can deduce that