Step 1:

Cauchy’s Theorem for a Triangle

As a first step in Cauchy’s theory of integration we consider the closed curve as a triangle.

Step 2:

Cauchy’s Theorem for a star-like domain

As a second more general step in Cauchy’s theory of integration we consider the closed curve as a star-like domain.

Step 3:

Cauchy’s Integral Theorem

We now consider still a more general step where the closed curve is a circle.

Step 4:

Cauchy’s Integral Formula

This generalizes Cauchy’s integral theorem.