Even though some of the mechanics had been invented before
him, and even though his ideas would not become practical for a
hundred years, Babbage’s engine was revolutionary.
The Difference Engine was designed to approximate the
solutions of polynomial functions using Newton’s method of
divided differences for the construction of astronomical and
mathematical tables. This machine was cranked by hand.
The Analytical Engine, in contrast, was designed as a
Ada Lovelace wrote her program to calculate the sequence of
Bernoulli numbers as an illustration for her translation of Luigi
Menabrea’s memoir on the Analytical Engine.
See also in The book of science:
Readings on wikipedia: