And a little more... (Regarding Charles Babbage)
"In 1821 Babbage invented an Engine to manufacture error-free mathematical tables, Difference Engine No.1, the world's first programmable automatic digital calculating machine, in which the only human intervention was the setting of the machine at the start of the production of a table and the turning of its handle."
"It was a machine embodying the mathematical principles of the Method of Differences using only mechanisms for addition repeated many times over."
It must be admitted, rather reluctantly, that this machine, and its later versions, never quite got into production in a way that made a significant impact on society -- but the mechanical design was correct in its application, and would have made an enormous "difference" in our histories had it been completed.
It was, literally, the first computer -- nearly two hundred years ago!!
http://www.csc.liv.ac.uk/~ped/teachadmin/histsci/htmlform/lect4.html
The history of calculating machines post-Leibniz can - admittedly with hindsight - be seen as a series of ideas and technological advances that progressively dealt with these lacunae. With the sole exception of the final point, ideas relating to all of these aspects were developed in the 19th century. In this lecture we shall examine the work of, principally, three people - Joseph-Marie Jacquard (1752-1834); Charles Babbage (1791-1871); and George Boole (1815-64) - and their contribution to the development of computational devices.