The method of differences is, in fact, a method of additions; and as it includes within its means a larger number of results attainable by addition simply, than any other mathematical principle, it was very appropriately selected as the basis on which to construct an Adding Machine, so as to give to the powers of such a machine the widest possible range.

In abstract mathematics, of course operations alter those particular relations which are involved in the considerations of number and space, and the results of operations are those peculiar results which correspond to the nature of the subjects of operation.

The Analytical Engine is an embodying of the science of operations, constructed with peculiar reference to abstract number as the subject of those operations.

Forget this world and all its troubles and if possible its multitudinous Charlatans-- everything in short but the Enchantress of Numbers.

Forget this world and all its troubles and if possible