It is however pretty evident, on general principles, that in devising for mathematical truths a new form in which to record and throw themselves out ….

The more I study, the more insatiable do I feel my genius for it to be..

One main reason why the separate nature of the science of operations has been little felt, and in general little dwelt on, is the shifting meaning of….

Indeed we may consider the engine as the material and mechanical representative of analysis, and that our actual working powers in this department of….

The Difference Engine can in reality (as has been already partly explained) do nothing but add; and any other processes, not excepting those of simpl….

The intellectual, the moral, the religious seem to me all naturally bound up and interlinked together in one great and harmonious whole..

That brain of mine is something more than merely mortal; as time will show..

Thus not only the mental and the material, but the theoretical and the practical in the mathematical world, are brought into more intimate and effect….

Understand well as I may, my comprehension can only be an infinitesimal fraction of all I want to understand..

This one fact implies everything; and it is scarcely necessary to point out, for instance, that while the Difference Engine can merely tabulate, and ….

Secondly, figures, the symbols of numerical magnitude, are frequently also the symbols of operations, as when they are the indices of powers. Whereve….

The further we analyse the manner in which such an engine performs its processes and attains its results, the more we perceive how distinctly it plac….

We might even invent laws for series or formula in an arbitrary manner, and set the engine to work upon them, and thus deduce numerical results which….

In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical ana….

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 s….

The Analytical Engine might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those o….

We cannot forbear suggesting one practical result which it appears to us must be greatly facilitated by the independent manner in which the engine or….

The Analytical Engine, on the contrary, can either add, subtract, multiply or divide with equal facility; and performs each of these four operations ….

It were much to be desired, that when mathematical processes pass through the human brain instead of through the medium of inanimate mechanism, it we….

A new, a vast, and a powerful language is developed for the future use of analysis, in which to wield its truths so that these may become of more spe….

One essential object is to choose that arrangement which shall tend to reduce to a minimum the time necessary for completing the calculation..