I. Once upon a time, long long ago, I learned how to reduce a fraction to its lowest terms. Whether I could still perform that operation is uncertain; but the discipline involved in early training had its uses, since it taught me that in order to understand the essential nature of anything it is well to strip it of all superficial and irrelevant accretions -- in short, to reduce it to its lowest terms. That operation I now venture, with some apprehension and all due apologies, to perform on the subject of history. I ought first of all to explain that when I use the term history I mean knowledge of history. No doubt throughout all past time there actually occurred a series of events which, whether we know what it was or not, constitutes history in some ultimate sense. Nevertheless, much the greater part of these events we can know nothing about, not even that they occurred; many of them we can know only imperfectly; and even the few events that we think we know for sure we can never be absolutely certain of, since we can never revive them, never observe or test them directly. The event itself once occurred, but as an actual event it has disappeared; so that in dealing with it the only objective reality we can observe or test is some material trace which the event has left -- usually a written document. With these traces of vanished events, these documents, we must be