The footnotes cover all the statements of the text except a few matters of common knowledge, but of course a fact once proved is not proved again. To some readers the number of references will seem unnecessarily great, and so they appear to the author himself. But as almost every foot of the ground is controversial, the per centage that could safely be omitted is rather small, and the saving would hardly justify the abandonment of a complete and logical system for one of the opposite character. In order not to fill the page with annoying figures, the references — standing in the order of the statements they support — are grouped by paragraphs, and an indication of the bearing of the reference is given when this is not obvious. Naturally in some cases a citation confirms more than a single sentence, and it should be remembered, too, that for reasons of convenience the first page of a document is the one specified unless there is a particular occasion for doing otherwise. To carry such a body of figures with perfect accuracy through the processes of compiling, revising, copying and printing is extremely difficult, especially as the author's attention is liable to be diverted momen tafily from the mathematics to the meaning of the citation; but it can be said that unsparing pains have been taken to ensure correct ness, and that a trained historical worker has gone over the entire work of verification independently.