In the present edition those
due to the former are signed A. De M., and those due to Mrs. De Morgan
appear with her initials, S. E. De M. For all other footnotes the present
editor is responsible. In preparing them the effort has been made to
elucidate the text by supplying such information as the casual reader might
wish as he passes over the pages. Hundreds of names are referred to in the
text that were more or less known in England half a century ago, but are
now forgotten there and were never familiar elsewhere. Many books that were
then current have now passed out of memory, and much that agitated England
in De Morgan's prime seems now like ancient history. Even with respect to
well-known names, a little information as to dates and publications will
often be welcome, although the editor recognizes that it will quite as
often be superfluous. In order, therefore, to derive the pleasure that
should come from reading the Budget, the reader should have easy access to
the information that the notes are intended to supply. That they furnish
too much here and too little there is to be expected. They are a human
product, and if they fail to serve their purpose in all respects it is
hoped that this failure will not seriously interfere with the reader's
pleasure.

In general the present editor has refrained from expressing any opinions
that would strike a discordant note in the reading of the text as De Morgan
left it. The temptation is great to add to the discussion at various
points, but it is a temptation to be resisted. To furnish such information
as shall make the reading more pleasant, rather than to attempt to improve
upon one of the most delicious bits of satire of the nineteenth century,
has been the editor's wish. It would have been an agreeable task to review
the history of circle squaring, of the trisection problem, and of the
duplication of the cube. This, however, would be to go too far afield. For
the benefit of those who wish to investigate the subject the editor can
only refer to such works and articles as the following: F. Rudio,
_Archimedes, Huygens, Lambert, Legendre,--mit einer Uebersicht ueber die
Geschichte des Problemes von der Quadratur des Zirkels_, Leipsic, 1892;
Thomas Muir, "Circle," in the eleventh edition of the _Encyclopaedia
Britannica_; the various histories of mathematics; and to his own article
on "The Incommensurability of [pi]" in Prof. J. W. A. Young's _Monographs
on Topics of Modern Math