If Mrs. De Morgan felt called upon to confess her hesitation at taking upon
herself the labor of editing these Paradoxes, much more should one who was
born two generations later, who lives in another land and who was reared
amid different influences, confess to the same feeling when undertaking to
revise this curious medley. But when we consider the nature of the work,
the fact that its present rarity deprives so many readers of the enjoyment
of its delicious satire, and the further fact that allusions that were
commonplace a half century ago are now forgotten, it is evident that some
one should take up the work and perform it _con amore_.
Having long been an admirer of De Morgan, having continued his work in the
bibliography of early arithmetics, and having worked in his library among
the books of which he was so fond, it is possible that the present editor,
whatever may be his other shortcomings, may undertake the labor with as
much of sympathy as any one who is in a position to perform it. With this
thought in mind, two definite rules were laid down at the beginning of the
task: (1) That no alteration in the text should be made, save in slightly
modernizing spelling and punctuation and in the case of manifest
typographical errors; (2) That whenever a note appeared it should show at
once its authorship, to the end that the material of the original edition
might appear intact.
In considering, however, the unbroken sequence of items that form the
Budget, it seems clear that readers would be greatly aided if the various
leading topics were separated in some convenient manner. After considerable
thought it was decided to insert brief captions from time to time that
might aid the eye in selecting the larger subjects of the text. In some
parts of the work these could easily be taken from the original folio
heads, but usually they had to be written anew. While, therefore, the
present editor accepts the responsibility for the captions of the various
subdivisions, he has endeavored to insert them in harmony with the original
text.
As to the footnotes, the first edition had only a few, some due to De
Morgan himself and others to Mrs. De Morgan. 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 Mathematics_, New York, 1911.
The editor wishes to express his appreciation and thanks to Dr. Paul Carus,
editor of _The Monist_ and _The Open Court_ for the opportunity of
undertaking this work; to James Earl Russell, LL.D., Dean of Teachers
College, Columbia University, for his encouragement in its prosecution; to
Miss Caroline Eustis Seely for her intelligent and painstaking assistance
in securing material for the notes; and to Miss Lydia G. Robinson and Miss
Anna A. Kugler for their aid and helpful suggestions in connection with the
proof-sheets. Without the generous help of all five this work would have
been impossible.