"Meum est propositum genti imperitæ
Artes frugi reddere melioris vitæ."[[668]]
To this end I have spoken with freedom of books as books, of opinions as opinions, of ignorance as ignorance, of
presumption as presumption; and of writers as I judge may be fairly inferred from what they have written. Some—to whom I am therefore under great obligation—have permitted me to enlarge my plan by assaults to which I have alluded; assaults which allow a privilege of retort, of which I have often availed myself; assaults which give my readers a right of partnership in the amusement which I myself have received.
For the present I cut and run: a Catiline, pursued by a chorus of Ciceros, with Quousque tandem? Quamdiu nos? Nihil ne te?[[669]] ending with, In te conferri pestem istam jam pridem oportebat, quam tu in nos omnes jamdiu machinaris! I carry with me the reflection that I have furnished to those who need it such a magazine of warnings as they will not find elsewhere; a signatis cavetote:[[670]] and I throw back at my pursuers—Valete, doctores sine doctrina; facite ut proxima congressu vos salvos corporibus et sanos mentibus videamus.[[671]] Here ends the Budget of Paradoxes.
APPENDIX.
I think it right to give the proof that the ratio of the circumference to the diameter is incommensurable. This method of proof was given by Lambert,[[672]] in the Berlin Memoirs for 1761, and has been also given in the notes to Legendre's[[673]] Geometry, and to the English translation of the same. Though not elementary algebra, it is within the reach of a student of ordinary books.[[674]]
Let a continued fraction, such as