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18 ''at Cambridge. About four hundred examples were added to the second'' edition, mainly collected from the Examination Papers of the last ten ''years. In this edition several new articles have been added, the examples'' have been largely increased, and a series of Examination Papers appended.

The author having felt the want of a short treatise to be used as a Text-Book after the Sixth Book of Euclid had been learned and some knowledge of Algebra acquired, which should contain satisfactory de&shy;monstrations of the propositions to be used in teaching Junior Students the solution of Triangles, and should at the same time lay a solid foundation for the study of Analytical Trigonometry, thinking that others may have felt the same want, has attempted to supply it by the publication of this little work.

Professor Boole has endeavoured in this treatise to convey as complete an account of the present state of knowledge on the subject of Differential Equa&shy;tions as was consistent with the idea of a work intended, primarily, for ''elementary instruction. The earlier sections of each chapter contain that'' kind of matter which has usually been thought suitable for the beginner, while the latter ones are devoted either to an account of recent discovery, or the discussion of such deeper questions of principle as are likely to present themselves to the reflective student in connection with the methods and ''processes of his previous course. “A treatise incomparably superior to'' any other elementary book on the same subject with which we are acquainted.” —.