A treatise on spherical trigonometry, and its application to geodesy and astronomy, with numerous examples. By John Casey.

and collections of problems (such as Wolstenholme's). Chapters v. and vi. (on triangles and quadrilaterals) contain an
exceedingly interesting store of results, numbered for reference
in the manner the writer has adopted in his previous books....
Adopting a practice introduced in one or two recent works on the
subject, Dr. Casey assigns a sufficient space to the explanation of
the hyperbolic series and cosines, and introduces some other
functions to the student. It will be inferred that the present
work is independent of the author's small introductory bookin fact, no reference whatever, we believe, is made to it. This
treatise contains everything that one could expect, and, besides,
has fresh matter-a section on interpolation, and one or two
other small things-which we have not hitherto come across in
similar works."
From the " EDUCATIONAL TIMES," OCt. 1, 1888.
"This treatise is very comprehensive, and quite sustains the
author's reputation as a writer of mathematical text-books.
While including all the usual propositions, Dr. Casey has, as
usual, found room for much interesting matter derived from
continental writers. The exercises are made to introduce much
of the modern geometry of the triangle, and the chapters on
triangles and quadrilaterals, one of the main features of the
work, contain a large number of elegant and useful propositions.
Imaginary angles and hyperbolic functions are fully treated,
while an innovation is made by introducing the angle r, Hoiel's
hyperbolic amplitude of 0. Dr. Casey fully recognises the value
of these functions, 'and their great and increasing importance
not only in pure mathematics but in mathematical physics.'..
From the " PRACTICAL TEACHER," Oct. 1888.
"The book which we have before us contains, we believe, the
most remarkable and complete treatment of its subject which has
yet appeared in the English language. Too many writers have
supposed that a knowledge of trigonometry only was necessary
to enable them to write a book thereupon, and it has been rare,
indeed, that a writer in every direction as competent as Dr. Casey,
or with a mathematical eyesight so far-reaching, has grappled
with an elementary subject like the present. Dr. Casey, fortunately for us, was known as an eminent mathematician before
he became a writer of text-books. His investigations into
geometry and higher algebra have gained him a European reputation; and when the first of his class text-books, the ' Sequel to
Euclid,' appeared some years ago, we welcomed it in these
columns as 'extraordinarily neat,' and extremely satisfactory
even in the form it then assumed, which has since, in subsequent
editions, been improved almost out of all likeness to its former
self. This was followed in the course of last year by an equally
remarkable treatise on analytical geometry, and it is little to be
wondered at, therefore, if we open the present volume with very
high anticipations. Nor are we disappointed. Alike in grasp
and clearness, this book outdistances its only real rival, the
venerable Todhunter. Of course we cannot help differing in a
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