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

From "NATURE," July 5, 1888.
"Dr. Casey's ' Treatise on Plane Trigonometry' is quite independent of the ' Elementary Trigonometry' by the same author.
It is a most comprehensive work, and quite as exhaustive as any
ordinary student will require. Dr. Casey shows his usual mastery
of detail, due to thorough acquaintance, from long teaching, with
all the cruces of the subject. He has embraced in his pages all
the usual topics, and has introduced several points of extreme
interest from the best foreign text-books. A very rigid proof is
given of the exponential theorem, and a section is devoted to
interpolation.... Chapters v. and vi., which are devoted to
triangles and quadrilaterals, are exceedingly interesting, and contain quite a crop of elegant propositions culled from many fields.
Following the course adopted by other recent writers, he gives a
systematic account of imaginary angles and hyperbolic functions.
'The latter are very interesting, and their great and increasing
importance, not only in pure mathematics but in mathematical
physics, makes it essential that the student should become acquainted with them.' We may remark that Dr. Casey adopts
the following notation: sh, ch, th, coth, sech, cosech, for sin h,
cos h, &c., and has gone further than his English predecessors in
introducing at this early stage the angle T, Hoùel's hyperbolic
amplitude of 0 (r = amh. 0). Numerous illustrative examples
and tables afford practice to the student in this branch...
The special results, which on Dr. Casey's useful plan are numbered
consecutively, reach 810. The book is rich in examples, and will
be sure to find for itself a place on the mathematician's shelves,
within easy reach of his hand."
FrIom the "ATHENETUM," July 21, 1888.
"Dr. Casey is no mere compiler. His heart is evidently in
his work, and nearly every page of it bears the stamp of his
individuality. The space at our disposal does not allow us to
enter into details, but we can conscientiously say that we know
of no work on plane trigonometry which contains so much new
and useful matter, or which contains old matter better treated... The most interesting chapter is the last, which gives an
exposition of imaginary angles and of hyperbolic functionsnovelties, we believe, hitherto in trigonometrical text-books,
though not in mathematical periodicals. The hyperbolic functions are not only interesting from their close resemblance to the
ordinary circular functions, but also important from their increasing
utility in physical problems-two good and sufficient reasons for
placing them early before mathematical students....
PFrom the "ACADEMY," Sept. 22, 1888.
"Dr. Casey's object has been to write a work which shall be
abreast of the best text-books on the subject, and in this he has
succeeded. No difficulties are slurred over; in fact, the demonstrations are full, accurate, and complete. The text is amply
illustrated by a rich collection of exercises. Not only have
preceding text-books been consulted, but considerable contributions have been levied upon memoirs in mathematical journals,
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