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

From "NATURE."
"Dr. Casey, by the publication of this third treatise, has
quite fulfilled the expectations we had formed when we stated
some months since that he was engaged upon its compilation.
It is a worthy companion of those which have preceded it. It
possesses many points of novelty, i. e. for the English mathematician. He has from the first introduction of certain recent
continental discoveries in geometry taken a warm interest in
them, and in the purely geometrical treatment of them, has himself given several beautiful proofs, and has added discoveries of
his own. We may here note that this work has met with a very
warm welcome in France and Belgium. The author himself has
added so much in years now long past to several branches of the
subject treated of in the volume under notice-the equation of
the circle (and of the conic) touching three circles (three conics),
and other properties-that he is specially fitted, by his intimate
acquaintance with it, and by his long tuitional experience, to
write a book on analytical geometry."
From the " EDUCATIONAL TIMES," September, 1886.
"In this book the author has added to those propositions
usually met with in Treatises on Analytical Geometry many
which we have seen in no other books on the subject; notably
extending the equations of circles inscribed in and circumscribed
about triangles to polygons of any number of sides, and extending to Conics the properties of circles cutting orthogonally. The
demonstrations are concise and neat. In many cases the author
has substituted original methods of proof advantageously, and in
some has also added the old methods. We would specially note
his treatment of the General Equation of the Second Degree,
which is more satisfactory than many we have seen. Throughout
the book there are numerous exercises on the subject matter, and
at the end of each section a collection of problems bearing on
that part of the subject. These problems have been obtained
from Examination Papers and other sources. They have been
selected with much care and judgment. The name of the proposer has in many cases been added, and will cause more interest
to be taken in the solution."
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