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

BY THE SAME AUTHOR.
Fifth Edition, Revised and Enlarged. 3s. 6d., Cloth.
A SEQUEL TO THE FIRST SIX BOOKS OF
THE ELEMENTS OF EUCLID.
Dublin: Hodges, Figgis, & Co.1 London: Longmans, Green, & Co.
EXTRACTS FROM CRITICAL NOTICES.
From the " SCHOOL GUARDIAN."
"This book is a well-devised and useful work. It consists of
propositions supplementary to those of the first six books of
Euclid, and a series of carefully arranged exercises which follow
each section. More than half the book is devoted to the Sixth
Book of Euclid, the chapters on the ' Theory of Inversion' and
on the' Poles and Polars' being especially good. Its method
skilfully combines the methods of old and modern Geometry;
and a student, well acquainted with its subject-matter, would be
fairly equipped with the geometrical knowledge he would require
for the study of any branch of physical science."
From the " PRACTICAL TEACHER."
"Professor Casey's aim has been to collect within reasonable
compass all those propositions of Modern Geometry to which
reference is often made, but which are as yet embodied nowhere.... We can unreservedly give the highest praise to the matter
of the book. In most cases the proofs are extraordinarily ncat... The notes to the Sixth Book are the most satisfactory.
Feuerbach's Theorem (the nine-points circle touches inscribed
and escribed circles) is favoured with two or three proofs, all of
which are elegant. Dr. Hart's extension of it is extremely well
proved.... We shall have given sufficient commendation
to the book when we say that the proofs of these (Malfatti's
Problem, and Miquel's Theorem), and equally complex problems,
which we used to shudder to attack, even by the powerful weapons of analysis, are easily and triumphantly accomplished by
Pure Geometry.
" After showing what great results this book has accomplished
in the minimum of space, it is almost superfluous to say more.
Our author is almost alone in the field, and for the present need
scarcely fear rivals."
From the " JOURNAL OF EDUCATION."
"Dr. Casey's ' Sequel to Euclid' will be found a most valuable
work to any student who has thoroughly mastered Euclid, and
imbibed a real taste for geometrical reasoning... The
higher methods of pure geometrical demonstration, which form
by far the larger and more important portion, are admirable; the
propositions are for the most part extremely well given, and will
amply repay a careful perusal to advanced students."
IO