A TREATISE

ON

PLANE TRIGONOMETRY.

WORKS BY

JOHN CASEY, ESQ., LL.D., F. R. S.,

FELLOW OF THE ROYAL UNIVERSITY OF IRELAND.

Second Edition, Price 3s.

A TREATISE ON ELEMENTARY TRIGONOMETRY, With Numerous Examples

AND

Questions for Examination.

Price 3s.

KEY TO THE EXERCISES IN THE TREATISE ON ELEMENTARY TRIGONOMETRY.

Fourth Edition, Revised and Enlarged, Price 3s. 6d., Cloth.
A SEQUEL TO THE FIRST SIX BOOKS OF THE
ELEMENTS OF EUCLID,

Containing an Easy Introduction to Modern Geometry.
With numerous Examples.

Fifth Edition, Price 4s. 6d.; or in two parts, each 2s. 6d.
THE ELEMENTS OF EUCLID, BOOKS I.-VI., AND
PROPOSITIONS I.-XXI., OF BOOK XI.;
Together with an Appendix on the Cylinder, Sphere,
Cone, &c.: with

Copious Annotations & numerous Exercises.

Second Edition, Price 6s.

A KEY TO THE EXERCISES IN THE FIRST SIX BOOKS OF CASEY'S "ELEMENTS OF EUCLID."

Price 7s. 6d.

A TREATISE ON THE ANALYTICAL GEOMETRY OF THE POINT, LINE, CIRCLE, & CONIC SECTIONS, Containing an Account of its most recent Extensions, With numerous Examples.

In the Press.

A TREATISE on SPHERICAL TRIGONOMETRY, uniform with a TREATISE ON PLANE TRIGONOMETRY.

LONDON LONGMANS & CO. DUBLIN: HODGES, FIGGIS, & Co.

A TREATISE

ON

31460

PLANE TRIGONOMETRY,

CONTAINING

AN ACCOUNT OF HYPERBOLIC FUNCTIONS,

WITH

Numerous Examples.

BY

JOHN CASEY, LL. D., F. R. S.,

Fellow of the Royal University of Ireland;

Member of the Council of the Royal Irish Academy;
Member of the Mathematical Societies of London and France;
Corresponding Member of the Royal Society of Sciences of Liége; and
Professor of the Higher Mathematics and Mathematical Physics
in the Catholic University of Ireland.

DUBLIN: HODGES, FIGGIS, & CO., GRAFTON-ST.
LONDON: LONGMANS, GREEN, & CO.

DUBLIN:

PRINTED AT THE UNIVERSITY PRESS,

BY PONSONBY AND WELDRICK.

PREFACE.

In the present Treatise my object has been to produce a work on Trigonometry fit to take its place with recent advanced text-books on other branches of Mathematics-a work in which the demonstrations will be accurate and complete, and the various parts of the subject, while avoiding too much detail, fully and comprehensively treated and properly co-ordinated.

A cursory examination will show that it contains not only everything that is usually given in books on Trigonometry, but also much that has hitherto appeared only in Mathematical periodicals.

I have given a systematic account of Imaginary Angles and Hyperbolic Functions; the latter, from their great analogy to Circular Functions, 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.

In compiling the work, the writers to whom I am principally indebted are SERRET and LAISANT, and, to a less extent, MANSION, BRIOT and BOUQUET, and HYMers.