Spherical Trigonometry - For the use of colleges and schools

I. (Isaac) Todhunter

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• Publié par: showyong
• Publié le: 01 décembre 2010
• Nombre de lectures: 48
• Langue: English

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The Project Gutenberg eBook of Spherical Trigonometry,
by I. Todhunter
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Title: Spherical Trigonometry
For the use of colleges and schools
Author: I. Todhunter
Release Date: November 12, 2006 [EBook #19770]
Language: English
Character set encoding: TeX
*** START OF THIS PROJECT GUTENBERG EBOOK SPHERICAL TRIGONOMETRY ***
Produced by K.F. Greiner, Berj Zamanian, Joshua Hutchinson and
the Online Distributed Proofreading Team at http://www.pgdp.net
(This file was produced from images generously made available
by Cornell University Digital Collections)SPHERICAL
TRIGONOMETRY.iiSPHERICAL TRIGONOMETRY
For the Use of Colleges and Schools.
WITH NUMEROUS EXAMPLES.
BY
I. TODHUNTER, M.A., F.R.S.,
HONORARY FELLOW OF ST JOHN’S COLLEGE,
CAMBRIDGE.
FIFTH EDITION.
London:
MACMILLAN AND CO.
1886
[All Rights reserved.]ii
Cambridge:
PRINTED BY C. J. CLAY, M.A. AND SON,
AT THE UNIVERSITY PRESS.PREFACE
The present work is constructed on the same plan as my treatise on Plane
Trigonometry, towhichitisintendedasasequel; itcontainsallthepropositions
usuallyincludedundertheheadofSphericalTrigonometry,togetherwithalarge
collection of examples for exercise. In the course of the work reference is made
to preceding writers from whom assistance has been obtained; besides these
writers I have consulted the treatises on Trigonometry by Lardner, Lefebure de
Fourcy, and Snowball, and the treatise on Geometry published in the Library of
Useful Knowledge. The examples have been chiefly selected from the University
and College Examination Papers.
In the account of Napier’s Rules of Circular Parts an explanation has been
given of a method of proof devised by Napier, which seems to have been over-
looked by most modern writers on the subject. I have had the advantage of
access to an unprinted Memoir on this point by the late R. L. Ellis of Trinity
College; Mr Ellis had in fact rediscovered for himself Napier’s own method. For
the use of this Memoir and for some valuable references on the subject I am
indebted to the Dean of Ely.
Considerable labour has been bestowed on the text in order to render it
comprehensive and accurate, and the examples have all been carefully verified;
and thus I venture to hope that the work will be found useful by Students and
Teachers.
I. TODHUNTER.
St John’s College,
August 15, 1859.
iiiiv
In the third edition I have made some additions which I hope will be found
valuable. I have considerably enlarged the discussion on the connexion of For-
mulæ in Plane and Spherical Trigonometry; so as to include an account of the
properties in Spherical Trigonometry which are analogous to those of the Nine
Points Circle in Plane Geometry. The mode of investigation is more elementary
than those hitherto employed; and perhaps some of the results are new. The
fourteenth Chapter is almost entirely original, and may deserve attention from
the nature of the propositions themselves and of the demonstrations which are
given.
Cambridge,
July, 1871.CONTENTS.
I Great and Small Circles. 1
II Spherical Triangles. 7
III Spherical Geometry. 11
IV Relations between the Trigonometrical Functions of the Sides
and the Angles of a Spherical Triangle. 17
V Solution of Right-angled Triangles. 35
VI Solution of Oblique-Angled Triangles. 49
VII Circumscribed and Inscribed Circles. 63
VIII Area of a Spherical Triangle. Spherical Excess. 71
IX On certain approximate Formulæ. 81
X Geodetical Operations. 91
XI On small variations in the parts of a Spherical Triangle. 99
XII OntheconnexionofFormulæinPlaneandSphericalTrigonom-
etry. 103
XIII Polyhedrons. 121
XIV Arcs drawn to fixed points on the Surface of a Sphere. 133
XV Miscellaneous Propositions. 143
XVI Numerical Solution of Spherical Triangles. 157
vvi CONTENTS.