Treatise on Plane and Solid Geometry for College Schools and Private Students: Written for the Mathematical Course of Joseph Ray, M.D.

288 Pages·1868·5.475 MB·English

by  Eli T. Tappan

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Cornell University Library
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Treatise on plane and solid geometi
3 1924 031 307 733
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Cornell University
Library
The original of tliis book is in
tine Cornell University Library.
There are no known copyright restrictions in
the United States on the use of the text.
http://www.archive.org/details/cu31924031307733

ICIEOTIG EDUCATIONAL SERIES.
TREATISE
PLANE AND SOLID GEOMETRY
COLLEGES, SCHOOLS, AND PRIVATE
STUDENTS.
WEITTENrOBTMEMATHEMATICAl COURSEOF
JOSEPH RAY, M.D.,
BY
ELI T. TAPPAN, M.A.,
PBOFBSSOB OF MATHEMATICS, MT. AUBOBN INSTITUTE.
VAN ANTWERP, BRAGG & CO.,
137 WALNUT STREET, 28 BOND STREET,
CINCINNATI. NEW YOKK.
; ;
Ra
k<-
A Thorough and Progressive Course in Arithmetic, Algebra,
and the Higher Mathematics.
TrimaryArititlhiimneettiicc. HigherArithmetic.
IntellectualArithmetic. TestExamples inArithmetic.
Rudiments of Arithmetic. New ElementaryAlgebra.
Practical Aritlimetic. New HigherAlgebra.
Plane and Solid Geometry. By Eli T. Tappan, A.M., Pres't
Kenyan College. 12mo, doth, 276pp.
Oeometry and Trigonometry. By Eli T. Tappan, A.M.
Prei't Kenyan College. Sra,sheep, 420pp.
Analytic Geometry. By Geo.H. Howisok, A.M., Prof,in Mass.
Instituteof Technology. Treatise on Analytic Geometry, especially
as applied to the Properties of•Conies; including the Modern
Methodsof Abridged Notation.
Elements of Astronomy. By S. H. Peaeody, A.M., Prof, of
Physics and Civil Engineering, Amherst College. Handsomely and
profuselyillustrated. 8to, sheep, 336pp.
K
E'VS.
Ray'sArithmetical Hey (ToIntellectual and Practical)
Hey to Ray's Higher Arithmetic
Key to Ray's New Elementary and Higher Algebras.
The Publishersfurnish DescriptiveCirculars ofthe ahoveMathe-
tnaHcal TextSoohs, with Prices and other information concerning
them.
Entered according to Act of Congress, in the year 1868, by Sargent, Wilson &
HlNKLE,intlieClerk'sOfiiceoftheDistrictCourtoftheUnited
StatesfortheSontheruDistrictofOhio.
PREFACE.
The science of Elementary Geometry, after remaining
nearly stationary for two thousand years, has, for a century
past, been making decided progress. This is owing, mainly,
to two causes: discoveries in the higher mathematics have
thrown new light upon the elements of the science and
;
the demands of schools, in all enlightened nations, have
called out many works by able mathematicians and skillful
teachers.
Professor Hayward, of Harvard University, as early as
1825, defined parallel lines as lines having the same direc-
tion. Euclid's definitions of a straight line, of an angle,
and of a plane, were based on the idea of direction, which
is, indeed, the essence of form. This thought, employed in
all these leading definitions, adds clearness to the science
and simplicity to the study. In the present work, it is
sought to combine these ideas with the best methods and
latest discoveries in the science.
By careful arrangement of topics, the theory ofeach class
of figures is given in uninterrupted connection. No attempt
is made to exclude any method of demonstration, but rather
to present examples of all.
The books most freely used are, "Cours de gfeomfetrie
el6mentaire, par A. J. H. Vincent et M. Bourdon;" "G6-
om§trie th^orique et pratique, etc., par H. Sonnet;" "Die
(iii)
IV PEEFACE.
reine elementar-mathematik, von Dr. Martin Ohm;" and
"Treatise on Geometry and its application to the Arts, by
Rev. D. Lardner."
The subject is divided into chapters, and the articles are
numbered continuously through the entire work. The con-
venience of this arrangement for purposes of reference,
has caused it to be adopted by a large majority of writers
upon Geometry, as it had been by writers on other scien-
tific subjects.
In the chapters on Trigonometry, this science is treated
as a branch of Algebra applied to Geometry, and the trig-
onometrical functions aredefined asratios. This method has
the advantages of being more simple and more brief, yet
more comprehensive/than the ancient geometrical method.
For many things in these chapters, credit is due to the
works of Mr. I. Todhunter, M. A., St. John's College, Cam-
bridge.
The tables of logarithms of numbers and of sines and
tangents have been carefully read with the corrected edi-
tion of Callet, with the tables of Dr. Schron, and with
those of Babbage.
ELI T. TAPPAN.
Ohio XJniveksitt, Jan. 1, 1868.