Elementary algebra for schools containing a full treatment of graphs, with answers

1907·21.4 MB·English

by  Hall, H.S

WALTER STiLV/£LL
H.
Gco'Jelic Gorvico, Ol-.av.a
a^
^ccyK
y/Auj<-^
PlS^e^qiZ.
S„SSu«Tc
TCJ/iOuJ^
ps^
^^„^^2—^ V
'JZ^<^ //,
/^

ELEMENTARY ALGEBRA
FOR SCHOOLS
CONTAINING A FULL TREATMENT OF GPiAPHS
WITH ANSWERS
BY
H. S. HALL, M.A.
FORMERLY SCHOLAR OF CHRIST'S COLLEGE, CAMBRIDGE
AND
S. R. KNIGHT, B.A., M.B., Ch.B.
FORMERLY SCHOLAR OF TRINITY COLLEGE, CAMBRIDGE
NEW EDITION
REVISED AND ENLARGED
MACMILLAiN AND LIMITED
CO.,
MARTIN'S STREET, LONDON
ST.
19^3
COPYRIGHT.
ERdeiFptirriisuntnt,EeddiFtei1bo8rnSu,9arpyr,iFnit1fe^tdh71E;8d8iF5to;iuorSnte,hcoREneddviitEisdoeindt,ioaOnnc,dt1o8b8Ee6nrl,;aTr1hg8ei8d7r,d;
November, 18S9;; Sixth Edition, Revised and Enlarged,
1E1E88dn99il80ta,ir:ognR1e,e9d0p,0r,Ri1en9vt10i93es0d1;e,d1R8e9ap11n,9r0di12n8t9;E2en,dlEa1i18rg99g3hue.*td>h1,819951E0,8d59i17t8i19:o96n06(,R.tewpirRNcieeen)vtwi;esdESe,dedivte1i8ano9nta8dh.,
1907; Reprinted 1908, 1910, 1911, January and September
1913.
GLASGOW PKI.VTED AT THE UNIVERSITY PRESS
:
BY ROBERT MACLEHOSE AND CO. 1-TD.
: :
PREFATORY NOTE.
The last edition of Hall and Knight's Elementary Algebra pub-
lished in Dr. Knight's lifetime was the sixth, issued in 1890.
Since his death in 1894 many alterations and additions have
been made, as occasion required. These, for which I am solely
responsible, may be summarized as follows
:
Extract from the Preface to the Seventh Edition {Jan.
1897)
*'The distinctive features are
:
" (1) The definitions of dimension, degree, homogeneous expresbion
are transferred from Art. 10 to Art. 24.
"(2) Greater proininence has been given to thefundamental Laics
of Algebra (see Arts. 22, 29-32, 46-^8). With this object
parts of the chapters on Multiplication and Division have
been re-written.
"(3) A short section on the use of Detached Coefficients has been
given on page 37.
*' (4) A fuller treatment of the Remainder Theorem and its appli-
cations will be found on pages 236, 237.
" (5) Five new sets of Miscellaneou^s Examples have been added at
convenient intervals beginning with one on page 32, which
replaces Examples IV. c.*"
Extract from the Preface to the Xew Edition {Oct. 1907)
' The leading features are
' :
"(1) A full treatment of Graphs occupying more than 50 pages.
"(2) A new set of Easy Examples on Substitution in Chapter I.
"(3) The greater part of Chapter VIII., on Simple Equations,
has been re-written so as to bring the use of the fundamental
axioms into greater prominence, and to urge the importance
of verifying solutions.
"
iv PREFATORY NOTE.
"(4) Chapter IX., on Symbolical Expression, has been enlarged.
In particular, the section on Formulae has been illustrated by
a new set of Examples.
" (5) A section on Square Root by inspection has been inserted
in Chapter XVI.
"(6) In Chapter XVII,, on Factors, a section on factorisation of
trinomials, by completing the square, has been introduced.
Also a large number of easy miscellaneous examples take the
place of the Exercise XVII. 1 of earlier editions.
*'(7) Considerable additions to the chapters on Quadratic Equa-
tions. In particular, a set of examples involving applications
to Geometry will be found at the end of Chapter XXVII.
"(8) The chapter on Logarithms has been re-written so as to
introduce and explain the use of Four-Figure Tables. The
Tables of Logarithms and Antilogarithms have been taken,
with slight modifications, from those published by the Board
of Education, South Kensington.
**(9) An easy first course has been mapped out enabling teachers
to postpone, if they wish, the harder cases of 'Long' Multi-
plication and Division, and the rules dependent on these
processes.
I am thus responsible for more than 100 pagesof new matter.
In particular, pages 371-431 are my sole work, being taken
verbatim from my little book, A Short Introduction to Graphical
Algebra^ which was first published in 1902.
H. S. HALL.
Fehniary, 1913.
SUGGESTIONS FOK A FIRST COUESE.
In the first thirty chapters an asterisk has been placed before
all articles and examples which may conveniently be omitted
in a first course. Notes are occasionally given suggesting
the most suitable place for a section which may have to be
postponed.
For those who wish to defer to a later stage all the rules
dependent on ' Long' Multiplication and Division, so as to
reach Quadratic Equations earlier, the following detailed
course is recommended.
Chap. I. Arts. 1-11, 13-15. [Omit Art. 12, Examples I. c]
Chap. II.-V. Arts. 16-40. [Omit all the rest of Chap. V.,
except Art. 44.]
Chap. VI. Arts. 46-50. [Omit Arts. 51-55.]
Chaps. YII.-XIII. Arts. 56-107. In connection with Chap.
Xin. Arts. 417-424 on Elementary Graphs may be read.
Chaps. XIV., XV. Arts. 108-113. [Omit Arts. 114, 115.]
Chap. XVL Arts. 116-118a. [Omit Arts. 119-124.]
Chap. XVII. Arts. 125-136. [Omit Arts. 136a-137.]
Chap. XVIII. Arts. 138, 139. [Omit Arts. 140-148.]
Chap. XIX. [Omit Arts. 152, 153.]
Chap. XX. [Omit Arts. 159-163.]
Chap. XXI. [Omit Arts. 171, 172.]
Chap. XXn. Arts. 173-179. [Omit Arts. 180-185.]
[Chaps. XXIII., XXIV. may be taken later.]
Chap. XXV. Quadratic Equations. In connection with this
chapter Arts. 425-428, 437-440 may be read.
From this point the omitted sections must be taken at the
discretion of the Teacher.