Ray's Arithmetic, Second Book: Intellectual Arithmetic, by Induction and Analysis

172 Pages·1860·11 MB·English

by  Joseph Ray

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ECLECTIC EDUCATIONAL SERIES.
JKAY'S ARITHMETIC, SECOND BOOK.
INTELLECTUAL
ARITHMETIC
BY
INDUCTION AND ANALYSIS.
BY JOSEPH RAY, M. D.,
LATB PROFESSOR OP MATHEMATICS IN WOODWARD COLLEGE.
ONE.THOUSANDTH EDITION-IMPROVED,
CINCINNATI
WILSON, HINKL:E & OOo
PHIL'A: CLAXTON,REMSEN&HAFFELFINGEB.
NEWYORK: CLARK& MAYNARD.
y_
RAY'S MATHEMATICAL WORKS.
TYPE ENLARGED NEW ELECTROTYPE PLATES.
EachBOOKofRaysArithmetical Course, alsooftheAlgebraic*
is a completework in itself, and, is sold separately.
FIRST BOOK.
PRIMARYLESSONSANDTABLES; simpleandprogressive
MentalLessons, for little learners.
SECOND BOOK.
INTELLECTUAL ARITHMETIC, by Induction and Analysis;
a thorough course on Intellectual Arithmetic.
THIRD BOO K.
PRACTICAL ARITHMETIC, by Induction and Analysis a sim-
;
ple, thorough work forschools and private students.
~J3Y TO RAY'S ARITHMETIC, THIRD BOOK.
RAY'S HIGHER ARITHMETIC. Principles of Arithmetic, ana-
lyzed and applied. For advanced students andbusiness men.
KEY TO RAY'SHIGHER ARITHMETIC.
ELEMENTARY ALGEBRA,
RAY'S ALGEBRA, FIRST BOOK, for Common Schools and
Academies; a simple, progressive, elementary treatise.
HIGHER ALGEBRA.
RAY'S ALGEBRA, SECOND BOOK, for Academies, and for Col-
leges; aprogressive, lucid, andcomprehensive work.
KEY TO RAY'S ALGEBRA, FIRST AND SECOND BOOKS.
EnteredaccordingtoActofCongress,intheyearEighteenHundredandFifty-
Seven,byWINTHROPB.SMITH,intheClerk'sOffice,oftheDistrict Courtofthe
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fortheSouthernDistrictofOhio.
PREFACE.
Few works on Intellectual Arithmetic have received more
nnqualified approbation, and a more extensive patronage, than
this, which, for several years, has been published under the
title Ray's Arithmetic, Part Second.
The numerous editions demanded, have again rendered
necessary a renewal of the plates, which has afforded an
opportunity for REMODELING the work.
Many important improvements have been introduced, with
a design to impart completeness, and give a concise and pro-
gressive course of arithmetical analysis.
The volume in its present form, embraces,
1st. Exercises on the primary principles and their applica-
tions, interspersed with appropriate models of analysis and
frequent reviews.
2d. A progressive and comprehensive presentation of Frac<
tions, intended torender the subject intelligible and attractive
to the pupil.
3d. A General Review,designedtotestthepupil's knowledge
ofprinciples,preparatoryto the applications of mentalanalysis
which follow.
4th. Percentage, Gain and Loss, Interest, and their appli-
cations.
The value ofIntellectual Arithmetic is sohighlyappreciated
by instructors, that little need be said in its commendation.
When'properly taught, it is one of the most useful and
interesting studies inwhich pupils can engage, and should be
omitted by no one.
By its study, learners are taught to reason, to analyze, ie
think for themselves; while it imparts co'nfidence in their ows
reasoningpowers, and strengthens the mental faculties.
HINTS TO TEACHERS.
LET the pupils be classified with reference to their attainments
and abilities. The recitation should be short and spirited, every
pupil being required to give undivided attention to the question
before the class.
Generally, whilereciting,thepupils shouldbe permitted tohave
their books open before them the test ofhaving properly studied
the lesson, being the readiness and accuracy with which the several
questions are analyzed and answered.
The explanations and operations termed ANALYSIS, are intended
as Model Solutions, pointing out to the learner themannerin which
the questions in the lessons are tobe solved and explained.
The pupil should be required to furnish a similarexplanation
to each of the jucceeding questions, and to give, not only a cor-
rect answer, but also, the reason for the method by which he
obtained it.
A method of solvingquestions in Mental Arithmetic,nowmucb
used, is the following, called the "Four Step Method."
ILLUSTRATIONS. First step, James gave 7cents for apples and
8 cents for peaches; how many cents did he spend? Second
step, as many as the sum of 7 cents and 8 cents. Third step, 1
cents and 8 cent1? are 15 cents. Fourthstep, hence, if Jamesgave
7 cents for apples, and 8cents for peaches, he spent 15 cents.
Again: Firststep, 4-fifths of 25 are howmany times 6? Second
ttep, as many times 6 as 6 is contained times in 4-fifthsof 25.
Thirdstep, 1-fifth of25 is 5, 4-fifths are 4 times 5, which are20;
6 in 20 is contained 3 and 2-sixths times. Fourth step, therefore,
4-fifthsof 25 are 3 and 2-sixths times 6?
Asa meansof keepingtheattentionof theclassdirectedtoeach
question, it. will be proper for the instructor occasionally to read
an example aloud, and, having allowed sufficient time for the
answer, to call upon some one for the result, and then for the
analysis. Bythis means, each one isobliged to solvetheexample^,
notknowingbut thathe may be required toanswerit.