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SHORT SYSTEM OF
PRACTICAL ARITHMETIC,

COMPILED

FROM THE BEST AUTHORITIES;

TO WHICH IS ANNEXED

A SHORT PLAN OF BOOK-KEEPING.

THE WHOLE DESIGNED

For the Use of Schools.

. - 94
BY WILLIAM KINNE, A. M.

Seventh Zdition,
WITH QUESTIONS

ON EVERY PART OF ARITHMETIC, AND A COMPENDIOUS

SYSTEM OF TAX MAKING.

REVISED, CORRECTED, AND GREATLY ENLARGED,

By DANIEL ROBINSON.

HALLOWELL:
PRINTED AND PUBLISHED BY GLAZIER, MASTERS & Co.
Sold by them at the Hallowell Bookstore, No. 1, Kennebec-Row, and by all

the Booksellers in the State.

fototottt
1829.

DISTRICT OF MAINE, ss.

BE IT REMEMBERED, That on the seventh day of December, in the year of our Lord one thousand eight hundred and twenty-two, and the forty-seventh year of the Independence of the United States of America, GOODALE, GLAZIER & COMPANY of the District of Maine, have deposited in this office, the title of a Book, the right whereof they claim as proprietors-in the words following, viz :"Improved edition with questions. * A short system of Practical Arithmetic, compiled from the best authori“ lies; to which is annexed a short plan of Book-keeping. The whole " designed for the use of Schools. By William Kinne, Å. M. Fourth " edition, with questions on every part of Arithmetic, and a compendious " system of Tax making. Revised, corrected and greatly enlarged, by " Daniel Robinson." Hallowell, printed and publisbed by Goodale, Glazier " & Co."-In conformity to the Act of the Congress of the United States, entitled, “ An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the times therein mentioned; and also to an Act, entitled An Act supplementary to an Act, entitled an Aci for the encouragement of learning, by securing the copies of maps, charts and books to the authors and proprietors of such copies, during the times therein mentioned, and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints."

JOHN MUSSEY, Jr., Clerk of the District Court of Maine. A true copy as of record.

Attest, J. MUSSEY, JR., Clerk D. C. Muine.

Advertisement to the Seventh Edition.

It has been the primary purpose, in each improved Edition of this Work, to render it more and mcre plain and practical, while it should embrace every useful rule and question which might occur in the ordinary business transactions of life. To effect this object, neither time nor thought has been, in any wise, riggardly expended. Whatever was judged to be wanted, to characterize it as a plain, practical, and useful system, has been amply, though gradually, supplied. In the edition now presented to the public, part of the questions in which avoirdupois weight is concerned, has been written anew, or so altered as to allow 25 pounds only to the quarter of a hundred weight; because this practice now generally obtains in business, among merchants and traders in the UnitedStates, and has moreover been established in Maine by legislative enactment. Considerable new maiter also has been crowded into the volume, and a small portion of the old withdrawn. Errour has been diligently sought for and corrected; and, it is confidently believed, is now nowhere to be found on its pages. Considered as an Epitome, whether it be susceptible of any farther degree of improvement, may be reasonably questioned, The hope is, therefore, indulged, thai, though the tougle of the captious caviller should blazon defects for which others might search in vain ; yet the eye of the candid critic will see nothing in this compendium which reason and truth would long hesitate to approve.

D. R. Gardiner, August 1, 1828.

LIBRARI

Dec 107824

Crommelt

PREFACE.

To adapt this work to the easy use of Instructers, I have endeavoured to simplify the definitions and rules, so as to render them as familiar and concise as the nature of the subject admits. At the same time, I have very considerably enlarged the Original System, by the insertion of a far greater number of practical examples, especially in the ground-rules, and by the introduction of many new rules, in order to furnish our Schools with a methodical and comprehensive Treatise of Practical Arithmetic.

Works of this kind have too often abounded with abstruse and intricate questions, more puzzling than beneficial to the learner.-And some authors have dwelt too much on those of a trifling nature, which, when understood, afford no useful know

knowledge. To avoid these extremes, to feed and invigorate the mind, and thus form our youth for entering, with fair promise, on the pursuits of active life, have been my principal aims, in preparing this edition for the press.

Most of the former demonstrations have been omitted, as being little suited to enlighten the pupil, and as excluding, in such compends, matter much more conducive to the purpose of his instruction. The book-keeping, also, has been somewhat abridged, for the admission of other matter; yet enough, it is conceived, has been retained to give the student no very imperfect idea of this branch of learning. Besides what has been substituted in place of this excluded matter, no fewer than 61 pages have been added to the last edition To the whole have been prefixed brief questions on all the most important parts of Arithmetic. But, instead of entering into a detail of these enlargements, I beg leave to refer the reader to the table of contents, or to the pages of the work itself.

During the many years that I have devoted to the instruction of youth in Arithmetic, I have used various systems, all of which have just claims to scientific merit. The authors, however, have, generally, appeared to be' deficient in an important point-the practical teacher's experience. They have been much too sparing of examples, more especially in the first rules. The consequence is, that the scholar is hurried through these fundamental rules faster than his comprehension and proficiency wonld justify, To obviate this objection, has been another design in the present undertaking. Considering that, to attain a thorough knowledge of vulgar fractions, is

alt a task for young students, whose progress in Arithmetic has extended only to compound division, and, that the difficulty frequently results in their utter discouragement; I have, therefore, deemed it most adviseable and advantageous to transfer these fractions (except two or three problems introductory to decimals ) beyond equation of payments. But, as decimal fractions may be more easily acquired, are more simple, useful, and necessary, and are sooner wanted in ihe practical branches of numbers, I have thought it expedient to let them occupy that part of the work which they did in former editions. The other rules I have likewise aimed so to arrange, as to give precedence to those which are most simple and necessary, introducing the more abstruse and difficult parts last. The teacher, however, will not consider himself as being obliged to adhere strictly to this arrangement. He can, notwithstanding, take the rules in such order as he may conceive to be the most proper.

D. R.

TABLE OF CONTENTS.

169

PAGE.]

PAGE

Notation or Numeration,

Vulgar Fractions,

147

| Addition,

Il Rule of Three in Vul. Frac. 160

Subtraction,

| Rule of Three in Dec. Frac. 161

Double Rule of Three in 162

(Division,

Vulgar Fractions, S

Practical Questions,

Simple Interest in Decimals, 163
Tableas Of Money, Weights, Table of Ratios,

163

Tables and Measures, S Compound Interest in Decimals,167

Reduction

Table of the amount of £1,)

Application of Reduction,

or $1, at 5 and 6 per cent.

Federal Money,

per annum compound in710

Reduction of Federal Money, terest, for 20 years,

Practical Questions in ?

Annuities at compound interest, 168

Federal Money,

Involution,

c Addition,

Evolution, or Extraction

) Subtraction,

Application and use of the

C Division,

Average Judgement,

The Cube Root,

177

Duodecimals,

Application and Use of the 2

Three Problems in Vulgar ?

Cube Roots

Fractions,

Roots of Powers in general,

Decimal Fractions,

Promocion S Arithmetical, 181

Reduction of Currencies,

Rule of Three,

allication S Medial,

187

Practice,

105

188

Tare and Tret,

108

190

Double Rule of Three,

Double,

191

Conjoined Proportion,

Permutation and Combination, 193

Barter,

115 i Miscellaneous Questions, 196

Loss and Gain,

117 Measurement of Grindstones,

201

Single,
Fellowship

on Sof Superfices,

Mensuration

122 lensuration of Solids, 211

Simple Interest,

Cask Guaging,

219

Short Practical Rules, 127 Ships' Tonnage and Length
To compute Interest on

of Masts,

130
Notes, Bonds, &c.

Weight of Anchor a Cable
Compound Interest,

135 may sustain-Burthen of
Commission,

137 Ships from their Propor-
Insurance,

137 tions,

Discount,

138 || Wood and Bark Measure,

Annuities at Simple Interest, 140 Assessing Taxes,

223

Equation of Payments, 141 || Book-keeping,

226

Exchange,

142 || Tables of' value of gold, 236

Progression } Geometrical,
Alligation > Alternate,

183

Position

Single,

114

119

202

123

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TOPICS FOR EXAMINATION IN THE ARITHMETIC.

What is Arithmetic? What are the four fundamental Rules for its
operation ? To understand these, what is previously necessary ? What.
does Notation teach ? How many characters or figures are employed in
it? By what common term are the first nine called? How named? What
does the tenth figure denote? Have not these digits a local, as well as a
simpie value? On what principle does their local value depend? Denom-
inate the names of the places, according to their order. How is the
used, in connexion with the significant figures ? In what manner are large
numbers divided ? Name the places, and read each line of numbers, in the
Numeration Table. What is the Rule for expressing numbers in figures
when above nine? Give the Rule lo read numbers. What is Addition?
Simple ? Let me examine you in the Table. Recite the Rule and modes
of Proof. What is Subtraction? When Simple ? Name its numbers.
Let me examine you in the Table. Give the Rule and way of Proof.
What is Multiplication ? Name its numbers. What common term is applied
10 the first two of them? When is it Simple? How is the Table used !
Let me examine you in it. When is it Case first ? Repeat the Rule.
When Case second ? Give the Rule, and modes of Proof. When does
the first Case of Contractions apply? Give the Rule. When the second
Case? Tell the Rule. What is shown by Division ? Name its numbers.
When is it Simple ? Let me examine you in the Table. Repeat the
Rule, Noles, and modes of Proof. Repeat the directions in Case first of
Contractions. What Case second and Rule? What says Case third ?
What its Note and Rule ? Repeat the Money 'Table. That of Troy
Weight, Apothecaries' Weight: Aroirdupois Weight. Cloth Measure.
Long Measure. Square Measure. Culic Measure. Dry Measure. Wine
Measure. Ale Measure. Time. Planetary Motion What is taught by
Reduction? Repeat the Rules and Proof. Tell me the mode of forma-
tion, and Table of Federal Money. Give the Rule for its Addition. For
its Subtraction. For its Multiplication. Recite the Note, and A Short
Rule. Give the Rule for its Division. Tell the Short Rule. Give the
Rules for the Reduction of Federal Money. What is the Direction in Case
first for changing New-England currency to Federal Money ? In Case
second ? In Case third? What is the Rule in Case first for changing
Federal Money to New-England currency? In Case second? What is
taught by Compound Addition? Give the Rule. What is Compound
Subtraction ? Tell the Rule. What does Compound Multiplication teach?
Give the Rule. What is the direclion in Case second ? What in Case.
third? What does Compound Division teach ? Rehearse the Rule.
What does Case second direct? What Case third ? Tell the Note before
exa nples in Average Judgment. What is observed of Duodecimals? Give
the Rile for multiplying them. What are Fractions ? How is a Vulgar
Fraciion represented ? Name its parts. Wbat is shown by the Denomina-
tor? What by the Numerator? When is a fraction in its lowest terms ?
Give the rule for Problem first. What is the intent of Problem second ?
Tell its rule. What of Problem third? What its rule? What is a De-
cimal Fraction? How expressed? What determines its relative value?
How are such fractions affected by cipher's ? Let me hear the Table.
What is the rule for their Addition? What for their Subtraction? For

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