Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

А

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.

BY WILLIAM KINNE, A. M.

Seventh 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 PUBLISHED BY GLAZIER, MASTERS & Co.
Sold by them at the Hallowell Bookstore, No. 1, Kennebec-Row, and by all
DISTRICT OF MAINE, ss.

the Booksellers in the State.

1829.

[ocr errors]

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“ ties; to which is annexed a short plan of Book-keeping. The whole

designed for the use of Schools. By William Kinne, A. M. Fourth " editicn, with questions on every part of Arithmetic, and a compendious

system of Tax making. Revised, corrected and greatly enlarged, by " Daniel Robinson. Hallowell, printed aud published 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 Act for the encouragement of learning, by securing the copies of maps, charts and books to ihe 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. Maine.

Advertisement to the Seventh Edition.

It has been the primary purpose, in each improved Edition of this Work, to render it more and more 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 màiter 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 nothmg in this compendium which reason and truth would long hesitate to approve.

D. R. Gardiner, August 1, 1828.

[ocr errors]

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 naiure 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 compreliensive 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 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, malter much more conducive io the purpose of his instruction. The book-keeping, also, has been somewhai 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 bl 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 ihe scholar is hurried through these fundamental rules faster than liis comprehension and proficiency would justify, To obviate this objection, has been another design in the present "undertaking.

Considering that, to attain a thorough knowledge of vulgar fractions, is usually too difficult 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 deciinal fractions may be more easily acquired, are more simple, useful, and necessary, and are sooner wanted in the 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.

}

}

m }

} - 173

PAGE.

PAGE
Notation or Numeration, 9 || Vulgar Fractions,

147

Addition,

12 || Rule of Three in Vul. Frac. 160

Subtraction,

15 | Rule of Three in Dec. Frac.

Simple

161

Multiplication, 16 Double Rule of Three in

Division,

21

162

Vulgar Fractions,

Practical Questions,

25 Simple Interest in Decimals, 163

Tables { Of Money, Weights,

Table of Ratios,

and Measures,

163

27

Compound Interest in Decimals,167

Reduction,

32 | Table of the amount of £1,

Application of Reduction, 37 or $1, at 5 and 6 per cent.

Federal Money,

38

167

per annum, compound in-

Reduction of Federal Money,

44

terest, for 20

years,

Practical Questions in ?

48

Annuities at compound interest, 168

Federal Money,

Involution,

169

Addition; 48 Evolution, or Extraction

Subtraction, 56

Compound

of Roots,

170

Multiplication, 61 || Application and use of the

Division,

66 Square Root,

Average Judgement,

72 || The Cube Root,

177

Duodecimals,

73 | Application and Use of the

178

Three Problems in Vulgar }

Cube Root,

75

Roots of Powers in general,

Decimal Fractions,

79

,

181

Reduction of Currencies, 88

183

Rule of Three,

98

187

Practice,

, 188

Tare and Tret,

108

Position

Single,

190

Double Rule of Three,

111

Double,

191

Conjoined Proportion,

114 | Permutation and Combination, 193

Barter,

115 Miscellaneous Questions, 196

Loss and Gain,

117 Measurement of Grindstones, 201

119
Single,

Fellowship

Double,

122

Mensuration of Superfices, 202

211

Simple Interest,

123 Cask Guaging,

219

Short Practical Rules, 127 Ships' Tonnage and Length

221

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,

023

Annuities at Simple Interest, 140 il Assessing Taxes,

223

Equation of Payments, 141 Book-keeping,

226

Exchange,

142 || Tables of value of gold, 236

Progression { Geometrical

)

105 Alligation Medial,

222

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 terın are the first nine called? How named? What
does the tenth figure denote? Have not these digits a local, as well as a
simple value? On what principle does their local value depend? Denom-
inate the names of the places, according to their order. How is the cipher
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 nuinbers. 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, Notes, 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. Avoirdupois 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 direction 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
examples in Average Judgment. What is observed of Duodecimals? Give
the Rule for multiplying them. What are Fractions ? How is a Vulgar
Fraction represented ? Name its parts. What 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 ciphers ? Let me hear the Table.
What is the rule for their Addition? What for their Subtraction? For

« ΠροηγούμενηΣυνέχεια »