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Scholars in Numbers, and at the same time, has relieved masters of a heavy burden of writing out Rules and Questions, under which they have so long labored, to the manifest neglect of other parts of their Schools.

To answer the several intentions of this work, it will be necessary that it should be put into the hands of every Arithmetician: the blank after each example is designed for the operation by the scholar, which being first wrought upon a slate, or waste paper, he may afterwards transcribe into his book.

The SUPPLEMENTS to the Rules in this work are something new; experience has shown them to be very useful, particularly those "Questions," unanswered, at the beginning of each Supplement. These questions the pupil should be made to study and reflect upon, till he can of himself devise the proper answer. They should be put to him not only once, but again, and again, till the answers shall become as familiar with him as the numbers in his multiplication Table. The Exercises in each supplement may be omitted the first time going through the book, if thought proper, and taken up afterwards as a kind of review.

Through the whole it has been my greatest care to make myself intelligible to the scholar; such rules and remarks as have been compiled from other authors are included in quotations; the Examples, many of them are extracted; this I have not hesitated to do, when I found them suited to my purpose.

Demonstrations of the reason and nature of the operations in the extraction of the Square and Cube Roots have never been attempted in any work of the kind before to my knowledge; it is a pleasure to find these have proved so highly satisfactory.

Grateful for the patronage this work has already received, it remains only to be observed that no pains nor exertions shall be spared to merit its continuance.

Mont-Vernon, (N. HI.) December 26th, 1815.

DANIEL ADAMS.

RECOMMENDATIONS.

New-Salem, Sept. 14th, 1801. HAVING attentively examined "The Scholar's Arithmetic," I cheerfully give it as my opinion that it is well calculated for the instruction of youth, and that it will abridge much of the time now necessary to be spent in the communication and attainment of such Arithmetical knowledge as is proper for the discharge of business.

WARREN PIERCE. Preceptor of New-Salem Academy.

Groton Academy, Sept. 2, 1801.

SIR.....I have perused with attention "The Scholar's Arithmetic," which you transmitted to me some time since. It is in my opinion, better calculated to lead students in our Schools and Academies into a complete knowledge of all that is useful in that branch of literature, than any other work of the kind I have seen. With great sincerity I wish you success in your exertions for the promotion of useful learning; and I am confident that to be generally approved your work needs only to be generally known.

WILLIAM M. RICHARDSON,
Preceptor of the Academy.

Extract of a Letter from the Hon. JOHN WHEELOCK, LL. D. President of Dartmouth College, to the Author.

"The Scholar's Arithmetic is an improvement on former productions of the same nature. Its distinctive order and supplement will help the learner in his progress; the art on Federal Money makes it more useful; and I have no doubt but the whole will be a new fund of profit in our country."

September 7th, 1807.

The Scholar's Arithmetic contains most of the important Rules of the Art, and something, also, of the curious and entertaining kind.

The subjects are handled in a simple and concise manner. While the questions are few, they exhibit a considerable variety. While they are generally easy, some of them afford scope for the exercise of the Scholar's judgment. It is a good quality of the Book, that it has so much to do with Federal Money. The plan of showing the reasons of the operations in the extraction of the Square and Cube Roots is good. DANIEL HARDY, JUN. Preceptor of Chesterfield Academy.

Extract of a Letter from the Rer. LABAN AINSWORTH of Jaffrey, to the publisher of the fourth Edition, dated August 3, 1807.

The superiority of the Scholar's Arithmetic to any book of the kind in my knowledge, clearly appears from its good effect in the schools I annually visit.-Previous to its intro duction, Arithmetic was learned and performed mechanically; since, scholars are able to give a rational account of the several operations in Arithmetic, which is the best proof of their having learned to good purpose."

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51 Method of casting Interest on
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Compound Interest

Multiplication

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Exchange

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Tables of Exchange

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- Rules occasionally useful to men in particular employments of life.

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THE

SCHOLAR'S ARITHMETIC.

INTRODUCTION.

ARITHMETIC is the art or science which treats of numbers.

It is of two kinds, theoretical and practical.

The THEORY of Arithmetic explains the nature and quality of numbers, and demonstrates the reason of practical operations. Considered in this sense, Arithmetic is a Science.

PRACTICAL ARITHMETIC shews the method of working by numbers, so as to be most useful and expeditious for business. In this sense Arithmetic is an Art.

DIRECTIONS TO THE SCHOLAR.

DEEPLY Impress your mind with a sense of the importance of arithmeticai knowledge. The great concerns of life can in no way be conducted without it. Do not, therefore, think any pains too great to be bestowed for so noble an end. Drive far from you idleness and sloth; they are great enemies to improvement. Remember that youth, like the morning, will soon be past, and that opportunities once neglected, can never be regained. First of all things, there must be implanted in your mind a fixed delight in study; make it your inclination; "A desire accomplished is sweet to the soul." Be not in a hurry to get through your book too soon. Much instruction may be given in these few words, UNDERSTAND EVERY THING AS YOU GO ALONG.--Each rule is first to be committed to memory; afterwards, the examples in illustration, and every remark is to be perused with care. There is not a word inserted in this Treatise, but with design that it should be studied by the Scholar. As much as possible, endeavour to do every thing of yourself; one thing found out by your own thought and reflection, will be of more real use to you, than twenty things told you by an Instructor. Be not overcome by little seeming difficulties, but rather strive to overcome such by patience and application; so shall your progress be easy and the object of your endeavours sure.

On entering upon this most useful study, the first thing which the Scholar has to regard, is

NOTATION.

NOTATION is the art of expressing numbers by certain characters or figures of which there are two methods. 1. The Roman method, by Letters. 2. The Arabic method, by Figures. The latter is that of general use

In the Arabic method all numbers are expressed by these ten characters or figures.

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Unit; or two; three; four; five; six; seven; eight; nine; cypher

one

[or nothing. The nine first are called significant figures, or digits, each of which standing by itself or alone, invariably expresses a particular or certain number; thus, 1 signifies one, 2 signifies two, 3 signifies three, and so of the rest, until you come to nine, but for any number more than nine, it will always require two or more of those figures set together in order to express that number. This will be more particularly taught by

NUMERATION.

Numeration teaches how to read or write any sum or number by figures. In setting down numbers for arithmetical operations, especially with beginners, it is usual to begin at the right hand, and proceed towards the left. EXAMPLE. If you wish to write the sum or number 537, begin by setting down the seven, or right hand figure, thus 7, next set down the three, at the left hand of the seven, thus 37, and lastly the five, at the left hand of the three, thus 537 which is the number proposed to be written.

In this sum thus written you are next to observe that there are three places, meaning the situations of the three different figures, and that each of these places has an appropriated name. The first place, or that of the right hand figure, or the place of the 7, is called unit's place; the second place, or that of the figure standing next to the right hand figure, in this the place of the 3, is called ten's place; the third place, or next towards the left hand, or place of the 5, is called hundred's place; the next or fourth place, for we may suppose more figures to be connected, is thousand's place; the next to this tens of thousand's place, and so on to what length we please, there being particular names for each place. Now every figure signifies differently, accordingly as it may happen to occupy one or the other of these places.

The value of the first or right hand figure, or of the figure standing in the place of units, in any sum or number, is just what the figure expresses standing alone or by itself; but every other figure in the sum or number, or those to the left hand of the first figure, have a different signification from their true or natural meaning; for the next figure. from the right hand towards the left, or that figure in the place of tens, expresses so many times ten, as the same figure signifies units or ones when standing alone, that is, it is ten times its simple primitive value; and so on, every removal from the right hand figure, making the figure thus removed ten times the value of the same figure when standing in the place immediately preceding it.

co Hund.

Tens.

co Units.

EXAMPLE. Take the sum 3 3 3, made by the same figure three times repeated. The first or right hand figure, or the figure in the place of units, has its natural meaning or the same meaning as if standing alone, and signifies three units or ones; but the same figure again towards the left hand in the second place, or place of tens, signifies not three units, but three tens, that is thirty, its value being increased in a tenfold proportion; proceeding on still further towards the left hand, the next figure or that in the third place, or place of hundreds signities neither three nor thirty, but three hundred, which is ten times the value of that figure, in the place immediately preceding it, or that in the place of tens So you might proceed and add the figure 3, fifty or

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