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PREFAÇE ( to the 2d. Edition.) DEDICATORY

TO

SCHOOL MASTERS.

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GENTLEMEN,

AFTER expressing my sincere thanks for your kind and very ready acceptance of the first Edition of the SCHOLAR’S ArithMETIC, permit me now to offer for your further consideration and favor, the SECOND EDITion, which with its CORRECTINS and ADDITIONS, it is hoped, will be found still more deserving of your approbation.

The testimony of many respectable Teachers has inspired a confidence to believe, that this work, where it has been introduce ed into Schools, has proved a kind assistant towards a more speedy and thorough improvement of 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 laboured, to the manifest neglect of other parts of their Schools.

То answer the several intentions of this work, it will ba neces. sary that it should be put into the hands of every Arithmetitian; 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 SUPPLEMENT to each Rule in this work is a novelty. I have often seen books with questions and answers, but in my humble opinion, it is no evidence that the Scholar comprehends the principles of that science which is his study, because that he may be able to repeat verbatim from his book the answer to a question on which his attention has been exercised, two or three hours to commit to memory. Study is of but little advantage to the human mind without reflection. To force the Scholar into reflections of his own, is the object of those. Questions unanswered, at the beginning of each Supplement. The Exercises are designed, tests of his judgment. The Supplements may be omitted the first time going through the book, if thought proper, and taken up afterwards as a review.

Thuo' 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 hoped these will be found satisfactory.

I wave only to add, that any intimation of amendments or de. fects by the candid and experienced of your order, will be thank. fully received by GENTLEMEN, Your most humble, and

most obcdient servant,

DANIEL ADAMS. Leominster, (Mass.) Oct. 1, 1802.

FOURTH EDITION. 'The Fourth Edition is printed page for page from the third; with this exception--the rule for Compound Interest is crowded into its proper place.

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The following 'ERRORS in the 3d Edition were not discovered until the 4th Edin

tion was nearly out of the Press. Page 43. Quest. 6. The answer instead of 454 16 ought to be £54 16 1. Page 66. In the solution of the 3d Quest. each of the seven whole years was called 365

days and 6 hours. As two of the years were leap years, the exact answer is 4079520

niinutes.
Page 79. Example 1. The second remainder, instead of 224 [in this edition) ought to be

214, and the last remainder 92.
Page 91. Example 4. For “ Answer, Dolls. 363,94”, read Answer, Dolls. 363, 9444
Page 127. Quest. 24. The Answer, instead of 119 ought to be 144 1-2.
Page 206, The Answer to the 1st Quest. about the Wheel and Axle, instead of 40, ought

to be 48.
In the example respecting the Screw, for 72 +3,14195218,1947-
read 72x3,14159-226,194+; and then read
Circumf.

in.
16.

10.
2 % 6,1 94 1

% % 4 0.: 9,90 3. Moreover, the reader is desired to bear this in his mind, that in a number of instances, when the Answer is not given exact to a fraction, there is no sign, that it is not so exact : particularly, when the Answer is in dollars, cents & mills.

In such instances, if the scholar gets the number of mills right, though he may bring out a fraction over, he may feel satisfied.

In one or two questions in Interest, where there are partial payments, le may feel satis, ked, though he may not bring out the Answer within a number of mills.

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THЕ.

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 arithmetical 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 thro' your book loo 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 are to be perused with care. There is not a word inserted in this Treatise, but with a design that it should be studied by the Scholar. As much as is possible, endeavor 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 seening difficulties, but rather strive to overcome such by patience and application ; so shall your progress be easy and the object of your endeavors sure.

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

Hotation.

/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.

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