That a mutual Agreement and Harmony may long fubfift amongst you, that you may long continue an Honour to your Town, Encouragers of Science, Benefactors to Society, Happy in Yourfelves, your Families and every other circumstance of Life, is the fincere Wish of him, who with the deepest fenfe of Gratitude, fubfcribes himself,

Your Faithful, Obedient,

And most humble Servant,

J. EADON.

PREFACE.

E must be little verfed in the common affairs of life, who does not know the great usefulness of Arithmeticas no business can be carried on without the help of numbers; no trade or commerce exercifed without regular accompts. And as the utility of Arithmetic is thus extenfive, fo there are extant many Treatifes on the fubject, fome of which are excellent in their method. But in my opinion there is till room for a general, concifé, and rational piece, better adapted to the ufe of Schools, as well as of those who have not the assistance of a Master: for all the Treatifes that have occurred to me, have either all, or none of their examples wrought at large; which, in the first place, renders them unfit for a Mafter in his School; and in the fecond place, not fit for those who would acquire a competent kill in Arithmetic, without the affiftance of a teacher. To remove this defect, is the intention of the following Treatife; and in what manner my design is executed, is wholly fubaited to the impartial Reader.

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In the courfe of this undertaking, I have exerted my utmost endeavours, to deliver the definitions and rules in as brief a manner as poffible; to make them, at the fame time general, and yet free from fuperfluities, which commonly attend definitions of this kind; and have given fuch notes after them, as defcribe fome particulars.. not flowing from the general rules themfelves, but tending to explain them, or facilitate the operations. To 120 eacht

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each rule also there is annexed, a great variety of the best chofen examples, with their anfwers, the greatest part of which are new, and which the reader cannot fail of understanding, by means of the previous examples wrought at large. After the four firft rules in fimple and Compourd numbers, I have expreffed the operations in algebraic figns, which in my opinion is far the best method, for it not only fhortens the work, but the operation, when finifhed, is itself a rule by inspection.

And it may be noted, that, where fractions are in the answers to any of the examples in the rules preceding vulgar fractions, they are wrote down as they arofe with out any abbreviations; but all fractions in the answers af. terwards are abbreviated as much as poffible. I have treat. ed the four fundamental rules, viz. Addition, Subtraction, Multiplication, and Divifion, first in fimple numbers, and afterwards in compound; for by teaching, them in this order, difficulties do not fo faft arife. Yet I have delivered them in fuch a manner, as to have little or no de pendence on each other, that they may be taught in what order every Mafter chufes.

I think it quite needlefs for the firft fimple rules to becopied out into the Scholars books; but if any Master chufes. to have it done, I would advife him to make his Scholars run over the examples firft upon their flates; then begin the rules again, and write them, with a few examples to each, in their books; and thus he may with eafe mix the fimple and compound rules together.. Tho' I faid before, there is nothing fuperfluous in any of the Problems or general rules; yet the judicious teacher may omit any notes, examples, or particular cafes he may think fit, And if every Scholar has a printed book, he may

either write all the rules and examples in his accompt book, or may omit the Rules, Notes, and Tables, and write down only the operation of each example, especiak ly where the rules are long and tedious. This book may alfo be of peculiar fervice to boys when taken from School, either in making a farther progrefs by their own application, or in the retainment of what they have already learned. I have, contrary to the practice of some Masters, inferted feveral wrought examples in each rule: having found by repeated experience, that a Scholar will focner get both the rule and its meaning, by feeing a few examples wrought, than by any other method. But any Mafter, if he pleases, may foon make new questions of thofe that are folved, by only changing a figure in the data; and when his Scholars have gone through the ope. ration, may make them invert the question in order to prove the truth of their work; that is, make a new question to prove the old one; and this will be no bad exercise for them.

This method of altering the data of a question is of great utility in a School; for, as Mr. Dilworth obferves, "fome boys, lazily inclined, when they fee another at

work upon the fame queftion, will be apt to make his ❝ operation pals for their own." But thefe little forgeries are foon detected by the vigilance of the Tutor. And this is best and most expeditiously performed by. changing a figure in the data; for then the Scholar muft of course go thro' the whole operation in order to obtain the solution, as alfo thro' a fecond operation, in order to prove the truth of the firft.

It is much the best way to enter upon Vulgar and Desimal Fractions, immediately after Reduction, if time:

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will permit, but there are a great number of Scholars that have not time to learn Vulgar and Decimal Fractions with their various application, who yet of courfe, ought to learn the rule of Three, Practice, Tare and Tret, Intereft, Rebate or Difcount, and Equation of Payments, fo effentially requisite in the common affairs of Life; and for that reafor, I have treated them in whole numbers: but the judicious Mafter inay teach them in what order he pletes, regard being had to the capacity of his Pupil, and the time he has to fpend therein. I have omited Duodecimal Arithmetic, becaufe its p'ace is better fupplied, in all cafes, by Decimal Fractions.

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In this Treatife are contained many useful and intereft. ing particulars, which might here be mentioned, but I ra ther chofe to refer to the Work, and to let the Book speak for itfelf, only requefling that theReader will not too haftily Genfure and condemn it; but that after impartially pe rufing it, he will candidly excufe fuch defects as may occur to him, and have escaped my observation; and if he fhould find a tranfpofition of a letter, or a falfe figure, to excuse it, as Errors of the Prefs will inevitably creep in, and fome may have efcaped my notice.

It is not in the leaft pretended that all things treated of there are new; for I have collected fome (fuitable to nîy plan) from the Writings of my predeceffors, and here make this public acknowledgement for the afiftance.

N. B. Those who may have occafion to learn Merchants Accompts, I would recommend to their perufal, Roose`s BOOK-KEEPING, as being in my opinion, the best extant, both in Theory and Practice.