That à inutúal Agreement and Harmony may long subsist amongst you, that you may long continue an Honour to your Town, Encouragers of Science, Benefactors to Society, Happy in Yourselves, your Families and every other circumstance of Life, is the fincere Wish of lim, who with the deepest sense of Gratitude, subscribes himself, P R E F A C E. sin nii ;) 1! TE must be little versed in the common affairs of life, who does not know the great usefulness of Arithmetic: as no business can be carried on without the help of numbers ; no, trade or commerce exercised with. out regular accompts. And as the utility of Arithmetic is thus extensive, so there are extant many Treatises on the subject, fome of which are excellent in their method. But in my opinion there is ftill room for å general, concise, and rational piece, better adapted to the ufe of Schools, as well as of those who have nor the afilistance of a Master: for all the Treatises 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 Master in his "School ; and in the second place; not fit for those who would acquire a competent kill in Arithmetic, without the allistance of a teacher. To remove this defect, is the intention of the following Treatise; and in what manner my design is executed, is wholly fubaited to the impartial Reader. In the course of this undertaking, I have exerted my utmost endeavours, to deliver the definitions and rules 'in ás brief a manner as posible; to make them, at the same time general, and yet free from superfluities, which commonly attend definitions of this kind ; and have given fuch notes after them, as describe fome particulars. not fowing from the general rules themselves, but tending to explain them, or facilitate the operations. To 33 it" each cach rule also there is annexed, a great variety of the best chosen examples, with their answers, the greatest part of which are new, and which the reader cannot fail of understanding, by means of the previous examples wsought at large. After the four first roles in fimple and compoard numbers, I have exprefked the operations in algebraic figns, which in my opinion is far the beft me hod, for it not only hortens 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 wiote down as they arose with. out any abbreviations; but all fractions in the answers af. terwards are abbrevịated as much as posible. I have treat.. ed the four fundamental rules, viz. Addition, Subtraction, Multiplication, and Division, forft in fimple numbers, and. afterwards in compound; for by teaching, them in this order, difficulties do not fo falt arise. Yet I have deli. vered 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 Master chuses. I think it quite necdlefs for the first simple rules to be copied out into the Scholars book s; but if any Malter chufes. to have it done, I. would advise him to make his Schna lars run over the examples fritt upon their lates; then begin the rules again, and write them, with a few exam. ples, to each, in their books ; and thus he may with eale mix the simple and compound rules together. Tho' I said before, there is nothing fuperfluous in any of the Problems or general rules; yet the judicious teacher may omit any notes, examplos, or particular cafes he may think fit, And if every Scholar, has a printed book, he may 1 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, especial ly where the rules are hog and tedious. This book may also be of peculiar service 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 Misters, inserted several wrought examples in each rule : baving 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 Master, if he pleases, may foon make new questions of those that are folved, by only changing a figure in the data ; and when his Scholars have gone throu, h the ope. sation, may make them invert the question in order to prove the truth of their work; that is, make a new queition: prove the old one, and this will be no. bad exercise for them. to This method of altering the dati of a question is of great utility is a School ; for, as Mr. Dilworth obferves, " fome boys, lazily inclined, when they see another at 66 work upon the fame question, will be apt to make his. " operation, pass for their own." But these littk forgsries are foon deiecied by the vigilance of the Tutor. And this is beft and most expeditiously performed by changing a figure in the data ;, for then the Scholar muit of course go thro' the whole operation in order to obtain the solution, as also thro' a second operation, in order to prove the truch of the first. It is much the best way to enter upon Vulgar and De. cimal Fractions, immediately after Reduction, if time: will permit; but there are a great pamber of Scholars that have not time to learn Vulgar and Decimal Fractions with their various application, who yet of course, ought to leajn the rule of Three, Practice, Tare and Tret, Interest, Rebate or Discount, and Equation of Payments, so uflentially requisite in the common affairs of Life ; and for that reason I have treated them in whole numbers : but the judicious Maites inay teach them in what order he pleites, regard being had to the capacity of his Pupil, and the time he has to spend thereis. I have omitud Duodecimal Arithmetic, because its p'ace is better supplied, in all cafes, by Decimal tractions. In this Treatife are cortained many useful and intereft. . ing particulars, which might here te mentioned, but I raa ther chose to refer to the Work, and to let the Book speak 'for itself, only requefling that theReader will not too hasily Gensure and condemn it; but that after impartially pe. Tufingit, he will candidly excufe-fach'defect as may occur 10 him, and have escaped my observation; and if he should find a transpoz!ion of a letter, or 4 false figure, to excuse it, as Errors of the Press will inevitably creep in, and some 'may have escaped my notice. ng 9:54 It is not in the least pretended that all things treated of there'are new ; for I have collected fome (suitable to niy plan) from the Writings of my predeceffors, and here make this publis aclinowdedgement for the afiftance. "11" , N. B. Those who'may have occafion to learn Merchants Accompta, L'would recommerid to their peruial, Roose's. Book-KEEPING, as being in yly opinion, the best extant, buth in Theory and Practice. ,,Inte" 101753807 1).: erili pijt |