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PREFACE.

CIENCE may be compared to a highly finished pile of building, all the parts of which being difpofed in the most exact fymmetry, they muft affect our preception, and gratify our internal fenfation with a more exquifite pleasure, than if viewed in a feparate state: For, in fuch a ftate, to all but the learned, they would appear broken and unconnected materials of a mighty ftructure, which the mind, wanting power to conceive, could enjoy no fatisfaction in the contemplation of fuch a train of imperfect and confufed ideas. But, when thus exhibited in their true proportion, it will be eafy, even for the youngest fcholar, to gain a perfect notion of each; and, as he advances, a gradual comprehenfion of the beauty refulting from their connexion, and how they mutually aflift and ornament each other.

When we confider the utility of Arithmetic, on which fcience almoft all others do abfolutely depend, we need not be furprised that fo many efforts have been made. to bring it to the utmost degree of perfection, fince the real value of its ufe, certainly merits all the ftudy and pains that can be beftowed upon it.

It must be owned, that the progrefs of mathematical fciences is but flow, owing to the difficulty of the feveral branches that come under confideration; but then, it is fure and certain: The acquifion here gained is real knowledge. For this reafon, it is the work of ages to bring even a fingle branch to perfection; therefore, it is no wonder if the ancients have, in many cafes, made ufe of round-about methods to encompass their ends, and given us long and tedious demonftrations, laying down many propofitions, either of no ufe, or too fimple and trifling to be taken notice of; whence most of their inventions

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inventions may be demonftrated fhorter, propounded eafier, difpofed in a better method, and taught in a more compendious way."

There are two things abfolutely neceffary to make the acquifition of any fcience as eafy as its nature will admit. First, the difpofition of the work, fo that the rules may be clear and diftinct; fecondly, the illuftra tion of thefe rules, by a fufficient number of proper and useful examples; and, as the great difficulty in this fcience is acquiring the knowledge of ftating and folving questions, I have given a great variety of these in all the different parts of this Treatife, in the moft particular, diftinct, and plain manner I poffibly could, with their anfwers at full length, and explicit directions, where the least difficulty feemed to occur.

The feveral rules follow in the fame order, as fpeci fied in the table of contents: thus, Part I Book I. contains the four primary rules. e. Addition, Subtraction, Multiplication, and Divifion, in integers, and Reduction afcending and defcending, with the tables of money, weights, meafures, &c. which the learner fhould be well acquainted with before he proceeds to the ufe of thofe rules in compound numbers. 5.5 T "git & vd boung duoins!

In Book H. the rules follow in the fame orderin which they are generally taught in fchools; but they are all placed in fuch a manner as to have little of no dependence on each other; therefore they may be taught in what order every mafter chufes. ovo ged Avonds dziob sau) et dive 1 In the fecond and third parts, which treat of vulgar and decimal fractions, the rules and examples are laid down in fo plain and intelligentia manner, as to be understood by the meanest capacities. The fourth part treats of Geometry, Menfuration, Gaugings Land Surveying, and the Specific Gravity of Metals, savin

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which I have given every thing that is useful, taking all the care I poffibly could to make them plain and eafy to be understood: and that the learner might not be at a lofs in the firft rudiments of Geometry, &c. I have given him the draught of every operation on a large Copper-plate, in order that he may the more eafily comprehend the Problems, having every where purpofely omitted the fpeculative part, or things that are Patare ufelefs to beginners, and would prove ftumbling blocks, rather than any way to improve the mind. b

As to thofe parts which treat of Chronology, Aftronomy, Geography, and Algebra, I have taken all the care poffible (within the compafs of fuch a limitation) to make them plain, and eafily understood by young beginners. gboilib hoon of stude

And in order to make this Book as ufeful as poffible, I have added, first, a courfe of Book-keeping, by fingle entry, with a difcription of the books, and directions for ufing them.--Secondly, Book-keeping, by double entry, according to the Italian method; with various Forms of Acquittances, Bills of Exchange, &c. &c.

These are the fubjects of the enfuing work; which, if feriously pursued by a thoughtful mind, the reader may attain to a competent knowledge in these useful arts.

Perhaps it may be faid, there are books of this kind already, and therefore you are only doing the fame thing over again That there are books published with the fame defign, is acknowledged, but that I have trod in the fame fteps with their authors, I múft beg leave to deny for the chief reafon that induced me to write this Treatife was, because very few had given the operations worked at full length; this. was an article I have heard a great many complain of, even teachers/themselves.

As to the work itfelf, it is laid down upon the best foundation I could procure from the moft celebrated authors; and the rules are built upon the beft principles now taught and practifed by the moft eminent mafters of our private and public academies in this kingdom, every difficulty being explained in the moft concife method, and the whole performance made perfectly eafy to be understood; fo that, by the help of this Treatife, any young man, of a tolerable capacity, máy in a fhort time make himfelf master of the most diffi cult parts here laid down.

The inftruction of youth in fchools and academies is certainly the most expeditious method of forming the minds of young perfons, and of bringing them acquainted with that kind of learning, which their intended ftation and degree of lifeems to require; thofe, therefore, that are bleft with affluent fortunes, and are under the care of prudent parents and guardians, will stand in no need of the affiftance of this Treatife, unless it be to refresh their memories with what they have formerly been taught, or to look into fuch fubjects as are quite foreign to the inftitution of thofe feminaries of learning; but there are a great many adult perfons, and grown up youth, who through the nat rowners of their circumstances, or the neglect of their friends, are forced to endeavour to improve their loft time as well as they can.

SOUYAT W

To fuch as thefe the following Treatife will be of great fervice; for the variety of the fubjects here treated of, muft needs gain the attention of all who have the leaft inclination to ftudy arts and fciences.

Perhaps fome of our most eminent teachers may fay, by inferting the operations at length, I have encouraged dull and lazy boys, by this means, to copy out their anfwers, in order to deceive their teachers; but fuch