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CIENCE may be compared to a highly finished pile of building, all the parts of which being disposed in the most exact fymmetry, they must affect our prcception, and gratify our internal sensation with a more exquisite pleasure, than if viewed in a separate ftate: For, in such a state, to all but the learned, they would appear broken and unconnected materials of a mighty structure, which the mind, wanting power to conceive, could enjoy no satisfaction in the contemplation of fuchi a train of imperfect and confused ideas. But, when thus exhibited in their true proportion, it will be eafy, even for the youngest scholar, to gain a perfect notion of each; and, as he advances, a gradual comprehension of the beauty resulting from their connexion, and how they mutually aslift and ornament each other.

When we consider the utility of Arithmetic, on which fcience almost all others do absolutely depend, we need not be surprised that so many efforts have been made to bring it to the utmoit degree of perfection, since the real value of its use, certainly merits all the ftudy and pains that can be bestowed upon


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It must be owned, that the progress of mathematical sciences is but flow, owing to the difficulty of the several branches that come under consideration; but then, it is fure and certain: The acquision here gained is real knowledge. For this reason, it is the work of ages to bting even a single branch to perfection; therefore, it is no wonder if the ancients have, in many cases, made use of round-about methods to encompass their ends, and given us long and tedious demonstrations, laying down many propositions, either of no use, or too simple and trilling to be taken notice of; whence most of their


inventions may be demonstrated shorter, propounded easier, disposed in a better method, and taught in a more compendious way.

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There are two things absolutely neceffary-to-make the acquisition of any science as easy as its nature will admit. First, the disposition of the work, so that the rules may be clear and diftinét ; fecondly, the illustra: tion of these rules, by a sufficient number of proper and useful examples; and, as the great difficulty in this science is acquiring the knowledge of stating and solving questions, I have given a great variety of these in all the different parts of this Treatise, in the most particular, diftin&t, and plain manner I possibly could, with their answers at full length, and explicit directions, where the least difficulty seemed to occur.

The several rules follow in the fame order, as fpecified in the table of contents: thus, Part 1 Book I. contains the four primary rules ; 1. es Addition, Subtraction, Multiplication, and Division, in integers, and Reduction afcending and descending with the tables of money, weights, measures, &c. which the learner should be well acquainted with before he proceeds to the use of thofe rules in compound numbers. 9. !T B 128gy odtetus

ons d 55/'15boitsi In' Book H. the rules follow in the fame order in which they are generally taught in schools; but they are all placed in such a manner as to have little or no dependence on each others therefore, they may be taught in what order every master ehufes. novo gris Come on olet sich ett drive

In the fecond and third parts, which treat of vulgar and decimal fractions, the rules and examples are laid *down in fo plain and intelligent a manner, nas to be understood by the meanest capacities. The fourth part treats of Geoinetry, Menfuration, Gauginggis Land Surveying, and the Specific Gravity of Metals, &c.vin

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which I have given every thing that is useful, taking all the care I possibly could to make them plain and easy to be understood: and that the learner, might not be at a loss in the first rudiments of Geometry, &c. I have given him the draught of every operation on a large Copper-plate, în order that he may the more easily comprehend the Problems, having every where pur pofely omitted the speculative part, or things that are useless to beginners, and would prove stumbling blocks, rather than any way to improve the mind. Witin bu

Laiuteri As to those parts which treat of Chronology, Astronomy, Geography, and Algebra, I have taken all the care possible (within the compass of fuch a limitation) to make them plain, and easily understood by young beginners.

Dit And in order to make this Book as useful as possible, I have added, first, a course of Book-keeping, by fingle entry, with a discription 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.

1 These are the subjects of the ensuing work; which, if seriously pursued by a thoughtful mind, the reader

may attain to a competent knowledge in these useful arts.

tudieloolit. 3 Perbaps it may be said, there are books of this kind already, and therefore you are only doing the same thing over against That there are books published with the same design, is acknowledged, but that I have trod sing the fame steps with their authors, I must beg leave to denys for the chief reafon that induced me to write this Treatise was, because very few had given the operations worked at full length; this wasl an article I have heard a great many complain of, even: teachers themselves, dos

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As to the work itfelf, it is laid down upon the best foundation I could procure from the most celebrated authors; and the rules are built upon the best principles now taught and practised by the most eminent masters of our private and public academies in this kingdom, every difficulty being explained in the most concise method, and the whole performance made perfectly easy to be understood; so that, by the help of this Treatise, any young man, of a tolerable capacity, máy in a short time make himself master of the most diffi, cult parts here laid down.

The instru&tion of youth in fchools and academies is certainly the most expeditious meihod of forming the minds of young persons, and of bringing them acquainted with that kind of learning, which their in, terded station and degree of lifa eems to require ;

sofe 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 such subjects as are quite foreign to the institution of those seminaries of learning; but there are a great many adult persons, and grown up youth, who through the narrowners of their circumstances, or the neglect of their friends arg forced to endeavour to improve their loft time as well as they can.


To fuch as these the following Treatise will be or great service ; for the variety of the subjects here treated of, must needs gain the attention of all who have the least inclination to dtudy arts and sciences.

Perhaps some of our most eminent teachers may fay; .by inserting the operations at length, I have encourage: dull and lazy boys, by this means, to copy out their answers, in order to deceive their teachers; but such

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