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TO THE SECOND EDITION OF WELCH'S AMERICAN
THE sale of the first Edition of this Arithmetic has much exceeded the expectation of the Author, and the present increasing demand for them has induced him to revise, correct, and give it another impression ; three thousand of the first edin tion have been sold in about one year, with very little exertion : since this Arithmetic was first published the author has used it constantly in his school, and of course has had opportunity to discover all the crrors in the first edition, as well as to discern where any alterations could he made for the better; the errors have been corrected, and such alterations made as he thought would render the work more useful, or easy to be understood. The design of the Author, in publishing this book, is to facilitate the education of the rising generation, by furnishing them with a concise, and cheap Arithmetic, calculated in the present currency of the United States, containing all necessary rules, which are used by those who are doing business in America ; having this in view he is of opinion that a book designed for a cominon school book, should contain, not only the principal rules of Arithmetic, but many other rules which are published only in books on Mathemnatics : Arithmetic and Mathematics are two distinct sciences, but they are so nearly connected, that it becoines necessary for every man of business to have some knowledge of Mathematics as well as of Arithmetic; Arithmetic is the art of computing by nunbers; and Mathematics is the science of number and magnitude, or is numbers applied in the mensuration of superficies and solids; it is not the intention of the Author to treat of mathematics in this small treatise in its full latitude, but he only intends to treat of some of the most useful probleins which often occur in business, in measuring the capacities of different bodies: to connect Arithmetic with the most useful part of Mathematics, and at the same time to comprise the whole in a book of moderate size, the Author has found it expedient to exclude many rules that are in other Arithmetics, which are of no real use in business, such as single and double Position, Arithmetical and Geometrical Progression, and several other rules which serve to amuse, rather than to give any useful information; the Author has not the least intention to censure other Arithmetics, but as he is aimivg wholly at improvement, it becomes necessary to point out some of the principal deficiences of other hooks of this kind ; the Arithmetics now extant are almost
wholly calculated in lawful money, and most of them are entirely destitute of any information on Mensuration, a subject highly necessary to be taught in every school; and the Author intends by the publication of this treatise, to furnish a great variety of useful problems in Mensuration which are not to be found in any other Arithmetic ; and as the present method of computing by dollars, cents and mills is the same in all the states and is much the easiest, he is of the opinion that it ought to supersede the method of computing in pounds, shillings, pence, and farthings, and of course has calculated this book wholly in Federal money; and has only given rules to reduce the former currency of the different states into the present, and the contrary : such arrangement has been made of the rules in this book, as the Author has found by long experience in school keeping to conduce most to forward the learner; and those who are beginning to cypher in this book should follow the order of the book, observing to commit all the tables, and rules to memory before they proceed tb do the questions: the Author knowing that children should be fed with milk rather than meat, has endeavoured to exclude from this treatise every thing that is intricate and hard, and has rendered the whole as simple, and easy to be understood as the nature of the work would admit of. Among the many new and useful rules in this Arithmetic is the method of making town taxes, a subject not generally understood ; also many new problems in measuring timber, ampong which is a new and easy method of finding how much square timber is contained in any round stick, or how inuch the stick would measure if hewn square; by which an error is detected in the common method'; guaging, waterleveling and tables of the monies of the world with their intrinsic value in the United States, occupy conspicuous places in this Arithmetic; and the Antbor flatters himself that the farmer, the mechanic, the trader, and merchant will find information in this book suited to their various occupations : and while he acknowledges his grateful thanks to the generous publick, for the kind reception of the first edition of this work, he solicits that share of publick patronage which this improved edition is entitled to; and with this expectation he submits it to publick examination without any other support than its own merits ; hoping that it will be highly useful in facilitating the education of youth, for whose advancement in knowledge he has spent fourteen years of the morning of his life.
THE AUTHOR. Exeter, January 1, 1814.
ARITHMETIC is the art of computing by numbers ; these numbers are called Figures, viz: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,~, of itself has no value, but when joined to the right of other numbers, it increases their value in a tenfold proportion. Thus, 1 is one. 10 is ten, 2 is two, 20
Of other Characters used in Arithmetic. This mark + Is the sign of Addition; and shews, that the
number which follows the sign, mustbe added to the number before it. Thus 9+10 signifies that 9 and 10 are to be added.
Is the sign of Subtractions and denotes the number following it, must be subtracted from the one before it. Thus, 16--4 signifies that 4 must be taken from
16. * Is the sign of Multiplication ; and denotes.
that all the numbers, between which it is placed, are to be multiplied together. Thus, 9X9 signifies that 5 is to be multipled by 9, or 9X9X9 must be multiplied. • Is the sign of Divison; and denotes the number standing before it, is to be divided by the number following it. Thus, 943 signifies that 9 is to be divided by 3. This is the signofequality, and signifies the sum or product of the numbers before it, is equal to the number after it, 244-45ll mean that 2, 4 and 5 added, their sum
would be 11; and 2X4X540 mean, that
is required. 3 This shews the Cube Root of the number
Millions of Millions.
OOOOoo Tens of Thousands.
23 | 24
the left or right hand,
1 | 2
7 8 8
9 | 10 | 11 | 12 | 13 | 14 | 15 16 17 18 19 20, 1 214
6 17 18 9 10 | 11 | 12 | 13 | 14 | 15 | 16 17 18 19 20 21 22 7 | 8 | 9
1011 12 | 13 | 14 | 15 | 16 17 18 19 20 21 | 22 23 6 7
8 | 9 | 10 Il 12 | 13 | 14 | 15 | 16 17 18 1.19 20 21 22
25 26 271
111 | 12 | 13 | 14 | 15 | 16 | 17 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 27 28 29 10 | 12 13 14 | 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30110
der. quired. swering to the remaintop, is a number anover that numberon the subtract, and directly from which you would you find the number right or left hand, till look along towards the lumn, and on that line left or right hand coto be subtracted on the Look for the number
Subtraction. The use of this Table in stands 20, the sum regle of the two lines ly over, and in the anon the top stands directlong on that line till 13 or right, and move a look for 7 on the left, ed to add 7 with 13, required.--It is requirmeet, stands the sum angle in which the lines and in the corner, or would add it on the top, number with which you or right hand, and the to be added on the left Look for the number