a From Mr. Henry Fisk, Instructor of schools in Concord. I have examined with much attention Pike's Arithmetick simplified by D. Leavitt, and think it the best calculated to facilitate the acquisition of this important branch of literature, of any treatise I have ever seen. I do cheerfully recommend it to the use of schools, thinking that greater utility may arise from it, than any other Arithmetick pow in use. HENRY FISK. Concord, July 5, 1826. From Hon. Matthew Harvey, President of the Senate of New Hampshire. Hopkinton, December 4, 1826. DEAR SIR, -After a careful examination of your improved edition of Pike's Arithmetick, I am decidedly of opiuion there is no system, I now in use, better arranged than this, for an easy acquirement of a correct and thorough knowledge of the principles of arithmetick. In all our schools, Leavitt's improvements must be convenient for the instructor, and useful to the scholar, With great respect, I am, Sir, Your obedient servant, MATTHEW HARVEY. Jacob B. Moore, The Hon. John Vosè, Preceptor of Pembroke Academy, concurs in the above recommendation of Mr. Harvey. From Amos J. Cook, Esq. Preceptor of Fryeburg Academy. Fryeburg, Jan. 6, 1827. DFAR SIR,--I have always entertained a great fondness for the System of Arithmetick, published more than forty years ago by Nicolas Pike, Esq. It is a work which brings to view great powers of mind, and displays deep mathematical research. This work has been abridged a number of times, and has appeared in different forms, and from different presses ; yet still it has never in my opinion, promised so much usefulness to the common school and academy, as it now does from the hand of Mr. Dudley Leavitt, “ Teacher of Mathematicks and Natural Philosophy." The judicious arrangement of the whole, and the nutes and questions at the foot of its pages, much enhance the value of the publication. The paper, the type and the execution throughout reflect credit on the American Press. I am, dear sir, affectionately your friend, AMOS J. COOK. Jacob B. Moore. a From Benjamin Doe, Esq. Preceptor of Kingston Academy. Kingston Academy, N. II. June 21, 1827. Mr. Jacob B. Moore,- Dear Sir, -The copy of your edition of Pike's Arithmetick, which you were pleased to present ine, I have carefully examined. I have ever considered Pike's large work as the most complete system ever published. His abridgment has pot, of late years, been so much used. I think, that the improvements which hare been made in your edition of it, will render it much more valuable ; and they will again be the means of bringing the work into more gen. eral use. The demonstrations and illustrations given in it, will make the science more attractive to the scholar. I wish you success in the undertaking: Yours respectfully, BENJAMIN DOE. PUBLISHER'S NOTICE. * THE SYSTEM OF ARITHMETICK, of which this work is a new aud careful abridgment, has been so long an inmate of our academies and higher seminaries of learning, that its merits are familiar to all. Though nuinerous treatises on the subject have successively appeared, since the work of Pike was first published,* few have been able to sustain even an ephemeral reputation, excepting such as were built upon the labours of our author, yet simplified in some of the more intricate parts. Excellent as that work is acknowledged to have been, it had its defects ; especially in its want of conformity to the federal notation, and of simplicity, and attraction to the scholar, in a few of the rules. An abridgment was some years since published, in which little else was done than to change the notation ;-and for want of that conciseness in the fundamental rules, which some treatises of less real merit possessed, the book was superseded, and has been neglected in this section of the country, even by those who avow their preference for Pike's as a complete system. At the suggestion of several experienced teachers, the Publisher was induced to put to press a New ABRIDGMENT of Pike's Arithmetick, enibracing all such portions of the original work as should be necessary for the use of common schools, or of private learners ; containing also, many new and practical illustrations of the more important rules. For this purpose, several improvements suggested by instructors of schools and academies have been incorporated in the work ; and the whole has undergone the patient and careful revision of a gentlemanı well known to the publick, as a teacher of great merit both in Mathematicks and Natural Philosophy, and who has devoted many years to the instruction of youth of both sexes. a native of Somersworth in New Hampshire ; was horn Oct. 6, 1743 ; gravluated at Harvard College. 1766; was employer a great portion of his life in instructing youth, and died at Newburyport, Ms. Dec. 9, 1819. * In 1789.--NICOLAS PIKE was One great object in this abridgment has been to simplify the general rules, by placing before the scholar their constituent parts illustrated by plain and easy examples. In executing the work, nothing superfluous has been added, and nothing omitted that would contribute to perfect its design, and render it serviceable to youth. Those, however, who are in the habit of teaching superficially, with the view of flattering the pupil and the parent with the mistaken idea of extraordinary progress, may probably raise objections against the work, as containing too many things to be committed to memory—that they will burden and confuse the mind of the scholar. Such persons have yet to learn the capacity of the young mind. For, though it may be true that a mass of complex ideas crowded into the mind of a scholar would embarrass and perplex him-it is equally true, that in proportion to the number of simple propositions impressed upon the memory of a child, will be the progress of his understanding in strength and capacity. In the arrangement of the present work, regard has been paid to the natural dependence of the several parts upon each other. Though in some instances, it differs from the common method, it is believed to be the more correct and useful. Some of the old and obsolete rules of Tare and Trett, &c. have been omitted, and the Duties and Custom-House Allowances of our own country substituted. Several rules, such as Position, Alligation, Permutation, &c. are inserted in this work, more for the purpose of gratifying the curiosity and exercising the mind of the scholar, than for their utility in business. The practical parts are those upon which the greatest attention has been and should be bestowed"; and it is upon the improvements in these generally, as well as upon the established character of the author, that the publisher rests his belief of the merits of this edition. April 14, 1826. TABLE OF CONTENTS. Page. 9 General Method of Making Taxes, 140 Problems, resulting from a comparison Evolution, 59 Extraction of the Square Root, 170 70 Extraction of the Cube Root, 89 Rule for extracting the roots of all Of the Screw, 198 The Single Rule of Three, 130 Useful and Diverting Questions, 199* INDEX TO THE TABLES. 33, 41 Addition, 14]Interest by decimals, 119, 123 Ale or Beer Measure, 50 Land or Square Measure, 48 Aliquot parts of money weight, Long do. 45, 46 &c. 112, 148, 149 Money, American Coins, 33|Motion, 47 Apothecaries' Weight, 44 Multiplication, 21 Avoirdupois do. 43 Notation, 12 Cloth Measure, 44 Numeration, 10 Decimals, 41 169 49 48 141 Duodecimals, 124 Time, 46 English Money, 42 49 391 EXPLANATION OF ARITHMETIOAL SIGNS. Signs. = Two parallel horizontal lines are the sign of equality. It shows that the number before, is equal in value to the number after it. Example, 1 dollar=100 cents, is read thus, 1 dollar is equal to 100 cents. + Two short lines, crossing each other at right angles, are the sign of Addition. It shows that numbers with this sign between them, are to be added together. Exumple, 5+7=12, is read thus, 5 added to 7, or 5 plus 7, is equal to 12. A short horizontal line is a sign of Subtraction. It shows that the number after it, is to be taken from the number before it. Example, 12—7=5, is read thus, 12 less 7, or 12 minus 7, is equal to 5. X Two short lines crossing each other in the form of an X, are the sign of Multiplication. It shows that the number before it, is to be multiplied by the number after it. Example, 6x5=30, is read thus, 6 multiplied by 5, is equal to 30. • A short horizontal line between two points, is the sign of Di vision. It shows that the number before it, is to be divided by the number after it. Example, 30-6=5, is read thus, 30 divided by 6, is equal to 5. :::: Four double points or colons are the sign of Proportion ; and to show that numbers are proportional, they are written thus, 2 :4::8:16, which are read, 2 is to 4 as 8 is to 16. 2 This sign signifies the second power or square. This sign signifies the third power or cube. ♡ This sign, prefixed to any number, shows that the square root of the number is required ✓ This sign, prefixed to any number, shows that the cube root , of the number is required. 2 3 |