TO THE FIRST EDITION OF WELCH'S AMERICAN ARITHMETIC REVISED. Considering the encouragement with which the original work has met, since its first appearance to the public, the author feels assured that a like system was wanted, and will still receive the entire approbation of a generous public. "If a quick sale and continued demand of a book are recommendations, this system of Arithmetic may claim a competent share of them; for since the first publication of the original, not less than 26000 copies have been published and sold, and yet an increasing demand." No other recommendations than these and its own merits will be offered in this edition: desirous to increase the benefit of the work, the author has made many important additions and corrections and omitted all matter which was deemed superfluous in the original. In revising the work, it was thought proper and beneficial that additions to the rules of Interest and to the method of casting interest on Notes, Bonds, &c. should be made, and also that it should comprise a few valuable rules which have never appeared in the original, viz.-Compound Average Judgment, Commission, Brokerage, Insurance, Barter, Loss and Gain, Single and Double Position, Arithmetical and Geometrical Progression; and a series of useful Miscellaneous Questions; all arranged and well calculated to promote instruction in this branch of science. The Revisor having been for many years engaged in instructing, found tha' a thorough knowledge of the Rule previous to the operation of the Example, was highly requisite before any progress could be made; and that the easiest method to simplify and make it familiar was far the best. This is presumed to be accomplished. Annexed to each Rule are interrogatories numbered by figures in their order, and these figures referring to a like, in the Rule, where the answer to the interrogative should commence; and when these are once perfectly committed to memory, all obscurity is removed and the Rule then becomes easy and plain and needs but little or no further explanation. As this work is now presented to the public, the author has full confidence in commending it to instructers, well assured it will lessen their own labor and facilitate the improvement of their pupils. It is perfectly obvious, that great convenience will be found both by instructers and scholars in having the interrogatives printed on the same page with the rule from which they are to be answered, as no labor is required in selecting appropriate answers by reading and studying the whole rule. This system, it is hoped, will supply the long sought for Classical Arithmetic, whereby whole schools can be examined, collectively or separately; and while the author expresses his confidence of the merits of such a work, he trusts that the following pages will sufficiently recommend themselves. Double Rule of Three, Division of Vulgar Fractions, Double Fellowship, Double Position, Duodecimals, Equation of Payments, Figures of equal sides, Frustum of a Cone, Hewn Lumber in round, Sides equal, 62 Multiplication of vulgar fractions, 92 121 Middle Zone of a Sphere, 177 121 Middle Frustum of an Eliptic 122 Spindle, 180 148 Numeration Table, 5 106 Practice, 115 110 Position, 125 A thing standing alone, as a ball, counts If another thing be put with it, they both count If two things be put with it, they all count If three things be put with it, they count If four things, they then count If five things, they then count The pupils must be taught to count the "s in different directions, and to count up the total of the four upper lines a sáhs, the object of the lesson *The lessons thus marked should be taught to classes by ocular demon- The instructer should follow up this plan of illustration, (from twenty- ADDITION. LESSON FOURTH.* How many balls are two balls and three balls? Henry has three balls, and George has five balls; how many balls have both? James lost four balls, and John lost five balls; how many balls did both lose? LESSON FIFTH. To be recited without the book or slate. One and two are how many? many Eight and three are how many? ? After a full explanation, the scholars should be made to recite from the lessons of this nature, without the illustrations upon the black board. |