PREFACE. CONSIDERING the number of works on Arithmetic which have been already published, it may be thought presumptuous in the Author to have added to the number. But in the present improved state of the art of imparting instruction to youth, and consequent attention to the books made use of for that purpose, it will scarcely be argued that it is impracticable to furnish schools with books on any of the usual branches of school education, better calculated for the purpose than those previously in use. Under this impression, the Author has presented "The New Federal Calculator" to the Public. Whether it is better calculated to facilitate the progress of the learner, in the branch of study of which it treats, than those which have preceded it, remains to be submitted to the test of experience. In forming the rules, particular care has been taken to render them as clear and explicit as possible, and to arrange them in such a manner, that they may be readily committed to memory. The acquisition of a thorough knowledge of the Rules, preparatory to working the Examples which follow each of them, is particularly recommended, as the progress of the learner cannot fail to be very much facilitated thereby. The Interrogations which follow the Rules, are intended as an exercise to direct the attention of the learner in a particular manner to the Rules, and to fix them more permanently in the memory. It will be observed, that the Examples are principally given in Federal money, or dollars and cents, as being more conformable to the currency of our country, and the general mode of keeping accounts throughout the United States. Observations might be made as to arrangement, &c.; but as those interested in the subject can only judge of the merits of the work by an examination of it, they are respectfully referred to the work itself, and solicited to give it such a perusal as may enable them to decide with impartiality on its claims for admission into schools, in comparison with other works on the same subject. THOS. T. SMILEY. Philadelphia, January, 1828. EXPLANATION OF CHARACTERS. Significations. Equal; as, 20s.=£1. More; as, 6+2=8. Less; as,.8-2—6. Into, with, or multiplied by; as, 6×2=12. Proportion; as, 2: 4 :: 6 : 12. ✔or Square Root; as, 2/64=8. 3 Cube Root; as, 3/64-4. Fourth Root; as, 4/64-2, &c. A Vinculum; denoting the several quantities over ARITHMETIC. ARITHMETIC is that part of the Mathematics which teaches the art of computation by numbers. All operations in Arithmetic are performed by means of the following figures: Cipher One Two Three Four Five Six Seven Eight Nine 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. NUMERATION. Numeration teaches the proper disposition of figures to express any proposed number, when that number is too great to be expressed by a single figure. When a number is expressed by more than one figure, the value of each figure is determined by the situation which it holds in relation to the others, as represented in the following table : |