THE PRACTICAL ARITHMETIC; IN WHICH THE PRINCIPLES OF OPERATING BY NUMBERS ARE ANALYTICALLY EXPLAINED AND SYNTHETICALLY APPLIED: TO WHICH IS APPENDED CONCISE ACCOUNT OF THE MENSURATION OF SUPERFICES ADAPTED TO THE USE OF IN THE UNITED STATES. Candidus imperti, si non, his utere mecum."-HORACE NEW YORK. G. & C. & H. CARVILL, 108 BROADWAY. Southern District of New-York, ss. BE IT REMEMBERED, That on the 17th day of September, in the fifty-fourti year of the Independence of the United States of America, Anno Domini 1829, TERTULLUS H. BABCOCK of the said District, has deposited in this office the title of a book, the right whereof he claims as Proprietor, in the words following, to wit: "The Practical Arithmetic; in which the principles of operating by numbers are analytically explained and synthetically applied: to which is appended, a concise account of the mensuration of superfices and solids, chronological problems, the mechanical powers, &c. &c.-adapted to the use of schools and academies in the United States.-by T. H. Babcock. "Si quid novisti rectius istis, Candidus imperti, si non, his utere mecum"-HORACE. In conformity to an Act of the Congress of the United States, entitled, "An Act for the encouragement of learning, by securing the copies of Maps, Charts, and Books, to the authors and proprietors of such copies, during the time therein mentioned." And also to the Act, entitled, "An Act, spplementary to an Act, entitled, an Act for the encouragement of learning, by securing the copies of Maps, Charts, and Books, to the authors and proprietors of such copies, during the times therein mentioned, and extending the benefits thereof to the arts of de Agning, engraving, and etching bistorical and other prints." FRED. J. BETTS. Clerk of the Southern District of New-York H. C. Sleight, Printer, No. 3, Marble Building, Chatham Square, New-York PREFACE. THE PLAN of the following pages was determined upon, and part of the work executed in the beginning of the year 1827. Since then the author has met with several new publications, claiming a great share of merit, and agreeing in many respects with his own views of the subject. But, with reference to these, and of course to all others preceding, he presumes the following will be found to contain some very valuable improvements. In preparing it, however, it has been his steady and undeviating principle never to innovate, except with a view to improve. He submits his work as containing more practical and necessary matter, the most important parts being exhibited more plainly to view, and the whole displayed in a manner more clear and interesting, than any heretofore published. Feeling, however, a just diffidence, arising from a consciousness of the imperfection of all things sublunary, he solicits the indul. gence of the public, and their FAVOUR and co-operation in furnishing him hints by which to meet, if possible, their more critical requisitions. The THEORETICAL QUESTIONS, inserted in the work, are for the purpose of recitation. These, the learner should be required to answer APPROPRIATELY; that is, in a manner suited to the questions: and he should be apprised of this when he has his lessons given him. Thus, in answer to the question-"Why is it that figures in combination have a TENFOLD relation to one another ?" instead of repeating it as in the book, he should reply, because we have TEN FIGURES in our notation; or in some other way in his own language. This, it is believed, will have the good effect of instructing him to form HIS OWN ANSWERS, and thus furnish an exercise in COMPOSITION. It is, therefore, to be hoped that no teacher will neglect these questions; but, on the contrary, that they will be thoroughly and punctually attended to, whenever they occur. It may be well too, for the teacher to propose other questions; as, in the illustrations, it is very desirable that every item should be pointed out, and the learner questioned, until he is thought to understand it fully and clearly. The use of the Almanac on the following page, is to find the day of the week answering to any given day of ANY MONTH.-RULE.-Look for the day against the proposed year, then at the top, under the given month, you will find the DAYS OF THE MONTH on which THAT DAY falls. EXAM. Com. Perry was born Aug. 21, 1785, on what day of the week was that? Against the proposed year we find Tuesday, and at the top under the given month, we find, that Tuesday is the 2d, 9th, 16th, and 23d; therefore, the 21st falls on Sunday, the day required. By this Almanac may also be found the DOMINICAL LETTER and EPACT of any year for ONE CENTURY, from the commencement of the AMERICAN INDEPENDENCE. N. B. In leap year, Jan. and Feb. must be taken in the columns marked * 4 '06 Sat. '07 Sun. '80 Wed. BA 23 '81 Thur. '82 Frid. F '83 Sat. E 26 '08 Tues. CB 3 '33 F. F FE 22 '13 Mon. C 28 '15 Wed. A 20 '16 Frid.t GF '17 Sat. E C '88 Sat.t '29 S. D 25 '54 W. A 1 F 29 '30 M. E 11 '31 Tu. B 23 12 D 22 32 Th.t AG 28 9 1 '41 M. C 4 '63 S. D 11 '64 Tu.t CB 22 ED 26 '65 W. A 3 GF 11 '69 M. C 17 70 Tu. 28 '71 W. A 9 C ERPE 14 '72 F. GF 20 '73 St. E 1 6 '74 S. D 12 |