How many yards werc $175, gaining 75 cents per yard. 63. There is a rectangular field containing 10 acres, 1 quarter, 5 rods, and the length of it exceeds the breadth by 12 rods. Required the dimensions of the field. 64. A man travelled 96 miles, and then found that if he had travelled 2 miles faster per hour, he should have been 8 hours less in performing the same journey. At what rate per hour did he travel? 65. A regiment of soldiers, consisting of 900 men, is formed into two squares, one of which has 6 men more in a side than the other. What is the number of men in a side of each square? 66. A and B travelled on the same road and at the same rate from Huntingdon to London. At the 50th mile stone from London, A overtook a drove of geese which were proceeding at the rate of three miles in two hours; and two hours afterwards met a stage waggon, which was moving at the rate of 9 miles in 4 hours. B overtook the same drove of geese at the 45th mile stone, and met the same stage waggon exactly forty minutes before he came to the 31st mile stone. Where was B when A reached London ? 67. Two men, A and B, bought a farm consisting of 200 acres, for which they paid $200 each. On dividing the land, A says to B, if you will let me have my part in the situation which I shall choose, you shall have so much more land than I, that mine shall cost 75 cents per acre more than yours. cepted the proposal. How much land did each have, and what was the price of each per acre? Bac 68. A person bought two cubical stacks of hay for 41£; each of them cost as many shillings per solid yard as there were yards in a side of the other, and the greater stood on more ground than the less by 9 square yards. What was the price of each? 69. Two partners, A and B, dividing their gain $60 B took $20; A's money was in trade 4 months, and if the number 50 be divided by A's money, the quotient will give the number of months that B's money, which was $100, continued in trade. What was A's money, and how long did B's continue in trade? IMPROVED SCHOOL BOOKS. Colburn's First Lessons, or, Intellectual Arithmciu. THE merits of this little work are so well known, and so highly appreciated in Boston and its vicinity, that any recommendation of it is unnecessary, except to those parents and teachers in the country, to whom it has not been introduced. To such it may be interesting and important to be informed, that the system of which this work gives the elementary principles, is founded on this simple maxim; that, children should be instructed in every science, just so fast as they can understand it. In conformity with this principle, the book commences with examples so simple, that they can be perfectly comprehended and performed mentally by children of four or five years of age; having performed these, the scholar will be enabled to answer the more difficult questions which follow. He will find, at every stage of his progress, that what he has already done has perfectly prepared him for what is at present required. This will encourage him to proceed, and will afford him a satisfaction in his study, which can never be enjoyed while performing the merely mechanical operation of ciphering according to artificial rules. This method entirely supersedes the necessity of any rules, and the book contains none. The scholar learns to reason correctly respecting all combinations of numbers; and if he reasons correctly, he must obtain the desired result. The scholar who can be made to understand how a sum should be done, needs neither book nor instructer to dictate how it must be done. This admirable elementary Arithmetic introduces the scholar at once to that simple, practical system, which accords with the natural operations of the human mind. All that is learned in this way is precisely what will be found essential in transacting the ordinary business of life, and it prepares the way, in the best possible manner, for the more abstruse investigations which belong to maturer age. Children of five or six years of age will be able to make considerable progress in the science of numbers by pursuing this simple method of studying it, and it will uniformly be found that this is one of the most useful and interesting sciences upon which their minds can be occupied. By using this work children may be farther advanced at the age of nine or ten, than they can be at the age of fourteen or fifteen by the common method. Those who have used it, and are regarded as competent judges, have uniformly decided that more can be learned from it in one year, than can be acquired in two years from any other treatise ever published in America. Those who regard economy in time and money, cannot fail of holding a work in high estimation which will afford these important advantages. Colburn's First Lessons are accompanied with such instructions as to the proper mode of using them, as will relieve parents and teachers from any cmbarrassment. The sale of the work has been so extensive that the publishers have been enabled so to reduce its price. that it is, at once, the cheapest and the best Arithmetic in the country. Colburn's Sequel. THIS work consists of two parts, in the first of which the author has given a great variety of questions, arranged according to the method pursued in the First Lessons; the second part consists of a few questions, with the solution of them, and such copious illustrations of the principles involved in the examples in the first part of the work, that the whole is rendered perfectly intelligible. The two parts are designed to be studied together. The answers to the questions in the first part are given in a Key, which is published separately for the use of instructers. If the scholar find any sum difficult, he must turn to the principles and illustrations, given in the second part, and these will furnish ali the assistance that is needed. The design of this arrangement is to make the scholar understand his subject thoroughly, instead of performing his sums by rule. The First Lessons contain only examples of numbers so small, that they can be solved without the use of a slate. The Sequel commences with small and simple combinations, and proceeds gradually to the more extensive and varied, and the scholar will rarely have occasion for a principle in arithmetic which is not fully illustrated in this work. Colburn's Introduction to Algebra. THOSE who are competent to decide on the merits of this work consider it equal, at least, to either of the others composed by the same author. The publishers cannot desire that it should have a higher commendation. The science of Algebra is so much simplified, that children may proceed with ease and advantage to the study of it, as soon as they have finished the preceding treatises on arithmetic. The same method is pursued in this as in the author's other works; every thing is made plain as he proceeds with his subject. The uses which are performed by this science give it a high claim to more general attention. Few of the more abstract mathematical investigations can be conducted without it; and a great proportion of those, for which arithmetic is used, would be performed with much greater facility and accuracy by an algebraic process. The study of Algebra is singularly adapted to discipline the mind, and give it direct and simple modes of reasoning, and it is universally regarded as one of the most pleasing studies in which the mind can be engaged. |