to the difficult. He is made to know the reason of everything he does, his memory is not loaded with rules which have not been approved by his intelligence, he is taught to discover them from established truths: and to illustrate their application, interesting examples are given. Every question is solved on its own data, and every solution contains a reasoning process, by which it becomes a demonstration, and thus arithmetic is made a captivating system of practical logic. The pupil is in this manner trained to learn ideas, not words; his memory is not made the recipient-the instrument, par excellence, to make him pass through his lesson without stumbling; but his intellectual faculties are called forth and exercised. In the production of this course we do not lay claim to much originality; for wherever we have found useful hints suitable to our purpose, they have been incorporated in the work, but the reader will find many new suggestions and applications. We have extended the scope of arithmetic by applying it to several parts of Natural Philosophy, Chemistry, Mechanics, &c., sciences which become every day more important. For the convenience of instructors the Answers have been printed separately, as the author is fully convinced that to have introduced them into the body of the work the progress of the pupil would have been retarded. We cannot recommend too strongly to Masters the necessity of inducing each youth to make problems for himself; at first they will be little else than copies of those in the book, but gradually they will throw off all semblance of imitation, and become quite original. Pupils rapidly acquire an astonishing degree of proficiency in this kind of work. The tendency of the human mind at the present time is eminently towards improvement, and we see daily our knowledge extended, both in the material and intellectual world; so that the mass of information which a man must possess in order to be a worthy and useful member of society, requires that from his youth, the mind be rightly disciplined, that the food it receives be administered with prudence and caution; and this in order to develop intellectual power, to adorn the understanding, and to create an inextinguishable thirst for knowledge. This has been the intention of the author, as far as the subject would allow, and if he has succeeded in leading the student along "the royal road," he will be amply compensated. 10 Origin of the English names of numbers. 11 to 17 Method of giving names to all numbers. 18 Properties upon which this method is based. Ternary period. 22, 23 Signs used to express numbers, and their origin. 24 to 27 Method of expressing every numerical quantity. Cipher or 43, 44 Definition of Addition. 48 The operation of Addition shortened. 70 Table of Prime Numbers and Multiples with the Factors from 1 79 Dividend. Divisor. Quotient. Explanation of÷. |