GA 103 TSG 3 Entered, according to Act of Congress, in the year 1847, BY AL MON TICKNOR, in the Clerk's office of the District Court of the United States, in and for the Eastern District of Pennsylvania.. STEREOTYPED BY REDFIELD & SAVAGE, 13 Chambers Street, N. Y. ADE 048-50 The first care of an author of an elementary work should be simplicity, combined with utility; but, in so doing, he should avoid the extreme, too frequently committed in some recent productions, of reducing his system below the standard of the juvenile mind, and making it puerile, whereby much time is required in the acquisition of unimportant trifles, such as require but a small portion of time, and will naturally appear perfectly plain in the regular course of instruction. The modern system of teaching arithmetic, recently introduced by authors and teachers into our schools, called “oral," "mental,” “inductive," "analytical,” &c., by the division and subdivision of an apple, counting balls, marbles, birds, bees, &c., may answer a good purpose, and prove highly beneficial, in the "infant school," and, under the management of a competent instructor, prepare the way for the introduction of a systematical course of instruction by the use of the state. As an introductory course, it is always expected that the pupil will be exercised in the elementary rules of the science, sufficient to acquire some knowledge of numbers, previous to the use of the slate ; but this can never exceed a mere introductory course, for no one will presume that calculations of importance can be made without the application of rules, and the use of the state. It is the duty of the teacher to resort to every rational and consistent means to communicate knowledge, and explain and illustrate his meaning, and the theory and practical operation, whether it be oral, mental, inductive, or analytical. But this alone is not sufficient; nor is much time required, for the pupil must come to the sober realities of the slate and black-board, otherwise it will be impossible to become master of the science-nor can we rely on the accuracy of mental calculation. It is a subject of regret, that so much time and paper has been employed in the introduction of this "juvenile mathematics" into our arithmetics and schools. The other works on arithmetic are apparently of one family-the lineal descendants of Master Dilworth's work; the rules, questions, and arrangement, are observable in all; th , examples chiefly in pounds, shillings, and pencema currency unknown to our laws; and an unnecessary amount of compound matter, in place of good practical examples which is a heavy tax on the mind, time, and patience, of both teacher and pupil, without an adequate return of scientific instruction. The time employed by the pupils in the district schools in making useless calculations in pounds, shillings, and pence, would be sufficient to take them through a regular course of mathematics; for it is nothing more nor less than a reduction of pounds to farthings, and farthings to pounds, which may be acquired in one hour. In France, the currency is similar to ours -namely, decimal. What would be the opinion of the Minister of Public Instruction, if a treatise on arithmetic should be prepared for the use of their schools, adapted to the currency of England or Prussia, to the exclusion of their own system ? " Would the book find a place in their schools ? This little volume has been prepared expressly for the use of young pupils, or those commencing the study of arithmetic; the questions are all original, and about eight hundred in number. It was the intention of the Author of the “Calculator," when it was first published, to prepare a work of this kind, from the fact that a work of that size is liable to be worn out before the pupil can go through it. As that work contains a greater amount of instruction and valuable matter than any other of the kind extant, and embraces a full and perfect system, it was not particularly intended for juvenile scholars—at least, until they had acquired some knowledge of numbers. The young student will gain more information from this small work than from those large works, now in use, whose pages are filled with anything except suitable practical examples. In this volume the examples, explanations, rules, reviews, etc., are presented in a rational, clear, lucid, and pleasing manner, such as can not but instruct. And that it may prove a benefit to those for whom it is intended, and receive the approbation of both teacher and pupil, is the sincere desire of the Author, with his best wishes for their prosperity and happiness. A. T. N. B. This volume, with the “Calculator," and stereotyped edition of the Key, will embrace about 3,500 questions for solution, nearly all of them original. CONTENTS. . PAGE 7 7 9 10 16 21 22 30 31 31 36 40 42 43 44 46 47 48 51 54 56 60 61 65 68 72 75 78 79 82 88 CG ...o EXPLANATION OF SIGNS. Signs. Explanations. = EQUAL: as, 10 mills=equal 1 cent: 10 cents=1 dime; and when placed between two numbers, it denotes that they are equal to each other, + MORE, or Addition: as, 2+2=4; it also denotes a re mainder, and when placed between two or more numbers, denotes that those numbers are to be added together; as, 2+3+4=9. Less, or Subtraction; as, 9-7=2: 7 from 9 and 2 remain; when placed between two numbers, it denotes that the number on the right is to be subtracted from the number on the left: 10–5=5. X INTO, or Multiplication; as, 4x4=16: 4 multiplied by 4 is 16; and when placed between two or more numbers, denotes that they are all to be multiplied into each other : 2x2x3=12. • Division; as 25-555: 25 divided by 5 is 5; that is, 5 is contained in 25 5 times, and 5x5=25; when placed between two numbers, denotes that the number on the left is to be divided by the number on the right: 16:4=4. ::: : PROPORTION: as, 2 : 4 :: 8:16; that is, as 2 is to 4, so is 8 to 16; or, 16 : 8 :: 4:2, as 16 is to 8, so is 4 to 2, &c. |