ARITHMETIC; 1. WHOLE NUMBERS, WEIGHTS, AND MEASURES, II. FRACTIONS, VULGAR AND DECIMAL, III. MERCANTILE ARITHMETIC, IV. EXTRACTIONS OF ROOTS, PROGRESSIONS; &c. Graham THE LARGE AND ENTIRE TREATISE. And adapted to the Commerce of Ireland as well as that of Athl FOR THE USE OF SCHOOLS. CON 19/8/16 BY JOHN GOUGH. AUTHOR OF THE PRACTICAL ENGLISH GRAMMAR. THE FOURTEENTH GENUINE EDITION, CAREFULLY REVISED BY LISHED BY ROBERT TELFAIR, OF BELFAST. And now fitted to the Commerce of America, WITH AN APPENDIX OF ALGEBRA. MUCH MORE EXTENSIVE THAN THAT HITHERTO PUBLISHED. DUBLIN: GRAISBERRY & CAMPBELL, PRINTERS, 10, BACK LANE, Sowderomeк t THE Reader is here presented witli a Treatise of Prac tical Arithmetic for the Use of Schools, being a complete Extract of the Practical Part from my Treatise of Arithmetic in Theory and Practice. The first edition of which work being now mostly disposed of, and having received some friendly remonstrances as to the execution of it, with respect to paper and type, I resolved to publish a second edition in an elegant octavo volume by subscription; but as this proposed edition might be thought too expensive for a common school book, I (having by experience in my profession as well as by the growing demand, found its usefulness as such) have thus published the Practical Part distinct, at a low price, which I apprehend will be thought sufficient for the common use of school boys, while the work at large, will be highly useful to masters for a fund of instruction, as well as to students who are well accomplished in the practical part. The method was partly suggested by a note on Rollin's thoughts concerning Education, p. 44, of the Dublin edition, which appearing to contain sonte useful hints, I transcribe at length, viz. "Arithmetic might be taught in schools, in a much " more expeditious way than it generally is, by dividing "the scholars into forms, in the same manner as in " teaching languages, the whole may be divided into five, " six or more classes; ten of the pupils, for instance may be in Multiplication, six in the Rule of Three, "thirteen in Practice, and so on. Whenever any class " is to proceed to a new rule, the master may explain to " them in chalk on two large boards, or some such thing, "the nature and genius of the rules into which they are "entering. A considerable time should be employed in "these explications, and the scholars might take places, " as in learning latin, &c. which could not fail of inspiring "them with great emulation. The several pupils in A2 1 a form should always be set the same sum or question, " but must be separated to prevent their copying one from "another. "Twould also be proper to draw up for their use, an epitome of Arithmetic, by way of question " and answer, containing the nature and explanation of "the several rules in that science, this they should copy, " and learn by heart perfectly; by which means they "would be able, not only to state the several questions very expeditiously, but to give a reason for every thing." I apprehend the usual method of teaching Arithmetic is two-fold, either the master or assistant writes down the rules and questions for the boys, or causeth them to write them themselves from printed books or manuscripts : The former method is much more toilsome to the teacher, and besides takes up much time, which I presume might be better employed in instructing the pupils, and explaining to them the nature of their rules. And as most of the printed books are intended to explain the doctrine of Arithmetic in general to those who may want to improve themselves by reading, the questions are most or at least too many of them wrought, for which reason they are not suitable to be laid before the boys, as they would make no scruple of copying the work of their Author to ease themselves of the trouble of performing it; besides as the number of these in a school is generally few, it occasions perplexity and delay, while one waits for another to copy out his rule or question; the same objection lies against one general manuscript, although it consists of questions and their answers only. To avoid this inconvenience, some teachers have disposed the several rules of Arithmetic, with proper questions and their answers, into little manuscripts of a sheet or two of paper orderly numbered; but these wearing out with continual use, it occasions very considerable labour to keep a school properly supplied therewith; from which considerations, the utility of introducing such a Book as this (properly drawn up) into our Schools, will be seen t the first view. Although Although regularity of method seemed to point out the order, or plan I have observed; yet I am not of opinion it will be necessary to teach all the parts in order as they lie; I think it will be best to begin with Whole Numbers, and proceed through Notation, Addition, Subtraction, Multiplication and Division: Addition and Subtraction of Numbers of divers Denominations, Reduction and the Rule of Three to Contractions, without meddling with the questions at the end of the rules: this may be a first course. 2dly, Suppose they go over the same with the questions, and Multiplication and Division of Numbers of divers Denominations; through the Rule of Three entirely, and then proceed through Fractions, Vulgar and Decimal. 3dly, Begin again at Multiplication of divers Denominations, and so proceed orderly quite through Mereantile Arithmetic, and in these reviews the learners may be detained a longer or shorter time in any rule, as they may appear more or less ready in the calculation thereof. 4thly, And if again they went through the whole, with the reasons of the rules, I do not apprehend such a method absurd; or such a revisal of the same rules unnecessarily tedious: But I only mean just to hint my apprehensions of the use to be made of such a book, without pretending to prescribe to Teachers, many of whonı, without doubt, are men of much more experience than myself, and of greater abilities likewise. If any of these find any material imperfections in this work, have any amendments to propose, or any improvenrents of the plan, if they will be so kind as to impart them to the author, he hopes to receive them with cander, give them the due deference, and to make the necessary use of them (with a suitable acknowledgment) in a future edition of the work, if there should be hereafter occasion for it.. JOHN GOUGH... AS |