TUTOR'S ASSISTANT; BEING A COMPENDIUM OF ARITHMETIC, AND COMPLETE QUESTION-BOOK: CONTAINING, I. Arithmetic in whole numbers; being a brief explanation of all its rules II. Vulgar Fractions, which are treated with a great deal of plainness and III. Decimals, with the Extraction of the Square, Cube, and Biquadrate IV. Duodecimals, or Multiplication of Feet and Inches, with Examples V. A Collection of Questions promiscuously arranged for the exercise of ALSO, A new and very short method of extracting the Cube Root, and a General Ta- The whole being adapted either as a QUESTION-BOOK for the Use of This work having been perused by several eminent mathematicians and BY FRANCIS WALKINGAME, WRITING-MASTER AND ACCOUNTANT; TO WHICH IS ADDED, A COMPENDIUM OF BOOK-KEEPING BY SINGLE ENTRY, BY ISAAC FISHER. DERBY: PUBLISHED BY THOMAS RICHARDSON AND SON; SIMPKIN, MARSHALL, AND CO., LONDON. 1843. PREFACE. THE Public, no doubt, will be surprised to find there is another attempt made to publish a book of ARITHMETIC, when there are such numbers already extant on the same subject, and several of them that have so lately made their appearance in the world; but I flatter myself, that the following reasons which induced me to compile it, the method, and the conciseness of the rules, which are laid down in so plain and familiar a manner, will have some weight towards its having a favourable reception. Having sometime ago drawn up a set of rules and proper questions, with their answers annexed, for the use of my own school, and divided them into several books, as well for more ease to myself, as the readier improvement of my scholars, I found them, by experience, of infinite use; for when a master takes upon him that laborious, (though unnecessary) method of writing out the rules and questions in the children's books, he must either be toiling and slaving himself after the fatigue of the school is over, to get ready the books for the next day, or else must lose that time which would be much better spent in instructing and opening the minds of his pupils. There was, however, still an inconvenience which hindered them from giving me the satisfaction I at first expected; i. e. where there are several boys in a class, some one or other must wait till the boy who first has the book, finishes the writing out of those rules or questions he wants, which detains the others from making that progress they otherwise might, had they a proper book of rules and examples for each; to remedy which, I was prompted to compile one, in order to have it printed, that might not only be of use to my own school, but to such others as would have their scholars make a quick progress. It will also be of great use to such gentlemen as have acquired some knowledge of numbers at school, to make them the more perfect; likewise to such as have completed themselves therein, it will prove, after an impartial perusal, on account of its great variety and brevity, a most agreeable and entertaining exercise book. I shall not presume to say any thing more in favour of this work, but beg leave to refer the unprejudiced reader to the remark of a certain author,* concerning compositions of this nature. His words are as follow: "And now, after all, it is possible that some who like best to tread the old beaten path, and to sweat at their business, when they may do it with pleasure, may start an objection, against the use of this well-intended Assistant, because the course of arithmetic is always the same; and therefore say that some boys, lazily inclined, when they see another at work upon the same question, will be apt to make his operation pass for their own. But these little forgeries are soon detected by the diligence of the tutor: therefore, as different questions to different boys do not in the least promote their improvement, so neither do the questions hinder it. Neither is it in the power of any master (in the course of his business) how full of spirits soever he be, to frame new questions at pleasure in any rule; but the same question will frequently occur in the same rule, notwithstanding his greatest care and skill to the contrary. "It may also be further objected, that to teach by a printed book is an argument of ignorance and incapacity; which is no less trifling than the former. He, indeed (if any such there be) who is afraid his scholars will improve too fast, will, undoubtedly, decry this method: but that master's ignorance can never be brought in question, who can begin and end it readily; and, most certainly, that scholar's nonimprovement can be as little questioned, who makes a much greater progress by this, than by the common method." To enter into a long detail of every rule, would tire the reader, and swell the preface to an unusual length; I shall, therefore, only give a general idea of the method of proceeding, and leave the rest to speak for itself; which I hope, the kind reader will find to answer the title, and the recommendation given it. As to the rules, they follow in the same manner as the table of contents specifies, and in much the same order as they are generally taught in schools. I have * Dilworth. gone through the four fundamental rules in Integers first, before those of the several denominations; in order that they being well understood, the latter will be performed with much more ease and dispatch, according to the rules shown, than by the customary method of dotting. In Multiplication I have shown both the beauty and use of that excellent rule, in resolving most questions that occur in merchandising; and have prefixed before Reduction, several Bills of Parcels, which are applicable to real business. In working Interest by Decimals, I have added tables to the rules, for the readier calculating of Annuities, &c. and have not only shown the use, but the method of making them: as likewise an In terest Table, calculated for the easier finding of the Interest of any sum of money at any rate per cent. by Multiplication and Addition only; it is also useful in calculating Rates, Incomes, and Servants' Wages, for any number of months, weeks, or days; and I may venture to say, I have gone through the whole with so much plainness and perspicuity, that there is none better extant. I have nothing farther to add, but a return of my sincere thanks to all those gentlemen, schoolmasters, and others, whose kind approbation and encouragement have now established the use of this book in almost every school of eminence throughout the kingdom: but I think my gratitude more especially due to those who have favoured me with their remarks; though I must still beg of every candid and judicious reader, that if he should, by chance, find a transposition of a letter, or a false figure, to excuse it; for, notwithstanding there has been great care taken in correcting, yet errors of the press will inevitably creep in; and some may also have slipped my observation; in either of which cases the admonition of a good-natured reader will be very acceptable to his much obliged, and most obedient humble servant, F. WALKINGAME. |