TUTOR'S GUIDE:

BEING A

COMPLETE SYSTEM OF ARITHMETIC:

or

WITH VARIOUS BRANCHES IN THE MATHEMATICS.

IN SIX PARTS, viz. I. Arithmetic in all its useful Rules, To which is added, the Specific

and to each a great Variety of Gravity of Metals, &c. Questions.

V. Chronology, the Method II. Vulgar Fractions, in all their of finding the several Cycles, Parts.

Epacts, Moveable Feasts, Time III. Decimal Fractions, with the of High Water, &c.; with a

Extraction of Roots of different Collection of Questions relating Powers ;

to which are added, 10 History: likewise all the most Rules, &c. for the easy Calcula- useful Examples on both the tion of Interest and Annuities, Globes. &c.

VI. Algebra, wherein the Method of IV. Mensuration of Superficies and raising and resolving Equations is

Solids, applied to measuring Ar- rendered easy, and illustrated with tificers' Works, &c. with a Col- a Variety of Examples and Numelection of Questions for Exercise. rical Questions.

TO WHICH IS ADDED,

AN APPENDIX,
CONTAINING DIFFERENT FORMS OF ACQUITTANCES,

BILLS OF EXCHANGE, &c. &c.
The whole being designed for the Use of Schools, as a Question Book, or a

REMEMBRANCER and INSTRUCTOR' to such as have some Knowledge of Figures: and adapted for the Use of the Gentleman and Scholar, as well as of the Man of Business : and recommended by several eminent Mathematicians and School-masters.

AUTHOR OF

BY CHARLES VYSE,
THE YOUNG LADIES' AND GENTLEMEN'S NEW GUIDE

TO THE ENGLISH TONGUE."

THE FIFTEENTH EDITION;

CAREFULLY REVISED AND CORRECTED.

LONDON: PRINTED FOR G. WILKIE ; SCATCHERD AND LETTERMAN; LACK

INGTON, ALLEN, AND CO.; J. RICHARDSON; J. M. RICHARDSON ; LONGMAN, HURST, ŘEES, OPME, AND BROWN; LAW AND WHITTAKER; SHERWOOD, NEELY, AND JONES; G. AND S. ROBINSON ; GALE AND FENNER; WALKER AND CO. ; AND SIMPKIN ANN MARSHALL

1815,

The MONTHLY REView, for January 1771, gives the following Account of the First Edition

:

“ The best method of conveying instruction is derived from experience; and though the author of the Tutor's Guide does not pretend to boast of new discoveries, yet it must be allowed that he has selected a great variety of necessary and useful rules for the obtaining a thorough knowledge in those sciences which depend upon arithmetic: and his book will be found particularly useful in this respect, as it contains a very considerable number of questions to exemplify the rules he has laid down, and to exercise the attention of the learner.-Many of them may be thought to surpass the capacity of young

scholars: but this circumstance is no just objeccion against the book itself; it rather recommends the work to an after-review, when the understanding is enlarged and ripened. The plan and execution of Mr. Vyse's performance do honour to his judgment and application, and entitle it to the general notice of those who are intrusted with the education of youth.”

The CRITICAL REView gives the following Account :

“ Notwithstanding there are many books already extant upon the same subject, yet we apprehend that the work before us will not be deemed either unnecessary or impertinent, after

having assured our readers it is recommended to the favour of o the Public by one of the most considerable mathematical

writers of the present age."

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Printed by S. Hamilton, Weybridge, Surrey.

07-24-acem

PREFACE.

When we consider the utility of ARITHMETIC, on which science almost all the others do absolutely depend, we need not be surprised that so many

efforts have been made to bring this liseful branch of learning to the utmost degree of perfection: and although the vast extent of the subject does in some measure defeat these attempts, yet, upon account of its real value and use, it certainly merits all the study and pains that can be bestowed upon it.

In the following pages I have delivered the Definitions and Rules in as brief and concise a manner as I possibly could, so as to make them general; and they follow in the same order as specified in the Table of Contents. Thus, Book the First contains the four primary rules, i.e. Addition, Subtraction, Multiplication, and Di

vision, in Integers; and Reduction, ascending and descending, with the Tables of Money, Weights, Measures, &c. with which the pupil should be well acquainted, before he proceeds to the use of those rules in Compound Num. bers.

In Book the Second, the rules follow in the same order in which they are generally taught in schools; but I apprehend the most expeditious method for the pupil would be to learn as far as the Rule of Three, then Vulgar and Decimal Fractions, and the Extraction of the Square and Cube Roots; after which a larger field may be opened to him, as he will be more capable to judge for himself, and, with a little assistance from the master, go through any rule, to his own satisfaction, and his teacher's honour. But in schools the master very seldom either knows the business for which his scholars are designed, or the length of time they are to continue at school, and is therefore obliged to pursue the old beaten path, and teach them first what is not perhaps the most essential.

In this work, amongst several hundred questions, are all those most excellent ones of the late MARTIN CLARE, arranged according to the

several rules to which they appertain; a thing wished for by school-masters and teachers in general.

I pretend not to boast of new discoveries, but flatter myself to have selected every necessary and useful rule or proposition for obtaining a thorough knowledge in those sciences which depend upon Arithmetic; and have given a great variety of such questions as will enable the tutor to supply his pupils with those that may be most conducive to the station of life for which they may be designed.

I have selected the most difficult questions of each rule, as exercises for leisure hours.

And, in order to make this book as useful as possible, I have added several examples of the different forms of Acquittances, Promissory Notes, Bills of Exchange, Bills of Parcels, &c. the frequent copying of which I would recommend to the pupil.

I have not adjoined the answers to the questions, as I have published (by desire of several mathematicians and school-masters) a KEY to the Tutor's GUIDE, wherein all the answers are worked at length, with proper references to the questions as they stand in this edition,