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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, 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 Allistance 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 Queftions, are all those most excellent ones of the late Martin CLARE, ranged 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,

And, in order to make this Book as useful as possible, I have added several examples of the different forms of Acquittances, Promiffory Notes, Bills of Exchange, Bills of Parcels, &ć. the frequent copying of which I would recommend to the Pupil.

I have not adjoined the Answers to the Queftions, 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.

I need not point out the great Utility of such a Performance; it is fufficiently evident to all who are employed in this Branch of Education, especially such as have the Care of a numerous School, and experience the Difficulties that Teachers in general labour under with Respect to Time; a Grievance that muft ftill continue, while the Prices they receive are so very inadequate to their Labours.

I hope the Gentlemen of the Profession will do me the Justice to believe, that my Design in this Performance was not to dictate to, but ease the Master; and the skilful Teacher will, no Doubt, vary the Work of the Questions according to the Nature of the several Rules.

The Tutor's Guide and its Key furnish a Complete System of ARITHMETIC, and will enable those, who are acquainted with the first Principles, to attain (without the Assistance of a Mafter) a competent Knowledge of the several Rules with Ease and Precision.

Ву

By the particular Desire of many eminent School-masters, an Abridgement of the GUIDE is published with this Addition, entitled the YOUNG ARITHMETICIAN'S ASSISTANT; wherein is contained only what is most immediately neceffary for the lower Forms, and those designed for Trade or Business; the Guide being thought too expensive to put in the Hands of young Beginners, therefore put it out of the Power of many Masters, particularly those who keep Day Schools, to make use of in their Schools. The Abridgement has the same Advantage with respect to the Key as the Guide.

The favourable Reception the former Editions have met with gives me Room to hope, that the Alterations and Additions I have made in this, will merit the Approbation of those Gentlemen who have kindly interested theinselves in Behalf of my former Endeavours, to whom I return my moft fincere Thanks, and am, With the utmost Esteem and Respect, Their's and the Public's much obliged,

obedient humble Servant, WEST HOS ABREY}

CHARLES VYSE..

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Τ Η Ε

CO N T E N T S.

PART I.

BOOK I.

TUMERATION 1 Multiplication of Integers 7 Addition of Integers 4

Division Subtraction

Reduction

16

II

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