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telligence and good senne. It is easy to make a boy, who does not reason, topruh, by rute, any technical rules, which a colomon writing nuaster, with mannerlal mlonunity, may lay dowu for him; but a child who reasons will mot be tbus easily inanaged; he stops, fruwas, hesitates, questions his mas wr, to wretched and refractory, until he can discover why he is to proceod in such and such a manner; he is not content with seeing his preceptor make figures and lines on the slalo, and perfurn, wondrous Operations with The self-complacent dexterity of a conjurer; he is not conteni w be led to The treasures of science blindfold; he would coas the bandage froin huis eyes, that he might know the way to inein again."

iu confirmation of the preceding remarks, and as fully expressive of the ontlaur's views on this subject, the following quotation is taken from the prufucr tu l'estalozzi's system.

“ 11e PESTALOZZIan plan of teaching ARITHMETIC, as one of the great branches of the mathematics, when coinniunicated to children upon the principles detailed in the following pages, necds not fear a comparison with her inore favured sistor, GEOMETRY, eillier in precision of ideas, in clearness and certainty of demonstration, in practical utility, or in the suba Lue deductions of the most interesting truths..

" Ju the regular order of instruction, arithinetic ought to take precedence of geometry, as it has a inore immediate connection with it than some aro willing lo ailmit. It is the science which the inind makes use of in teas uring all things that are capable or augmentation or diminution; and, wben ratioually taught, affords to the youthful mind the most advantage eus exercise of its reasoning powers, and that for which the human iniel. lect becomes early ripe, while the more advanced parts of wax lry ubo energies of the laust vigorous and matured understanding"

THE AUTHOR

TABLE OF CONTENTS.

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Reduction of Currencies,

159

Questions on the foregoing................

ICO

Interest,..

J63

Concise Rule for calculating Interest in New York State,.....

170

Cominiesion, Insurance, Stock, Loss and Gain,..

Time, Rate per cent., and Amount, given, to find the Principal,...........173

Tiine, Rate per cent., and Interest, being given, to find the Principal,......176

The Principal, Interest, and 'Time, being given, to find the Rate per rent.,. . 176

The Principal, Rato per cent., and Interest, being given, lo tind ihe Time,.,178

Compound Interest-Compound Interest by Table,..

Equation of layinents,...................

..........................182

Questions on the foregoing,.

..........................183

Rule of Three, by Analysis,...........

Ratio, or the Relation of Numbers,..

Proportion arising from Ratio, or from Multiplication and Division......... 189

Application of Ratio hy Rur....

192

Rule of 'Threr in Vulga and Decimul Irurtions,

.196

L'ompound Proportion, 1 Double Rule of Three, by Ratio und Analysis,...190

Questions on the foregoing,.

..21r2

To compute the inte rust on Notes with Endorsements-three movies,......27

Practice in Compound Nuinhers,....

..211

Fellowship by Analysia-moy Patio,.......

.213

Compound Fellowship-y Analysin-by Rutio........ ................216

Mensuration-Fquare Measure,..... ..........................217

Solid, or Cubic Measure,...

................

.2

Duodecin al-- Multiplication of luodecimals,...... ...............225,

Questions on the foregvinss...

To carrulate Difference in Tiine. Tare and 'l'rett, m, 16, 17,........206

er. 14...........

.231 | Position by Fructions, u. 66–76. 240

Barter, er.2431,

..231 | Diacoust,... que
Molland of'assessin, Waxts er. 10,13, 215

...023

4.174

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Miscellaneous Examples.

To and the Area of a Triangle,...

The Diameter of a Circle beirg given, to find the Circumference,..... 273

The Circumference of a Circ.e being given, to find the Diameter,..... 273

To find the Area of a Circle,.....

.273

To find the Area of a Globe,

.273

To find the Solid Contents of a Globe,.........

.273
To find the Solid Contents of a Cylinder,.. ..............................274
To find the Solid Contents of a Pyrainid,.

..274
To find the Solid Coutents of a Cone,....................................274
Anithinetical Questions,.........

................................274

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SUGGESTIONS TO TEACHERS

ON THE ULTHOD OF USING THIS WORK.

Por u conre of Mental Arithmetic, adapted to the capacities of very yormy pupils, they may take the Mental Éxereisen in each rile, as far as the tirst Example for the State. This course is nul ineant i wclude any of the exercises styled “ Questions on the foregoing."

This course embraces the whole of the first 27 pages, together with the Arith. netical Tables, extending to the Appendix. The neressity of impressing wese Tables on the minds of pupils at an early age is sufficiently obvious. When the pupil is perfect master of this course, as will, not probably, be the case after one or two reviews, the teacher will find no ditfirewlty in making him "undur stand the Operations by Slute. He may then take the whole in course.

In every school, it would be well to institute classes; and as there are seldur any answers given to the mental questions, the pupils may be allowed to read in their turns the questions from the book; thus giving the teacher no further trouble than occasionul corrections. By this, the reader will perceive, that the work may be used to advantage in monitorial schools, as the former editionis have been. In large schools, these corrections may be made by an advarced scholar, instead ut'the teacher. Whenever an advanced scholar takes up the book with a view of profiting from it, he should omit nothing us he progrosses, but make it his practice to quality himself to answer any question, in the mental exerciser, rules, or respecting the reason of the operations.

Teachers will find it to be a useful occupation for their scholars, to arrign them a morning lesson, to be recited as soon as they come into school. With little exertion on the part of touchers, pupils in this way may be male assidvono and ambitious, very much to their advantage, and tu the credit of theis teachers,

The mental questions, under the head of “ Questions on the foregoing,” will, Intelligently answered, furnish to cunimitlees un admirable test of the pupil's krwledge of this subject.

lbe Appendix is designed for those who hare tine and opportunity to devote to the study of the cure abstruse parts of Mathemutics.

Nole.-lest some may mistake the object of the figures annexed to the ques dio is, it may here he remarked, that there bgures are separute answers, les without ansigiring any value to them, reserving this particticar for the discretion of the pupil, which he must necessarily rxercise, in order to ublain the answer which follows, that being the aggregate of the whole.

T'he above directions are those which seen the best to the author ; hut us overy intelligent leucher has a way of his own, which, thuugh not intrinsicully the best, is, perhaps, the best for him, the subject is inseclfully submitted to he own clanica

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