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N O R M A L

WRITTEN ARITHMETIC, ,

BY

Analysis and Synthesis ;

DESIGNED FOR

COMMON SCHOOLS, NORMAL SCHOOLS, HIGH SCHOOLS,

ACADEMIES, ETC.

BY

EDWARD BROOKS, A.M.,

PROFESSOR OF MATHEMATICS IN PENNSYLVANIA STATE NORMAL SCHOOL, AND AUTHOR 07
"TIE NORMAL PRIMARY ARITHMETIC,

NORMAL MENTAL ARITHMETIC,” ITO.

" Analysis and Synthosis ;--the magic wand whose touch unfolds the mysterious and beautiful

relations of numbers."

PHILADELPHIA:
SOWER, BARNES & CO.,

37 NORTH THIRD STREET.

MARYAAD GALLEGE LAY

SY EXCHANGE FROM
NEW YORK STATE LIBRARY

FEC 27 1932

Entered, according to Act of Congress, in the year 1863, by

EDWARD BROOKS, in the Clerk's Office of thĄ District Court of the United States, iu and for the Easto

District of Pennsylvania.

MRARS & DUSENBERY, ELECTROTIPERS.

PRINTED BY SMITH & PETERS,
Franklin Buildings, Sixth Street, below Areti,

Philadelphia

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SECTION IV.

89

Definitions .........

89

Principles of Fractions...............

91

Reduction of Fractions...............

92

99

100

102

105
Complex Fractions...

106

Relations of Numbers and Fractions 109

Addition

Subtraction

Multiplication...

Division

158

***..., 163

........... 169

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PAGE

PAGE

Difference of Dates....

Four cases......

253

Multiplication...

165 Problems for advanced pupils........ 258

Division....

166

Longitude and Time.......

SECTION XI.

DENOMINATE FRACTIONS........................ 172 ARITHMETICAL PROGRESSION................. 253

Denominato Decimals................... 174 Definitions ....

253

Three cases.................................

259

SECTION VII.

GEOMETRICAL PROGRESSION..................

CONTRACTIONS .....

177

Definitions............

261

Multiplier an aliquot part of 10,

Two cases.......

262

100, 1000, etc......

177

Infinite Series..

264

Multiplier a number of 9’S............. 179

Squaring and multiplying mixed

SECTION XII.

numbers................

179

INVOLUTION

205

Definitions..

265

SECTION VIII.

Principles

268

: RATIO........

182

Squaring, Analytically...

266

Definitions..

182

Cubing, Analytically

268

Principles...

183 EVOLUTION...

269

PROPORTION.

184 Definitions..........

Definitions......

Evolution by Factoring

270

Principles.

184 Square Root, Analytically.

............ 270

Simple Proportion...........

185 . Applications............

273

Compound Proportion............... 189 Cube Root, Analytically..

276

Applications ...

278

281

SECTION IX.

Square Root, Geometrically

Cube. Root, Geometricaliy..... 283

PERCENTAGE.....

192

Principles of Involuticn and Evo-

Definitions..

lution

284

Six cases

.............. 192

ANNUITIES....

286

Gain and Loss..........

199

Stocks and Dividends................

Annuities at Simple Interest......... 286

203

Premium and Discount................. 206

Annuities at Compound Interest... 288

DUODECIMALS..........

Commission and Brokerage........... 209

Insurance

213

SECTION XIII.

Simple Interest............

215

MENSURATION

292

Partial Payments

224

The Triangle....

293

True Discount....

227

294

Discounting and Banking.

The Quadrilateral.

228

The Circle........

Taxes ........ni

232

The Ellipsă......

297

Duties

233

The Pyramid.............

298

Compound Interest...

235

The Cylinder.........

298

Exchange, Domestic.........

237

Exchange, Foreign........

The Frustum of a Pyramid and

240

Cone.......................................

299

Exchange, Arbitration of..... 241

The Sphere......

300

Partnership, Simple ..

243

Measure of Lumber....

300

Partnership, Compound.

244

Masons' and Bricklayers' Work..... 301

Equation of Payments....

246

Settlement of Accounts....

252

SECTION XIV.

ANALISIS

.......................... 302

SECTION X

ALLIGATION, or MEDIAL PROPORTION...... 253

SECTION XV.

Definitions................................. 253 MISCELLANEOUS PROBLEM.................... 811

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