EDWARD BROOKS, A. M., Ph. D.,

SUPERINTENDENT OF PUBLIC SCHOOLS OF PHILADELPHIA,
PRINCIPAL AND PROFESSOR OF MATHEMATICS IN PENNSYLVANIA STATF NORMAL
SCHOOL, AND UTHOR OF "THE NORMAL BERIES OF ARITHMETICS," "NORMAL
ELEMENTARY ALGEBRA," "NORMAL GEOMETRY AND TRIGOXOXKTBY,"

"PHILOSOPHY OF ARITHMETIC," ETC.

'Analysis and Synthesis ;-the magic wand whose touch unfolds the mysterious and

beautiful relations of numbers."

PHILADELPHIA: : 3, ::
CHRISTOPHER SOWER COMPANY.

614 ARCH STREET...

239

282

PAGE. !

PAGE,

SECTION VIII.

Squaring Numbers, . .356

Cubing Numbers, . 357

ERCENTAGE.

Simple Percentage,. . 232

Evolution, . . . . 359

General Formulas, .

Square Root, . . 362

Profit and Loss, . . 240

Right-angled Triangles, . 365

Commission, . . . 246

Similar Figures, . . 367

Stocks and Dividends, . 249

Cube Root, . . . 368

Par, Premium and Discount, 253

Similar Volumes, . 374

Brokerage, . . . 257

Higher Roots, . . .375

Income from Investments, 260

SECTION XI.

General Taxes, . . 266

Simple Interest, : 272

ARITIMETICAL AND GEOMETRI-

Promissory Notes, ..

CAL SERIES.

Annual Interest, . . 286

Arithmetical Progression, . 376

Partial Payments, . . 287

Geometrical Progression, - 880

True Discount and Present

Infinite Series, . . 382

Worth, . . . 290

SECTION XII.

Bank Discount and Banking, 291

HIGHER PERCENTAGE.

Investments with Interest, . 296

Annuities at

Compound Interest, : 297

Simple Interest, . . 383

Exchange, . . . 300

Compound Interest,. .385

Domestic, . . .

Insurance, . . . 387

Foreign, ... . 305

Life Insurance,. . . 393

Arbitration of Exchange, . 309

Building Associations, . 395

Duties, . . . . 311

SECTION IX.

SECTION XIII.

RATIO AND PROPORTION.

MENSURATION.

Ratio,

Mensuration of Surfaces, . 403

.

316

• .

Simple Proportion, . 318

The Triangle, . . 404

Compound Proportion, . 323

The Quadrilateral, . . 405

Partitive Proportion, . 326

The Circle, . . . 406

Conjoined Proportion, . 332 The Ellipse, .

. 408

Medial Proportion, . 335

Mensuration of Volumes, . 408

Partnership,

The Prism, . . . 408

Simple, . . . . 340

The Pyramid, . . . 409

Compound, . . .342

The Cylinder, . . 410

Equation of Payments, . 345

The Cone,

. . . 410

Averaging Accounts, . 349

The Frustums, .

Settlement of Accounts, . 351

The Sphere, . . 412

Account Sales, . . 352

APPENDIX.

SECTION X.

Metric System, . , 413

INVOLUTION AND EVOLUTION

Table of Fire Insurance, . 423

Involution, . .

354 | Table of Life Insurance, . 424

301

411