|
Union Arithmetic by Edward Brooks 1877 State Normal School Hard Cover
Union Arithmetic by Edward Brooks SEE PHOTOS - Binding edge missing BACK COVER LOOSE
Hard Cover
429 pages
Copyright 1877
CONTENTS
PREFACE, V
SECTION I.
ARITHMETICAL LANGUAGE,9
Numeration, 10
Notation, 11
SECTION II.
FUNDAMENTAL OPERATIONS.
Addition, 22
Subtraction,. 32
Multiplication,.42
Division,55
General Principles,.70
SECTION III.
SECONDARY OPERATIONS.
Composition,72
Factoring, . . . 76
Greatest Common Divisor, . 78
Least Common Multiple, . 82
Cancellation, . . . 86
PRIME NUMBERS, ... 88
SECTION IV.
COMMON FRACTIONS,.. 90
Numeration and Notation, 91
Principles,.92
Reduction, .... 93
Addition, .... 100
Subtraction, .102
Multiplication, .. 104
Division, 108
Complex Fractions, . . 113
Relation of Numbers. . 114
Arithmetical Analysis, . . 118
SECTION V.
DECIMAL FRACTIONS,. 131
Reduction,134
Addition,136
Subtraction, .190
Multiplication, 192
Division, 193
United States Money, . .144
Commercial Transactions, 148
Bills and Accounts, . . 159
SECTION VI.
DENOMINATE NUMBERS.
Measures of
Value, 158
Weight,162
Length, 166
Surface,169
Volume, 171
Capacity,172
Angles, 175
Time, 176
Miscellaneous Tables, .. 180
Reduction, .182
Addition, 188
Subtraction, 190
Multiplication, 192
Division, . . . 193
Difference between Dates, . 195
Longitude and Time, . 199
DENOMINATE FRACTIONS.
Reduction, 202
SECTION VII.
PRACTICAL MEASUREMENTS.
Rectangle, Triangle, Circle, 210
Measurement of Land, . 213
Artificers' Work, 215
Carpeting, Papering, etc., 216
Cube and Cylinder, . 217
Wood Measure, 219
Boards and Timber,. 220
Masonry, Brickwork, etc.. 221
Capacity of Cisterns, etc.,223
Capacity of Bins, etc., .225
Comparison of Measures, . 227
Comparison of Weights, .228
Comparison of Money,. 228
SECTION VIII.
PERCENTAGE.
Simple Percentage 232
General Formulas, 239
Profit and Loss, 240
Commission, 246
Stocks and Dividends, . 249
Par, Premium and Discount, 253
Brokerage, 257
Income from Investments, 260
General Taxes, . 266
Simple Interest,272
Promissory Notes, 282
Annual Interest, .286
Partial Payments,. 287
True Discount and Present Worth, 290
Bank Discount and Banking,291
Investments with Interest,. 296
Compound Interest,297
Exchange, 300
Domestic,301
Foreign, . . . 305
Arbitration of Exchange, 309
Duties, 311
SECTION IX.
RATIO AND PROPORTION.
Ratio, 316
Simple Proportion, 318
Compound Proportion, . 323
Insurance, 326
Partnership,
Simple,334
Compound, 366
Equation of Payments,. 339
Averaging Accounts, .343
Settlement of Accounts, . 345
Account Sales, 346
SECTION X.
INVOLUTION AND EVOLUTION.
Involution, 348
Squaring Numbers,350
Cubing Numbers, 351
Evolution,353
Square Root, 352
Right-angled Triangles,359
.Similar Figures, 361
Cube Root, .362
Similar Volumes,368
Higher Roots,369
SECTION XI.
SUPPLEMENT.
Arithmetical Progression, . 370
Geometrical Progression,374
Infinite Series,376
Annuities at
Simple Interest,377
Compound Interest, .379
Partitive Proportion,. 381
Conjoined Proportion, .386
Medial Proportion, 388
Life Insurance,393
Building Associations,395
SECTION XII.
MENSURATION.
Mensuration of Surfaces, 403
The Triangle, 404
The Quadrilateral 405
The Circle, 406
The Ellipse, 408
Mensuration of Volumes,408
The Prism, 408
The Pyramid,409
The Cylinder, 410
The Cone,410
The Frustums, 411
The Sphere, 412
APPENDIX.
Metric System, 413
Table of Fire Insurance,423
Table of Life Insurance, 424
PREFACE
EDUCATION is progressive. The development of the popular mind Is becoming the transcendent question of the day. Improvements are being. made in every department, dull routine is giving way to intellectual activity, instruction is becoming a science, and teaching a profession.
This advance in education has been nowhere more noticeable than in the improvements of text-books upon Arithmetic. A few years ago an unpretending little work, Colburn's Intellectual Arithmetic, was presented to the public. That little work touched Arithmetic as with the wand of an enchantress, and transformed it from a dry collection of mechanical processes to a thing of interest and beauty. It laid the foundation of that system of Mental Arithmetic which has infused a new spirit into the science of numbers, and has done more than any other influence to vitalize the methods of common school instruction in this country.
In presenting a new work upon the subject, I desire to acknowledge my obligations to this and other works which have followed it. Bringing to the task the reflection and experience of many years of educational labor, I hope to be able to present a text-book upon Arithmetic which will take an honorable position among the many valuable works upon the subject which are doing so much for the educational interests of the country. Some of the general and special features of this work will be briefly noticed.
METHOD OF TREATMENT.-The method of treatment is both Inductive and Deductive, embracing Analysis and Synthesis. In some cases both of these methods are employed in the development of the same subject; in other cases they are combined in the same solution or explanation, and such combination is characteristic of the entire work. I have endeavored to meet the wants of both teacher and pupil, by pre. paring a work convenient for instruction, adapted to the natural and logical development of the mind of the pupil in the study of numbers, and containing such applications as will prepare students for the business relations of life.
ARRANGEMENT.-The arrangement of the work is believed to be strictly logical and at the same time, practical, being adapted to the natural mental growth and development of the pupil. The mottoes have been, from the easy to the difficult, from the simple to the complex, from the known to the unknown. Care has been taken to present the simpler and more practical subjects first, and not to anticipate any principles or processes before the pupil is prepared for them. Thus, I have placed Compound Numbers after Fractions, Percentage before Ratio and Proportion, Equation of Payments after Proportion, and other arrangements have been determined by the same principle.
THE REASONING.-All reasoning is comparison. A comparison re quires a standard, and this standard is the fired, the axiomatic, the known. The law of correct reasoning, therefore, is to compare the complex with the simple, the theoretic with the axiomatic, the unknown with the known. This law is kept prominently before the mind in the development of this work, and upon it are based its definitions, solutions and explanations, etc. As an illustration, notice the definitions of Ratio, Proportion, etc., the method of stating a proportion, etc.
SOLUTIONS.-The solutions and demonstrations are so simple and clear, that they may be understood by very young pupils, yet they are expressed in language concise and logically accurate, and in the form which the pupil should be required to use at recitation. A solution may be too concise to be readily understood, and it may also be too prolix, the idea being smothered or concealed in a multiplicity of words. Both of these errors I have endeavored to avoid, remembering that the highest science is the greatest simplicity.
RULES.-The rules or methods of operation are expressed in brief and simple language, and are given as the results of solutions and explanations. I have endeavored to lead the pupil to see the reason for the different processes, thus enabling him to derive his own method of operation based upon such reasoning. The object has been to develop mind es well as the power of computation-to make thinkers rather than arithmetical machines.
APPLICATIONS.-One of the most prominent features of the work is its practical character. The applications of the science are not the thought of the scholar as what business may be, but represent the actual business of the day. Macey of the problems and processes are derived from actual business transactions. Our Bills and Accounts came out of the stores ; our Taxes, Banking, Exchange, etc., have been submitted to and endorsed by those connected with the business; several of the problems on Duties are out of the Glastom House; Insurance has been examined by experts in the business ; the subject of Building Associations, for the first time introduced into an arithmetic, was partly prepared by one practically familiar with the subject; etc.
UNION OF MENTAL AND WRITTEN.-Another leading feature of the work is the union of mental and written arithmetic in one book: Many who recognize the importance of Mental Arithmetic think that it takes too much time for the pupil to study two separate books-one on Mental and the other on Written Arithmetic-and hold that these two sub jects should be embraced in one book. To meet this demand 1 have made a complete and harmonious combination of the two subjects, introducing many of those forms of analysis that have given such popularity to my Mental Arithmetic. It is this combination that gives the work its name, The Union Arithmetic; and this union will be found to be not a mere nominal thing, but a reality. In the study of the work the pupil can obtain quite a thorough course in arithmetical analysis while he is becoming familiar with the art of computation and the application of the art to business. These mental exercises are so arranged and printed that any teacher who prefers to omit them can do so without any inconvenience to either the pupil or the teacher.
SPECIAL FEATURES.-There are several special features peculiar to this work, to which we desire to call attention.
1st. Many new definitions, as of Fraction, Least Common Multiple, Percentage, Ratio, etc.
2d. New and concise method of explaining Greatest-Common Divisor, Ind a method of Least Common Multiple not usually given.
3d. The two distinct methods of the development of Fractions, the relation of fractions, the method of stating a problem in Simple Proportion and reason for it, and the development of Compound Proportion.
4th. The Analytic and Synthetic methods of developing Involution and Evolution, the greater attention to Involution as a preparation to Evolution, a new method of cube root, etc.
5. Great number and variety of problems, especially after the Fundamental Rules, Fractions, etc., and at the close of the book. Other features also important, will present themselves upon a careful examination.
It should be stated that this work was first published in 1863, and that some of the definitions and processes which were then new have since been introduced into other works. The present edition is thoroughly revised, and brought up to the very latest methods of business calculations.
Thanking my friends for the cordial reception given to my previous labors, I send forth this new volume, with the earnest desire that it may meet their approbation, and aid in the development and diffusion of a deeper interest in the beautiful science of numbers-a science which practically lies at the foundation of all science and all thought, and ons which is doing so much to promote the cause of popular education.
EDWARD BROOKS STATE NORMAL SCHOOL, May 10, 1877
All pictures are of the actual item. There may be reflection from the lights in some photos. We try to take photos of any damage. If this is a railroad item, this material is obsolete and no longer in use by the railroad. Please email with questions. Publishers of Train Shed Cyclopedias and Stephans Railroad Directories. Large inventory of railroad books and magazines. Thank you for buying from us.
Shipping charges
US Shipments: Ebay will add $1.25 each additional items, there are a few exceptions.
Ebay Global shipping charges are shown. These items are shipped to Kentucky and forwarded to you. Ebay collects the shipping and customs / import fees. Refunds may be issued if you add multiple items to your cart and pay with one payment. For direct postage rates to these countries, send me an email. Shipping varies by weight.
Payment options
Payment must be received within 7 days. Paypal is accepted.
Terms and conditions
All sales are final. Returns accepted if item is not as described. Contact us first. No warranty is stated or implied. Please e-mail us with any questions before bidding.
Thanks for looking at our items.
|
