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Book A Textbook on the Teaching of Arithmetic  Classic Reprint

Download or read book A Textbook on the Teaching of Arithmetic Classic Reprint written by Alva Walker Stamper and published by Forgotten Books. This book was released on 2016-06-20 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from A Textbook on the Teaching of Arithmetic IN planning the present book, the author has kept in mind three aspects of the teacher's preparation: the need of the perspective gained through a comprehen sion of the larger teaching problems concerned in the teaching of arithmetic, the need of a clear insight into the content of arithmetic, and the need of an understand ing of arithmetic method. The book exploits no new doctrine. It lays no claim to completeness. It has been prepared with the primary aim of supplying the practical needs of prospective teachers, or teachers new in the ser vice. On account of the efiort made to refresh the mind of the reader in the subject matter of arithmetic, the read ing frequently goes beyond the requirements of the grades, this being especially noticeable in the treatment of percen tage and in the solution of problems. If any dogmatism appears in the context, it is the result of efiorts to be clear and convincing. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book The Teaching of Arithmetic  Classic Reprint

Download or read book The Teaching of Arithmetic Classic Reprint written by David Eugene Smith and published by Forgotten Books. This book was released on 2017-12-18 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Teaching of Arithmetic This work has been prepared with a view to the needs of Teachers' Reading Circles and of those who are giving in struction or supervising the work in arithmetic in the elemen tary schools. The effort has been made to free it from the more difficult technicalities of mathematics as far as possible, and from that phraseology of the world of pedagogy that renders educational problems unnecessarily difficult. It is the author's desire to place before the large body of teachers of arithmetic, rather than the few who are interested in the technicalities of experiment, a brief silmmary of the develop ment of the science and of the reasons for teaching it; a statement of the subject matter that may properly be selected for school purposes, and the arrangement of this matter in a course of study; a consideration of a few of the technical features of arithmetic; and a discussion of the work of the several school years. He feels it quite unnecessary, however, to repeat at length the simple explanations and devices that are found in any good textbook, believing that the teacher will usually find it advantageous in such matters to follow the book that she is using. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book A Study of Mathematical Education Including the Teaching of Arithmetic  Classic Reprint

Download or read book A Study of Mathematical Education Including the Teaching of Arithmetic Classic Reprint written by Benchara Branford and published by Forgotten Books. This book was released on 2018-01-11 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from A Study of Mathematical Education Including the Teaching of Arithmetic This study is based upon twenty years' experience Of school and college education ranging through all grades, including the very elements of counting and form in the kindergarten, the mathematics appropriate to the school, and the standard required Of students for an Honours Degree in our universities. Conclusions based on class-teaching and those arrived at by experiment and by a private study Of the individual have served both to correct and to supplement each other. The substance of the present volume has also formed the introductory part Of a course of lectures on the teaching of mathematics, which, for many years, I have given in various institutions to classes of teachers from almost all types and grades Of schools, elementary as well as secondary and tertiary. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book The Teaching of Arithmetic

Download or read book The Teaching of Arithmetic written by Paul Klapper and published by . This book was released on 2015-07-08 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Teaching of Arithmetic: A Manual for Teachers A statement of the aims of a book on the methods of teaching should set forth its distinctive purpose. Books on the pedagogy of arithmetic which have contributed to improvement in methods of teaching this subject may be divided into three classes. Some seek to give a general survey of the aims and methods of teaching arithmetic, concerning themselves with no details in any specific topic, and leaving it to each teacher to apply the general method to the specific problems of his grade work. Other books give the philosophy and psychology of mathematics in the hope that a clearer comprehension of the basic concepts of arithmetic by the teacher will inevitably lead to more effective methods of instruction. The third group of books devotes itself merely to the task of giving remedial devices to meet specific teaching difficulties. General methods of teaching any subject may set forth ideals of instruction without regard to possibility of attainment. Specific devices tend to establish stereotyped forms to be followed slavishly without a comprehension of the basic principles. The writer has sought to evolve a book that is eclectic in aim. The early chapters study critically the values of arithmetic, the principles governing the organization of the course of study, and the psychology underlying sound method in arithmetic. The later chapters set forth methods rather than the method of teaching each of the important branches of arithmetic. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book Teaching Arithmetic

    Book Details:
  • Author : Middlesex A. Bailey
  • Publisher : Forgotten Books
  • Release : 2018-03-08
  • ISBN : 9780364156735
  • Pages : 214 pages

Download or read book Teaching Arithmetic written by Middlesex A. Bailey and published by Forgotten Books. This book was released on 2018-03-08 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Teaching Arithmetic: A Handbook for Teachers and a Textbook for Normal and Training Schools There is a science of teaching arithmetic. The feeling of needs and the finding of means for their satisfaction is the law of advancement; logical division is the law of classifications and definitions; induction, deduction, and the complete method are the laws for the discovery of principles; experimentation and reasoning are the laws for the solution of simple problems; and the analysis of complex problems into simple problems is the law for the solution of problems in general. In Part I the author has endeavored to develop and state these laws. In Part II he has endeavored to illus trate their application; much has been omitted but enough has been given to suggest the rest. In Part III he has endeavored to give an idea of the advance in complexity from grade to grade in elementary schools and of what is required to secure primary and higher licenses for teaching arithmetic. As a handbook, this work should help the superintend ent to secure uniformity in his schools the principal to harmonize the work of the grades and the teacher to get a clear view of fundamental laws. As a textbook, this work should help the teacher in normal and training schools to supplement his lectures and prospective teachers In school and out of school to prepare for their chosen profession. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book The Art of Teaching Arithmetic

Download or read book The Art of Teaching Arithmetic written by Jeannie Barbara Thomson Davies and published by Forgotten Books. This book was released on 2017-09-17 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Art of Teaching Arithmetic: A Book for Class Teachers Another limitation must be mentioned. I have accepted the present system of teaching children in large classes, not because I consider this ideal, but because it seems worth while to attempt the improvement in one direction of a state of matters likely to continue yet awhile. Some. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book The Teaching and History of Mathematics in the United States  Classic Reprint

Download or read book The Teaching and History of Mathematics in the United States Classic Reprint written by Florian Cajori and published by . This book was released on 2015-07-09 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Teaching and History of Mathematics in the United States On the study of mathematics in elementary schools of the American colonies but little can be said. In early colonial days schools did not exist except in towns and in the more densely settled districts; and oven where schools were kept, the study of mathematics was often not pursued at all, or consisted simply in learning to count and to perform the fundamental operations with integral numbers. Thus, in Hampstead, N. H., in 1750, it was voted "to hire a school-master for six mouths in ye summer season to teach ye children to read and write." Arithmetic had not yet been introduced there. As late as the beginning of this century there were schools in country districts in which arithmetic was not taught at all. Bronson Alcott, the prominent educator, born in Massachusetts in 1799, in describing the schools of his boyhood, says: "Until within a few years no studies have been permitted in the day school but spelling, reading, and writing. Arithmetic was taught by a few instructors one or two evenings in a week. But in spite of the most determined opposition arithmetic is now permitted in the day school." This was in Massachusetts at the beginning of this century. In secondary schools, "ciphering" was taught during colonial times, which consisted generally in drilling students in the manipulation of integral numbers. He was an exceptional teacher who possessed a fair knowledge of "fractions" and the "rule of three," and if some pupil of rare genius managed to master fractions, or even pass beyond the "rule of three," then he was judged a finished mathematician. The best teachers of those days were college students or college graduates who engaged in teaching as a stepping-stone to something better. An example of this class of teachers was John Adams, afterwards President of the United States. Immediately after graduating at Harvard and before entering upon the study of law, he presided, for a few years, over the grammar school at Worcester. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book A Manual of Arithmetic  Classic Reprint

Download or read book A Manual of Arithmetic Classic Reprint written by Emerson Elbridge White and published by . This book was released on 2018-02-11 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Principles and Methods of Teaching Arithmetic  Classic Reprint

Download or read book Principles and Methods of Teaching Arithmetic Classic Reprint written by James Robert Overman and published by . This book was released on 2015-07-13 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Principles and Methods of Teaching Arithmetic This book, as its title indicates, is a discussion of principles and methods of teaching arithmetic. A complete study of methods of teaching any subject involves two things (a) A study of guiding principles, and (b) A study of the details of method - of possible methods of presenting the various parts of the subject. The best place to study the details of method is in connection with a review of subject matter, but such a study should be preceded or accompanied by a study of general principles. It is the purpose of this book to do three things (a) To give a clear conception of the ends to be accomplished through the work in arithmetic (b) To analyze the teaching of arithmetic into the different kinds or types of teaching that occur in the subject and to give an understanding of guiding principles and a knowledge of possible methods of procedure, tools and devices to be used in each of these types; and (c) To make clear, by means of numerous illustrations and lesson plans, how these general principles and methods of procedure apply to the teaching of the particular subject of arithmetic. The material of this book has all been developed and used in the author's classes during the last six years, and is presented here in book form in. the hope that it may contribute something toward improving and standardizing the teaching of arithmetic. It is believed that this book will be found suitable for use as a text for normal schools and teachers' reading circles. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book Essentials of Arithmetic

Download or read book Essentials of Arithmetic written by George Wentworth and published by Forgotten Books. This book was released on 2016-09-28 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Essentials of Arithmetic: Primary Book This book is the first of a series of three intended to cover the essentials of arithmetic in the eight school years of the elementary course. It consists of five chapters, the first of which reviews the work usually done in the first and second grades, the others covering the work of the successive half grades through the fourth school year. If it is introduced in Grade II, the pupils should complete Chapter I in that year; but if it is first placed in the hands of the class in Grade III, it will suffice to take a rapid review of Chapter I, omitting such portions as may already be perfectly familiar to the children. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book School Arithmetic

    Book Details:
  • Author : John Marvin Colaw
  • Publisher : Forgotten Books
  • Release : 2016-06-27
  • ISBN : 9781332807024
  • Pages : 288 pages

Download or read book School Arithmetic written by John Marvin Colaw and published by Forgotten Books. This book was released on 2016-06-27 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from School Arithmetic: Primary Book From the concrete TO the abstract. - The child's mind must be approached through those ever open doors, the senses. Primary number teaching must be begun by the pupil's Observ ing and handling Objects, yet the mere presence of concrete things does not guarantee the presence of definite numerical ideas in the mind of the pupil. They must be so presented as to stimulate and aid the mental movement of discriminating and relating which leads to definite ideas of number. The mind must (a) recognize the like Objects as distinct individuals, and (b) group (put together) the objects into a whole. The child's own activity must conceive a whole of parts, and relate the parts in a definite whole. It is not enough that he knows our country as 45 states; he must know the 45 states as one country. He should recognize five, for example, not only as five ones, but also as one fire, considering the component ones not chiefly for their own sake, but as giving definite value to the whole the' group. By repeated acts Of such measurement or valuation the mind advances naturally and inevitably from things to relations, from facts to principles, from the concrete to the abstract. Believing that the concept of ratio - an abstract idea - must be evolved in the young mind by its own activity, and that therefore it should not be thrown at the child in the earlier stages of his progress, the authors have not explicitly stated the ratio idea until it has had time to grow into a recognizable and useful product of the pupil's mind. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book Special Method in Arithmetic  Classic Reprint

Download or read book Special Method in Arithmetic Classic Reprint written by Charles A. Mcmurry and published by Forgotten Books. This book was released on 2015-07-14 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Special Method in Arithmetic IT is our purpose in this volume to make plain to teachers in elementary schools the purpose of teach ing arithmetic, to outline fully a course of study based upon this controlling idea, and to discuss and illustrate the method of handling some of the chief topics. It is strictly a teacher's book, and not designed for use by children. It has been generally felt that arithmetic stands aloof from other studies, but the attempt is made here to show a very intimate and important relation to the other studies, one vital in fact to the proper plan and treatment of the whole subject. This volume is one in a series of special methods, as follows: Reading of English Classics, Primary Reading and Story Work, Geography, History, Ele mentary Science, Language, and Manual Arts. The course of study for the eight grades based on the plans worked out in these eight volumes is now in press and will appear in two volumes. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book Milne s New York State Arithmetic

Download or read book Milne s New York State Arithmetic written by William J. Milne and published by Forgotten Books. This book was released on 2017-11-16 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Milne's New York State Arithmetic: Second Book This series of arithmetics has been written to supply the demand for a sound and modern interpretation of present-day educational ideas concerning the teaching of arithmetic. It is intended especially to meet the need -for a definite and complete interpretation of the Course of Study in Arithmetic prescribed by the Education Department of the State of New York. The series consists of two books. The First Book for years three, four, and five, is divided into half-year units, but within each half year the treatment is topical. The Second Boo is a complete topical arithmetic, covering, in order, the Syllabus requirements for years six, seven, and eight. The first two chapters of the Second Book are designed to gather up in a compact and comprehensive review so much of the work of the First Book as the Syllabus does not mention again in the last three years of the course. The needs of any class about to enter upon the sixth year work will determine whether or not any or all of this part of the book should be used. The next two chapters are review chapters included by the Syllabus in the sixth year. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book American Elementary Arithmetic  Classic Reprint

Download or read book American Elementary Arithmetic Classic Reprint written by Middlesex Alfred Bailey and published by Forgotten Books. This book was released on 2017-10-22 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from American Elementary Arithmetic It is now recognized that suitable apparatus 18 as necessary to the teacher of primary arithmetic as to the teacher of the physi cal sciences. The apparatus called for in this book consists of paper, pasteboard, etc., and of toy money, blocks, and splints, which may be prepared by the teacher, or obtained of any dealer in kindergarten materials. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book A System of Arithmetic

Download or read book A System of Arithmetic written by Samuel Webber and published by Forgotten Books. This book was released on 2018-03-21 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from A System of Arithmetic: Reprinted From the Mathematical Text-Book The number, or letter, belonging to the above signs of powers and roots, is called the index, or exponent. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book Walsh Suzzallo Arithmetic  Classic Reprint

Download or read book Walsh Suzzallo Arithmetic Classic Reprint written by John H. Walsh and published by Forgotten Books. This book was released on 2017-11-20 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Walsh-Suzzallo Arithmetic These books will develop all the mathematical power needed by the average person in the accurate control of his affairs. The purpose has been to teach first the most important topics of arithmetic and last those least fre quently used. In consequence, the teacher may feel that the child who is leaving school at the end of any particu lar grade has been taught whatever would be most useful to him, considering that his schooling had to stop just then. Nothing in the next grade beyond is more impor tant than what he has just studied. These books are so constructed as to complete the fun damental processes of arithmetic by the end of the sixth year of school life. No pupil studying from this course through the first six years will be left without an essen tial mathematical power. With this foundation, he can proceed by himself, as need confronts him, to learn shorter or more convenient methods of calculation and to make new applications of the processes learned. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Book Intermediate Arithmetic  Classic Reprint

Download or read book Intermediate Arithmetic Classic Reprint written by William James Milne and published by Forgotten Books. This book was released on 2017-09-16 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Intermediate Arithmetic His work has been prepared to meet a demand for a book that contains, within brief compass, an elementary course in arithmetic. It is also designed to be an introduction to the more thorough and exhaustive treatment of the science which is given in the author's standard arithmetic. The first part of the book contains exercises arranged in such a manner that they secure an easy and natural development of the ideas of numbers, and they afford sufficient practice to fix the results in memory. Ready knowledge of results can be secured only by frequent repetition and thorough drill, and the lessons that have been prepared are believed to be admirably adapted to produce expertness in computing, without sacrificing interest in the subject through constant practice with abstract numbers. When the more systematic treatment of the science is presented, the pupil is led by natural, progressive, and logical steps to an understanding of the definitions, principles, processes, and rules, before he is required to state them; consequently, all definitions, principles, and rules are but the expressions of what he already knows. It is evident, therefore, that the plan pursued in the work will develop in the student the habit of investigating for himself any subject which may claim his attention, and this is an extremely important part of proper teaching. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.