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Book The Teaching of Mathematics  in the Elementary and the Secondary School  Classic Reprint

Download or read book The Teaching of Mathematics in the Elementary and the Secondary School Classic Reprint written by J. W. A. Young and published by Forgotten Books. This book was released on 2017-09-12 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Teaching of Mathematics, in the Elementary and the Secondary School The analytic and the synthetic method The function of these methods The synthetic method in the class-room Geometric analysis y. 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 Mathematics in the Elementary School  Classic Reprint

Download or read book Mathematics in the Elementary School Classic Reprint written by David Eugene Smith and published by Forgotten Books. This book was released on 2016-09-05 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Mathematics in the Elementary School The May issue of the teachers college record will deal with Methods of Teaching French and German, according to the new or reform method, by Dr. Leopold Bahlsen, of Berlin, Lecturer on Methods of Teaching Modern Languages, Teachers College. Other issues will discuss the principles which should govern the curriculum of primary and secondary schools, illustrated from outlines of courses as conducted in the Teachers College Schools, and followed by special issues dealing with specific work in the first, second, third, and fourth grades, and in the high school. Numbers concerning Kindergarten work and Music in Schools may also be expected. 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 Training of Teachers of Elementary and Secondary Mathematics

Download or read book Training of Teachers of Elementary and Secondary Mathematics written by and published by Forgotten Books. This book was released on 2018-01-29 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Training of Teachers of Elementary and Secondary Mathematics: International Commission on the Teaching of Mathematics; The American Report; Committee No. V Subcommittee l. The Training of Teachers of Mathematics in Professional Schools of Collegiate Grade, separate from or connected with Colleges or Universities.' 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 . This book was released on 2015-06-28 with total page 456 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. I may perhaps be permitted here to acknowledge the benefit derived from the sympathetic criticism and cooperation of these teachers, in particular Mr. Hodgson, lately of Bingley Grammar School, and Mr. Walker, of Sunderland, the blind teacher of blind children. I should be ungrateful did I not also mention the stimulus received in my college days from the lectures and teaching of Professor Chrystal and the late Professor Tait, of Edinburgh University. 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 Mathematics  in the Elementary and the Secondary School

Download or read book The Teaching of Mathematics in the Elementary and the Secondary School written by J. W. A. Young and published by Forgotten Books. This book was released on 2015-06-24 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Teaching of Mathematics, in the Elementary and the Secondary School I Should have been untrue to my profound conviction of the need of pedagogic preparation antecedent to entrance upon the actual work of teaching mathematics if I had not kept prospective teachers of mathematics in mind throughout the preparation of this book; I should have ignored the patent fact that it is experienced teachers who feel most keenly the problems of teaching and the need for their study if I had addressed myself to the inexperienced exclusively. As a consequence, unity of treatment and homogeneity of style have been in a measure sacrificed in what follows; the experienced teacher will, according to his experience, find this or that trite and superfluous; the inexperienced aspirant will occasionally feel the lack of the perspective of experience. I appreciate deeply the importance of the historical aspect of the teaching of mathematics, but in view of its genial treatment in the excellent and well-known work of Smith, I have felt at liberty not to touch upon it. Some writers on methods in mathematics discuss more or less extensive topics of subject matter, in the form either of presentations to pupils or of a more Intensive study from the teacher's viewpoint. Such work is important - an essential element of progress, indeed; but I have found it advisable here strictly to confine myself to illustrative use only of subject matter. Within the bounds of the field thus limited I have further restricted myself, in the main, to conditions as they exist in the United States. 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 Elementary Mathematics  Classic Reprint

Download or read book The Teaching of Elementary Mathematics Classic Reprint written by David Eugene Smith and published by Forgotten Books. This book was released on 2017-12-20 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Teaching of Elementary Mathematics If this work shall help, even in a small way, to open a wider field, or to offer a better point of view, to some one just entering the profession, the author will feel repaid for his labors. 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 Place of the Elementary Calculus in the Senior High School Mathematics

Download or read book The Place of the Elementary Calculus in the Senior High School Mathematics written by Noah Bryan Rosenberger and published by Forgotten Books. This book was released on 2016-10-20 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Place of the Elementary Calculus in the Senior High-School Mathematics: And Suggestions for a Modern Presentation of the Subject Even a little less than a decade ago, the trained teacher of high school mathematics had the pleasure of teaching real mathematics as found in such subjects as trigonometry, solid and plane geometry, and advanced and elementary algebra. It is doubtless true that this kind of work was inclining too much toward formalism and that the needs of the learner were not being given sufficient attention. The strong reaction against formalism in general in education during the decade just past made the position of any genuine mathematics in our high schools very precarious. This threatened elimination of all real mathematics in our high schools was viewed with regret by those of us who had had the pleasure of starting many a pupil with a vigorous mind upon his mathematical way; and a number of prom inent educators who are especially interested in the teaching of mathematics have been working toward a readjustment of the mathematics curriculum so that it will fit into and fulfill its mission in the changed conditions as found in our schools to-day. The following study is the author's contribution toward this attempted readjustment. The kind of mathematics that should be taught in the first six school years has been definitely settled; the main points of the work in mathematics that should be included in the junior high-school period have been agreed upon; and the author hopes that his study will be of some value in helping us to formulate the content of the mathematics curriculum of the senior high school. 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 2018-02-02 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Teaching of Arithmetic The Teachers College Record for March, 1903, contained an article on Mathematics in the Elementary School by the author's colleague Professor mcmurry and himself. This number, how ever, has long since been out of print, and as a result of this fact it was thought best in the autumn of 1908 to prepare a new number of the.record on The Teaching of Arithmetic. This was done by the author, and the article appeared in January, 1909. Although it was thought that the unusually large edition was sufficient for all demands for some years to come, it was ex hauste\d within a few weeks, and it became necessary to print the article in book form. In spite of the fact that the work was originally written in a popular style, to the end that it might be read by those who have no more interest in mathematics than in the various other subjects of the curriculum, it has been thought best to make but a few changes in arranging for its publication in the present form. Intended as it is for those who are teaching or supervising the work in arithmetic in the elemen tary schools, it would hardly serve its purpose if it departed widely from the practical and entered the domain of pure theory. As between influencing the few or the many on a topic of such general interest 'it has been thought better to adopt the latter course, and to prepare a book that might have place in educational reading circles generally and serve as a basis for the work in the class-room for the training of teachers. 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 Elementary School Mathematics by Grades  Vol  6

Download or read book Elementary School Mathematics by Grades Vol 6 written by William Estabrook Chancellor and published by Forgotten Books. This book was released on 2017-11-24 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Elementary School Mathematics by Grades, Vol. 6: Commercial Affairs Boys and girls in the upper grammar grades of the free common schools of American towns and cities are pursuing courses Of study by no means uniform. There is perhaps no general agreement in educational practice beyond the fact that it is considered desirable that boys and' girls should advance from elementary to secondary schools at about fourteen years of age. There are, however, marked tendencies to agree upon several other points. There is increasing agreement to the effect that pupils in the upper grammar grades should study what will most benefit them in discipline and in knowledge. We have come to see in the light of the new knowledge Of the facts and principles Of mental and moral growth, presented by genetic psychology, that what a child enjoys learning he profits by, and that what he profits by develops in him the normal life Of the child, which is the guarantee of an efficient life as an adult. There is a growing tendency to decrease the range of arithmetical instruction and to introduce much more geometrical instruc tion. There is also a distinct tendency to rely more and more upon the various forms of manual training in the education Of boys and girls; and this development along the lines of the industrial arts, which afford the materials of manual mental discipline, lends itself notably to the encouragement Of the study of geometry early in life. 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 Mathematics  Pedagogy  and Secondary Teacher Education

Download or read book Mathematics Pedagogy and Secondary Teacher Education written by Thomas J. Cooney and published by Heinemann Educational Books. This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each of the chapters shed new light on what it means to integrate content and pedagogy in a teacher-education context.

Book The Teaching of Mathematics in the Elementary and the Secondary School

Download or read book The Teaching of Mathematics in the Elementary and the Secondary School written by J. W. A. Young and published by Wentworth Press. This book was released on 2019-03-06 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Book Knowing and Teaching Elementary Mathematics

Download or read book Knowing and Teaching Elementary Mathematics written by Liping Ma and published by Routledge. This book was released on 2010-03-26 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.

Book The National Council of Teachers of Mathematics  1935

Download or read book The National Council of Teachers of Mathematics 1935 written by Council of Teachers of Mathematics and published by Forgotten Books. This book was released on 2018-10-08 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The National Council of Teachers of Mathematics, 1935: The Tenth Yearbook, the Teaching of Arithmetic Bound Copies of all except the first two Yearbooks can be secured from the Bureau of Publications, Teachers College, Columbia Uni versity', New York, N. Y., for each postpaid. The first Year book is now out of print and the second is obtainable only in paper covers postpaid). A complete set of Yearbooks (numbers 2 to 10 inclusive) will be sent postpaid for a saving of practically 20 per cent. The purpose of the Tenth Yearbook is to present some of the most important ideas and proposals concerning the teaching of arithmetic in the schools. Through this Yearbook the National Council of Teachers of Mathematics wishes to express its interest in the more elementary phases of mathematics and in the teachers who present it in the Classroom. 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 Preston Stevens Elementary Arithmetic  Classic Reprint

Download or read book Preston Stevens Elementary Arithmetic Classic Reprint written by Deforest A. Preston and published by Forgotten Books. This book was released on 2017-10-29 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Preston-Stevens Elementary Arithmetic Note to Teacher. The work in number for the first year or two can be most satisfactorily presented by the use of objects, oral instruction, free use of the blackboard by teacher and pupils, simple stories and exercises in applied number, carefully planned busy work and directed motor activities, and by daily use of the drill cards, etc. The exercises, therefore, in this chapter are not intended to show the full work of the pupils, but are given as suggestions and as outlines, which are to be expanded by the teacher and the pupils into such fullness as the natural progress of the class may require. The exercises here outlined may also aid the teachers of the third year grades in reviewing the introductory work in number, and may help them to determine the class need for further instruo tion in any particular line. It is also hoped that the exercises of this chapter may prove helpful in aiding pupils, on entering school at an advanced age with considerable general knowledge of number, to pass rapidly over the introductory work and take up the regular exercises of the third year in a short time. 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 First Year Mathematics for Secondary Schools  Classic Reprint

Download or read book First Year Mathematics for Secondary Schools Classic Reprint written by George William Myers and published by Forgotten Books. This book was released on 2018-03-24 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from First-Year Mathematics for Secondary Schools This volume aims to present in teachable form an inter weaving Of the more concrete and the easier portions of the first courses in both algebra and geometry. It is intended as a text for students of the first year of secondary schools. The type of work begun here will be continued by a second year text, to appear soon and to include not less than the rest of the subject-matters that make up the customary two years of required secondary work in algebra and plane geometry. The present book places chief emphasis upon algebra, but weaves in a considerable body of related fundamental notions and principles Of geometry, even advancing somewhat in one direction or another upon the most concrete, graphic, and practical aspects of elementary geometry. Geometrical treat ments are at first intuitive, inductive, and experimental, fol lowed in a few instances by the quasi-experimental methods of superposition. A like informality as to method characterizes the first half of the algebra. The algebraic treatments feature distinctly: (i) the liberal use of inductions from arithmetic; (2) the early and persistent use of the equation, both as an instrument for problem - solving, and as a means of suggesting and of treating topics; (3) the early, varied, and systematic use Of pictured and graphic modes of rendering algebraic truths Vivid and appealing to beginners. The algebra of the last half of the book is more formally deductive in character. Even as early as p. 26 the four pro cess-axioms are given as simple statements of the four ways in which equations have been changed in solving arithmetical and mensurational problems. They are stated as laws forusing the equation, and are given only as much generality as the antecedent work justifies. Transformations of equations are then made on the basis of these laws and of others brought out from time to time as the work proceeds, until p. 216 is reached, where a fifth general axiom is added, and the five are here given final statement. These five axioms are hence forth made the reasons for all changes in equations. The root-axiom is added later when an ocrasion to use it arises. Thus the transition from the informal procedure of the earlier part of the algebra to the formal procedure of the later part is gradual, while throughout the latter half the reasoning becomes more and more highly deductive. This is in accord with what both Classroom practice and a-priori reasoning Show to be the natural order for secondary mathematical education. 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 Elementary Algebra  Classic Reprint

Download or read book Elementary Algebra Classic Reprint written by G. A. Wentworth and published by Forgotten Books. This book was released on 2017-12-24 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Elementary Algebra In preparing a new algebra for secondary schools, the author has provided a new set of examples throughout the book. These examples have been selected and graded with great care. There are nearly four thousand of them, surely a sufficient number for practice in fixing in the minds of pupils the principles of elementary algebra. At the request of many teachers a sufficiently full treatise on graphs and several pages of exercises in physics have been introduced. The first chapter contains the necessary definitions and illustra tions of the commutative, associative, and distributive laws of algebra. This chapter should be read carefully at first, and later particular attention should be given to the principal definitions. The second chapter treats of simple equations and is designed to lead the beginner to see the advantages of algebraic methods before he encounters negative numbers. Only positive numbers are involved in the first two chapters, and the recognition of the fact that the true nature of subtraction is counting backward, and that the true nature of multiplication is forming the product from the multipli cand in the same way as the multiplier is formed from unity, leads to an easy explanation in the third chapter of all the elementary processes with negative numbers. All the rules of this chapter are illustrated and enforced by examples that involve simple algebraic expressions only. The more common Operations with compound expressions, including resolution into factors and the treatment of fractions, follow the third chapter. The immediate succession Of topics that require similar work is of the greatest importance to the beginner, and it is expected that the exercises in compound expressions will give sufficient practice in the use of symbols. 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 Graded School Arithmetic  Vol  2

Download or read book Graded School Arithmetic Vol 2 written by Frank J. Browne and published by Forgotten Books. This book was released on 2018-02-14 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Graded School Arithmetic, Vol. 2: An Elementary Text for Use in Public and Private Schools, From the Fifth to the Eight Year, Inclusive But little need be said as to methods, aside from the plans indicated by the text itself. Whatever of general method is applicable to the teaching of arithmetic is stated in the following extracts from a bulletin on arithmetic, written by Prof. W. H. Baker of the State N ormal School, San Jose, California. 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.