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Mathematical Essays and Recreations   By: (1848-1911)

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IN THE SAME SERIES. ON THE STUDY AND DIFFICULTIES OF MATHEMATICS. By Augustus De Morgan. Entirely new edition, with portrait of the author, index, and annotations, bibliographies of modern works on algebra, the philosophy of mathematics, pan geometry, etc. Pp., 288. Cloth, $1.25 (5s.). LECTURES ON ELEMENTARY MATHEMATICS. By Joseph Louis Lagrange. Translated from the French by Thomas J. McCormack. With photogravure portrait of Lagrange, notes, biography, marginal analyses, etc. Only separate edition in French or English. Pages, 172. Cloth, $1.00 (5s.). HISTORY OF ELEMENTARY MATHEMATICS. By Dr. Karl Fink, late Professor in T¨ubingen. Translated from the German by Prof. Wooster Woodruff Beman and Prof. David Eugene Smith. (In preparation.) THE OPEN COURT PUBLISHING CO. 324 dearborn st., chicago. MATHEMATICAL ESSAYS AND RECREATIONS BY HERMANN SCHUBERT PROFESSOR OF MATHEMATICS IN THE JOHANNEUM, HAMBURG, GERMANY FROM THE GERMAN BY THOMAS J. McCORMACK Chicago, 1898 Produced by David Wilson Transcriber’s notes This e text was created from scans of the book published at Chicago in 1898 by the Open Court Publishing Company, and at London by Kegan Paul, Trench, Truebner & Co. The translator has occasionally chosen unusual forms of words: these have been retained. Some cross references have been slightly reworded to take account of changes in the relative position of text and floated figures. Details are documented in the LATEX source, along with minor typographical corrections. TRANSLATOR’S NOTE. The mathematical essays and recreations in this volume are by one of the most successful teachers and text book writers of Germany. The monistic construction of arithmetic, the systematic and organic development of all its consequences from a few thoroughly established principles, is quite foreign to the general run of American and English elementary text books, and the first three essays of Professor Schubert will, therefore, from a logical and esthetic side, be full of suggestions for elementary mathematical teachers and students, as well as for non mathematical readers. For the actual detailed development of the system of arithmetic here sketched, we may refer the reader to Professor Schubert’s volume Arithmetik und Algebra, recently published in the G¨oschen Sammlung (G¨oschen, Leipsic),—an extraordinarily cheap series containing many other unique and valuable text books in mathematics and the sciences. The remaining essays on “Magic Squares,” “The Fourth Dimension,” and “The History of the Squaring of the Circle,” will be found to be the most complete generally accessible accounts in English, and to have, one and all, a distinct educational and ethical lesson. In all these essays, which are of a simple and popular character, and designed for the general public, Professor Schubert has incorporated much of his original research. Thomas J. McCormack. La Salle, Ill., December, 1898.

CONTENTS. page Notion and Definition of Number . . . . . . . . . . . . . 1 Monism in Arithmetic . . . . . . . . . . . . . . . . 8 On the Nature of Mathematical Knowledge . . . . . . . . . . 25 The Magic Square . . . . . . . . . . . . . . . . . 36 The Fourth Dimension . . . . . . . . . . . . . . . . 63 The Squaring of the Circle . . . . . . . . . . . . . . . 107

NOTION AND DEFINITION OF NUMBER. Many essays have been written on the definition of number. But most of them contain too many technical expressions, both philosophical and mathematical, to suit the non mathematician. The clearest idea of what counting and numbers mean may be gained from the observation of children and of nations in the childhood of civilisation. When children count or add, they use either their fingers, or small sticks of wood, or pebbles, or similar things, which they adjoin singly to the things to be counted or otherwise ordinally associate with them. As we know from history, the Romans and Greeks employed their fingers when they counted or added. And even to day we frequently meet with people to whom the use of the fingers is absolutely indispensable for computation... Continue reading book >>

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