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Editorial Review Book Description
LECTURES ON THE GEOMETRY OF POSITION BY THEODOR REYE PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF STRASSBURG TRANSLATED AND EDITED BY THOMAS F. HOLGATE, M. A, Ph. D. PROFESSOR OF APPLIED MATHEMATICS IN NORTHWESTERN UNIVERSITY PART I. JUto ork THE MACMILLAN COMPANY LONDON MACMILLAN AND CO,, LIMITED 1808 GLASGOW PRINTED AT THE UNIVERSITY PRESS BY ROBERT MAOLKHOSE AND CO. TRANSLATORS PREFACE. IN preparing this translation of Professor Reyes Geometric der Lage, my sole object has been to place within easy reach of the English-speaking student of pure geometry an elementary and systematic development of modern ideas and methods. The in creasing interest in this study during recent years has seemed to demand a text-book at once scientific and sufficiently comprehensive to give the student a fair view of the field of modern pure geometry, . and also sufficiently suggestive to incite him to investigation. The recognized merit of Professor Reyes work in all these regards is my - only apology for offering this translation as an attempt to satisfy our present needs. It has been my aim to present in fair readable English the geometric ideas contained in the text, rather than to hold myself, at All points, to a literal translation yet I trust that I have not alto gether destroyed the charm of the original writing. Some changes have been made the articles have been numbered, the examples set at the end of the lectures to which they are related and a few new ones added, explanatory notes have been inserted where they seemed necessary or helpful, and an index has been compiled. I have not deemed it advisable to omit from this edition any part of the original prefaces or introduction, even though, at this distance from their first publication, they might not be demanded in their entirety. For the most part I have endeavoured to hold rigorously to well established terminology. A few instances of deviation from this principle, however, may be mentioned. I have preferred the terms sheaf of rays, sheaf of planes, and bundle of rays or planes, to the more common though I think less expressive terms, flat pencil, axial pencil, and sheaf of lines or planes instead of the expression conformal representation as an equivalent for the German conforme vt TRANSLATORS PREFACE. Abbildung I have ventured conformal depiction. The term ideal has elsewhere been applied to infinitely distant points and lines with this I have associated the word actual to apply to points and lines of the finite region. I desire to acknowledge my indebtedness to my colleague Professor Henry S. White for valuable assistance my thanks also and the gratitude of all who may profit by the use of this translation are due to Dr. M. C. Bragdon of Evanston whose interest and generosity made its publication possible. What is commonly known as Modern Synthetic Geometry has been developed for the most part during the present century. It differs from the geometry of earlier times, not so much by the subjects dealt with and the theorems propounded, as by the processes which are employed and the generality of the results which are attained. Geometry was to the ancients a subject of entrancing interest, Its progress is prominently connected with the names of Thales of Miletus 640-546, Pythagoras 569-500, P lat o 429-348, who cultivated geometry as fundamental to the study of philosophy, Menaechmus 375-325, the first to discuss the conic sections, Euclid of Alexandria 330-275, Archimedes 287-212, and Apollonius of Perga 260-200 these among others before the Christian era. Of the numerous writings of Euclid, the Elements in which was collected and systematized much of the geometrical knowledge of that time, has remained for two thousand years a marvellous monument to his skill... ... Read more |
