비 유클리드 기하학의 요소들. The Elements of non-Euclidean Geometry,by Julian Lowell Coolidge

Julian Lowell Coolidge 지음

뉴가출판사 2020년 03월 12일 출간

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비 유클리드 기하학의 요소들. The Elements of non-Euclidean Geometry,by Julian Lowell Coolidge
BY
JULIAN LOWELL COOLIDGE Ph.D.
ASSISTANT PROFESSOR OF MATHEMATICS
IN HARVARD UNIVERSITY
OXFORD
AT THE CLARENDON PRESS
1909.

1901년도 발행된 아래 책보다도 더 확장된 1909년도 발행된 책.
아래.
비 유클리드 기하학. Non -Euclidean Geometry ,byHenryManning
2000년 이전쯤의 그리스 수학자 유클리드의 기하학에서 1650년경의 뉴톤의 수학으로부터 1900년도 초에 비유클리드기하학 및 미적분학이 영국에서 발달하고 1916년도경에 아이슈타인의 상대성이론이 나옴.
이책 즉, 비유클리드기하학은 미국의 브라운대학교 교수가 1901년도에 지은책.
HENRY PARKER MANNING, Ph.D.
Assistant Professor of Pure Mathematics
in Brown University

목차

비 유클리드 기하학의 요소들. The Elements of non-Euclidean Geometry,by Julian Lowell Coolidge
TABLE OF CONTENTS
CHAPTER I
FOUNDATION FOR METRICAL GEOMETRY IN A LIMITED REGION
CHAPTER II
CONGRUENT TRANSFORMATIONS
CHAPTER III
THE THREE HYPOTHESES
CHAPTER IV
THE INTRODUCTION OF TRIGONOMETRIC FORMULAE
CHAPTER V
ANALYTIC FORMULAE
CHAPTER VI
CONSISTENCY AND SIGNIFICANCE OF THE AXIOMS
CHAPTER VII
THE GEOMETRIC AND ANALYTIC EXTENSION OF SPACE
CHAPTER VIII
THE GROUPS OF CONGRUENT TRANSFORMATIONS
CHAPTER IX
POINT, LINE, AND PLANE TREATED ANALYTICALLY
CHAPTER X
THE HIGHER LINE GEOMETRY
CHAPTER XI
THE CIRCLE AND THE SPHERE
CHAPTER XII
CONIC SECTIONS
CHAPTER XIII
QUADRIC SURFACES
CHAPTER XIV
AREAS AND VOLUMES
CHAPTER XV
INTRODUCTION TO DIFFERENTIAL GEOMETRY
CHAPTER XVI
DIFFERENTIAL LINE-GEOMETRY
CHAPTER XVII
MULTIPLY CONNECTED SPACES
CHAPTER XVIII
THE PROJECTIVE BASIS OF NON-EUCLIDEAN GEOMETRY
CHAPTER XIX
THE DIFFERENTIAL BASIS FOR EUCLIDEAN AND NON-EUCLIDEAN
GEOMETRY
Index

책 속으로

비 유클리드 기하학의 요소들. The Elements of non-Euclidean Geometry,by Julian Lowell Coolidge
BY
JULIAN LOWELL COOLIDGE Ph.D.
ASSISTANT PROFESSOR OF MATHEMATICS
IN HARVARD UNIVERSITY
OXFORD
AT THE CLARENDON PRESS
1909.

1901년도 발행된 아래 책보다도 더 확장된 1909년도 발행된 책.
아래.
비 유클리드 기하학. Non -Euclidean Geometry ,byHenryManning
2000년 이전쯤의 그리스 수학자 유클리드의 기하학에서 1650년경의 뉴톤의 수학으로부터 1900년도 초에 비유클리드기하학 및 미적분학이 영국에서 발달하고 1916년도경에 아이슈타인의 상대성이론이 나옴.
이책 즉, 비유클리드기하학은 미국의 브라운대학교 교수가 1901년도에 지은책.
HENRY PARKER MANNING, Ph.D.
Assistant Professor of Pure Mathematics
in Brown University

출판사 서평

비 유클리드 기하학의 요소들. The Elements of non-Euclidean Geometry,by Julian Lowell Coolidge
PREFACE
The heroic age of non-euclidean geometry is passed. It is long since the days
when Lobatchewsky timidly referred to his system as an ‘imaginary geometry’,
and the new subject appeared as a dangerous lapse from the orthodox doctrine
of Euclid. The attempt to prove the parallel axiom by means of the other usual
assumptions is now seldom undertaken, and those who do undertake it, are
considered in the class with circle-squarers and searchers for perpetual motion？
sad by-products of the creative activity of modern science.
In this, as in all other changes, there is subject both for rejoicing and regret.
It is a satisfaction to a writer on non-euclidean geometry that he may proceed
at once to his subject, without feeling any need to justify himself, or, at least,
any more need than any other who adds to our supply of books. On the other
hand, he will miss the stimulus that comes to one who feels that he is bringing
out something entirely new and strange. The subject of non-euclidean geometry is, to the mathematician, quite as well established as any other branch of
mathematical science; and, in fact, it may lay claim to a decidedly more solid
basis than some branches, such as the theory of assemblages, or the analysis
situs.

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저자(글) Julian Lowell Coolidge

Julian Lowell Coolidge 미국 하버드 대학교 수학과 교수