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유클리드의 기하학, 기하학 요소의 처음여섯 책들 (First Six Books of the Elements of Euclid, by John Casey)


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유클리드의 기하학, 기하학 요소의 처음여섯 책들 (First Six Books of the Elements of Euclid, by John Casey)

J Casey 저 | 뉴가출판사

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유클리드의 기하학,기하학 요소의 처음여섯 책들.First Six Books of the Elements of Euclid,by John Casey . 이책은 아일랜드 에이레 대학에서 만든후에 미국 코넬대학에서 내놓은책. 기하학은 수학에서 중요함.

유클리드 Euclid .
BC 300년경에 활약한 그리스의 수학자. 그리스기하학, 즉 ‘유클리드기하학’ 만듬.
고대 그리스 수학 기하학원론 Stoikheia
그리스식 표기는 Eukleid?s. 그리스기하학, 즉 ‘유클리드기하학’의 대성자이다.
유클리드 Euclid
이책의 기하학의 도형 원 도형등은 1660년도경의 뉴톤의 책인 자연철학의수학적원리에서 원 도형및
선은 뉴톤의 자연철학의수학적원리 책에서 지구에서 달까지 거리 및 지구에서 태양까지 거를 계산해 내는데 도움을 준듯함 그리고 미적분학을 만드는데 도움됨. 그리고 1910년경에 영국에서 발행된 알기쉽게 만든 미적분학 칼큐러스 만드는데 기여함. 1942년도경 2차세계대전에 로케트의 궤도거리를 계산해내서 그후에 우주의 궤도 거리 계산함. 지금은 컴퓨터및 시티 엠알이등 의학에서도 사용됨.

Contents
preface
INTRODUCTION.
BOOK I.
THEORY OF ANGLES, TRIANGLES, PARALLEL LINES, AND
PARALLELOGRAMS.
BOOK II.
THEORY OF RECTANGLES
BOOK III.
THEORY OF THE CIRCLE
BOOK IV.
INSCRIPTION AND CIRCUMSCRIPTION OF TRIANGLES AND
OF REGULAR POLYGONS IN AND ABOUT CIRCLES
BOOK V.
THEORY OF PROPORTION
BOOK VI.
APPLICATION OF THE THEORY OF PROPORTION
BOOK XI.
THEORY OF PLANES, COPLANAR LINES, AND SOLID
ANGLES
APPENDIX.
PRISM, PYRAMID, CYLINDER, SPHERE, AND CONE
NOTES.
_____
NOTE A.
MODERN THEORY OF PARALLEL LINES.
- - - - - - - - - - - -
NOTE G.
ON THE QUADRATURE OF THE CIRCLE.
CONCLUSION.
END

목차

유클리드의 기하학,기하학 요소의 처음여섯 책들.First Six Books of the Elements of Euclid,by John Casey
Contents
Introduction, . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 1
BOOK I.
Theory of Angles, Triangles, Parallel Lines, and
parallelograms., . . . . . . . 2
Definitions, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 2
Propositions i.?
xlviii., . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Questions for
Examination, . . . . . . . . . . . . . . . . . . . . . . . . 45
Exercises, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 46
BOOK II.
Theory of
Rectangles, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
Definitions, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 49
Propositions i.?
xiv., . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Questions for
Examination, . . . . . . . . . . . . . . . . . . . . . . . . 65
Exercises, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 66
BOOK III.
Theory of the
Circle, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Definitions, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 68
Propositions i.?
xxxvii., . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Questions for
Examination, . . . . . . . . . . . . . . . . . . . . . . . . 97
Exercises, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 98
BOOK IV.
Inscription and Circumscription of Triangles and of
Regular Polygons in and
about
Circles, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Definitions, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 101
Propositions i.?
xvi., . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Questions for
Examination, . . . . . . . . . . . . . . . . . . . . . . . . 112
Exercises, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 112
BOOK V.
Theory of
Proportion, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
116
Definitions, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 116
Introduction, . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 116
Propositions i.?
xxv., . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Questions for
Examination, . . . . . . . . . . . . . . . . . . . . . . . . 133
Exercises, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 134
BOOK VI.
Application of the Theory of
Proportion, . . . . . . . . . . . . . . . . . . . . 135
Definitions, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 135
Propositions i.?
xxxiii., . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Questions for
Examination, . . . . . . . . . . . . . . . . . . . . . . . . 163
BOOK XI.
Theory of Planes, Coplanar Lines, and Solid
Angles, . . . . . . . . . . . . . . 171
Definitions, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 171
Propositions i.?
xxi., . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Exercises, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 181
APPENDIX.
Prism, Pyramid, Cylinder, Sphere, and
Cone, . . . . . . . . . . . . . . . . . 183
Definitions, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 183
Propositions i.?
vii., . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Exercises, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 192
NOTES.
A.―Modern theory of parallel
lines, . . . . . . . . . . . . . . . . . . . . . 194
B.―Legendre’s proof of Euclid, i.,
xxxii., . . . . . . . . . . . . . . . . . . 194
,, Hamilton’s ,, . . . . . . . . . . . . . . . . . . . . . . . . . . . .
195
C.―To inscribe a regular polygon of seventeen sides
in a circle―Ampere’s
solution
simplified, . . . . . . . . . . . . . . . . . . . . . . . . . . 196
D.―To find two mean proportionals between two
given lines―Philo’s
solution, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 197
,, Newton’s
solution, . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
E.―McCullagh’s proof of the minimum property of
Philo’s line, . . . . . . 198
F.―On the trisection of an angle by the ruler and
compass, . . . . . . . . 199
G.―On the quadrature of the
circle, . . . . . . . . . . . . . . . . . . . . . 200
Conclusion, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 202

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