Hinton - The Fourth Dimension.pdf

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266 Sen San Sin Senan THE FOURTH DIMENSION 10 11 12 * Senat Senin Senil Senit Sanan Sinan Senet Senel Sanin Sanet Sanit Sinet Sinel Sinat Sanel Senal Sinin Sinil Sinit Sanal Sinal Sanil Set Sat Sit Setan Satan Sitan Setet Setel Satet Sitet Setat Setin Setil Setit Satin Sitat Satit Satel Sitel Setal Satal Sital Satil Sitin Sitil Sitit Selan Salan Silan Selet Selel Salet Silet Selat Selin Selil Salit Salin Silat Salit Silet Salel Selal Salal Silal Salil Silin Silil Silit Interior Sanat Interior Satat Interior Salat We can now name any section. Take e.g. the line in the first cube from senin to senel, we should call the line running from senin to senel, senin senat senel, a line light yellow in colour with null points. Here senat is the name for all of the line except its ends. Using “senat” in this way does not mean that the line is the whole of senat, but what there is of it is senat. It is a part of the senat region. Thus also the triangle, which has its three vertices in senin, senel, selen, is named thus: Area: setat. Sides: setan, senat, setet. Vertices: senin, senel, sel. The tetrahedron section of the tesseract can be thought of as a series of plane sections in the successive sections of the tesseract shown in fig. 114, p. 191. In b0 the section is the one written above. In b1 the section is made by a
APPENDIX II: A LANGUAGE OF SPACE 267 plane which cuts the three edges from sanen intermediate of their lengths and thus will be: Area: satat. Sides: satan, sanat, satet. Vertices: sanan, sanet, sat. The sections in b2, b3 will be like the section in b1 but smaller. Finally in b4 the section plane simply passes through the corner named sin. Hence, putting these sections together in their right relation, from the face setat, surrounded by the lines and points mentioned above, there run: 3 faces: satan, sanat, satet 3 lines: sanan, sanet, sat and these faces and lines run to the point sin. Thus the tetrahedron is completely named. The octahedron section of the tesseract, which can be traced from fig. 72, p. 129 by extending the lines there drawn, is named: Front triangle selin, selat, selel, setal, senil, setit, selin with area setat. The sections between the front and rear triangle, of which one is shown in 1b, another in 2b, are thus named, points and lines, salan, salat, salet, satet, satel, satal, sanal, sanat, sanit, satit, satin, satan, salan. The rear triangle found in 3b by producing lines is sil, sitet, sinel, sinat, sinin, sitan, sil. The assemblage of sections constitute the solid body of the octahedron satat with triangular faces. The one from the line selat to the point sil, for instance, is named
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THE FOURTH DIMENSION
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THE FOURTH DIMENSION BY C. HOWARD H
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PREFACE I HAVE endeavoured to prese
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CONTENTS CHAP. PAGE. I. FOUR-DIMENS
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THE FOURTH DIMENSION ————
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FOUR-DIMENSIONAL SPACE 3 existence
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FOUR-DIMENSIONAL SPACE 5 Bringing i
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THE ANALOGY OF A PLANE WORLD 7 him.
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THE ANALOGY OF A PLANE WORLD 9 to a
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THE ANALOGY OF A PLANE WORLD 11 Aga
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THE ANALOGY OF A PLANE WORLD 13 sec
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CHAPTER III THE SIGNIFICANCE OF A F
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SIGNIFICANCE OF A FOUR-DIMENSIONAL
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CHAPTER IV THE FIRST CHAPTER IN THE
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THE FIRST CHAPTER IN THE HISTORY OF
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CHAPTER V THE SECOND CHAPTER IN THE
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SECOND CHAPTER IN THE HISTORY OF FO
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CHAPTER VI THE HIGHER WORLD IT is i
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THE HIGHER WORLD 63 dimensions. His
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THE HIGHER WORLD 65 If now he turns
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THE HIGHER WORLD 67 to him that, by
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THE HIGHER WORLD 69 simply the plan
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THE HIGHER WORLD 71 turn these rods
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THE HIGHER WORLD 73 revolution, the
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THE HIGHER WORLD 75 the mode of act
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THE EVIDENCES FOR A FOURTH DIMENSIO
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CHAPTER VIII THE USE OF FOUR DIMENS
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5 THE USE OF FOUR DIMENSIONS IN THO
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THE USE OF FOUR DIMENSIONS IN THOUG
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CHAPTER IX APPLICATION TO KANT’S
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APPLICATION TO KANT’S THEORY OF E
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3 APPLICATION TO KANT’S THEORY OF
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A FOUR-DIMENSIONAL FIGURE 123 The r
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A FOUR-DIMENSIONAL FIGURE 125 new d
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A FOUR-DIMENSIONAL FIGURE 127 pick
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A FOUR-DIMENSIONAL FIGURE 129 Now s
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A FOUR-DIMENSIONAL FIGURE 131 of me
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A FOUR-DIMENSIONAL FIGURE 133 note
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A FOUR-DIMENSIONAL FIGURE 135 These
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NOMENCLATURE AND ANALOGIES 137 to a
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NOMENCLATURE AND ANALOGIES 139 null
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NOMENCLATURE AND ANALOGIES 141 laye
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NOMENCLATURE AND ANALOGIES 143 a li
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NOMENCLATURE AND ANALOGIES 145 oppo
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NOMENCLATURE AND ANALOGIES 147 the
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NOMENCLATURE AND ANALOGIES 149 dime
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NOMENCLATURE AND ANALOGIES 151 larg
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NOMENCLATURE AND ANALOGIES 153 axes
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NOMENCLATURE AND ANALOGIES 155 lie
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CHAPTER XII THE SIMPLEST FOUR-DIMEN
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THE SIMPLEST FOUR-DIMENSIONAL SOLID
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Purple Red THE SIMPLEST FOUR-DIMENS
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Light blue Gren Light purple THE SI
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REMARKS ON THE FIGURES 179 ochre cu
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REMARKS ON THE FIGURES 181 for it i
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REMARKS ON THE FIGURES 183 that is
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REMARKS ON THE FIGURES 185 yellow l
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REMARKS ON THE FIGURES 187 As the r
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REMARKS ON THE FIGURES 189 cubes, w
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4 4 REMARKS ON THE FIGURES 191 The
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REMARKS ON THE FIGURES 193 face or
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REMARKS ON THE FIGURES 195 face in
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REMARKS ON THE FIGURES 197 space, a
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REMARKS ON THE FIGURES 199 Hence wh
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REMARKS ON THE FIGURES 201 sections
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CHAPTER XIV * A RECAPITULATION AND
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RECAPITULATION AND EXTENSION 205 ou
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RECAPITULATION AND EXTENSION 207 ha
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RECAPITULATION AND EXTENSION 209 Bu
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RECAPITULATION AND EXTENSION 211 We
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RECAPITULATION AND EXTENSION 213 Th
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Page 241 and 242: APPENDIX I THE MODELS IN Chapter XI
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Page 251 and 252: APPENDIX I: THE MODELS 241 The four
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Page 257 and 258: APPENDIX I: THE MODELS 247 sponding
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Page 275: Sil Sit Sin Sil Sit Sin Silan Sitan
Page 281 and 282: TRANSCRIBER’S NOTE. Do what thou
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