Hinton - The Fourth Dimension.pdf

More documents

Recommendations

Info

52 Fig. 29. THE FOURTH DIMENSION This relation always holds. Look at fig. 29. Shear square on hypothenuse— 7 internal . . . 7 4 at corners . . . 1 —— 8 Square on one side—which the reader can draw for himself— D 4 internal . . 4 8 on sides. . 4 E 4 at corners . 1 —— 9 C K and the square on the other side is 1. Hence in this case again the difference is A B equal to the shear square on the hypothenuse, 9 – 1 = 8. Thus in a world of shear the square on the hypothenuse would be equal to the F G Fig. 29 bis. difference of the square on the sides of a right-angled triangle. In fig. 29 bis another shear square is drawn on which the above relation can be tested. What now would be the position a line on turning by shear would take up? We must settle this in the same way as previously with our turning. Since a body sheared remains the same, we must find two equal bodies, one in the straight way, one in the slanting way, which have the same volume. <strong>The</strong>n the side of one will be turning become the side of the other, for the two figures are each what the other becomes by a shear turning.
SECOND CHAPTER IN THE HISTORY OF FOUR SPACE 53 We can solve the problem in a particular case— In the figure ACDE D (fig. 30) there are— 15 inside . . 15 4 at corners . 1 E a total of 16. C Now in the square ABGF there are 16— 9 inside . . 9 12 on sides . 6 A B 4 at corners . 1 — 16 Hence the square on AB F G would, by the shear turning, become the shear square Fig. 30. ABDE. And hence the inhabitant of this world would say that the line AB turned into the line AC. <strong>The</strong>se two lines would be to him two lines of equal length, one turned a little way round from the other. That is, putting shear in place of rotation, we get a different kind of figure, as the result of the shear rotation, from what we got with our ordinary rotation. And as a consequence we get a position for the end of a line of invariable length when it turns by the shear rotation, different from the position which it would assume on turning by our rotation. A real material rod in the shear world would, on turning about A, pass from the position AB to the position AC. We say that its length alters when it becomes AC, but this transformation of AB would seem to an inhabitant of the shear world like a turning of AB without altering its length. If we now suppose a communication of ideas that takes place between one of ourselves and an inhabitant of the
Page 3 and 4:
THE FOURTH DIMENSION
Page 5 and 6:
THE FOURTH DIMENSION BY C. HOWARD H
Page 7 and 8:
PREFACE I HAVE endeavoured to prese
Page 9 and 10:
CONTENTS CHAP. PAGE. I. FOUR-DIMENS
Page 11 and 12: THE FOURTH DIMENSION ————
Page 13 and 14: FOUR-DIMENSIONAL SPACE 3 existence
Page 15 and 16: FOUR-DIMENSIONAL SPACE 5 Bringing i
Page 17 and 18: THE ANALOGY OF A PLANE WORLD 7 him.
Page 19 and 20: THE ANALOGY OF A PLANE WORLD 9 to a
Page 21 and 22: THE ANALOGY OF A PLANE WORLD 11 Aga
Page 23 and 24: THE ANALOGY OF A PLANE WORLD 13 sec
Page 25 and 26: CHAPTER III THE SIGNIFICANCE OF A F
Page 27 and 28: SIGNIFICANCE OF A FOUR-DIMENSIONAL
Page 33 and 34: CHAPTER IV THE FIRST CHAPTER IN THE
Page 35 and 36: THE FIRST CHAPTER IN THE HISTORY OF
Page 51 and 52: CHAPTER V THE SECOND CHAPTER IN THE
Page 53 and 54: SECOND CHAPTER IN THE HISTORY OF FO
Page 61: SECOND CHAPTER IN THE HISTORY OF FO
Page 71 and 72: CHAPTER VI THE HIGHER WORLD IT is i
Page 73 and 74: THE HIGHER WORLD 63 dimensions. His
Page 75 and 76: THE HIGHER WORLD 65 If now he turns
Page 77 and 78: THE HIGHER WORLD 67 to him that, by
Page 79 and 80: THE HIGHER WORLD 69 simply the plan
Page 81 and 82: THE HIGHER WORLD 71 turn these rods
Page 83 and 84: THE HIGHER WORLD 73 revolution, the
Page 85 and 86: THE HIGHER WORLD 75 the mode of act
Page 87 and 88: THE EVIDENCES FOR A FOURTH DIMENSIO
Page 95 and 96: CHAPTER VIII THE USE OF FOUR DIMENS
Page 97 and 98: 5 THE USE OF FOUR DIMENSIONS IN THO
Page 99 and 100: THE USE OF FOUR DIMENSIONS IN THOUG
Page 113 and 114:
THE USE OF FOUR DIMENSIONS IN THOUG
Page 115 and 116:
THE USE OF FOUR DIMENSIONS IN THOUG
Page 117 and 118:
CHAPTER IX APPLICATION TO KANT’S
Page 119 and 120:
APPLICATION TO KANT’S THEORY OF E
Page 121 and 122:
Page 123 and 124:
3 APPLICATION TO KANT’S THEORY OF
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
A FOUR-DIMENSIONAL FIGURE 123 The r
Page 135 and 136:
A FOUR-DIMENSIONAL FIGURE 125 new d
Page 137 and 138:
A FOUR-DIMENSIONAL FIGURE 127 pick
Page 139 and 140:
A FOUR-DIMENSIONAL FIGURE 129 Now s
Page 141 and 142:
A FOUR-DIMENSIONAL FIGURE 131 of me
Page 143 and 144:
A FOUR-DIMENSIONAL FIGURE 133 note
Page 145 and 146:
A FOUR-DIMENSIONAL FIGURE 135 These
Page 147 and 148:
NOMENCLATURE AND ANALOGIES 137 to a
Page 149 and 150:
NOMENCLATURE AND ANALOGIES 139 null
Page 151 and 152:
NOMENCLATURE AND ANALOGIES 141 laye
Page 153 and 154:
NOMENCLATURE AND ANALOGIES 143 a li
Page 155 and 156:
NOMENCLATURE AND ANALOGIES 145 oppo
Page 157 and 158:
NOMENCLATURE AND ANALOGIES 147 the
Page 159 and 160:
NOMENCLATURE AND ANALOGIES 149 dime
Page 161 and 162:
NOMENCLATURE AND ANALOGIES 151 larg
Page 163 and 164:
NOMENCLATURE AND ANALOGIES 153 axes
Page 165 and 166:
NOMENCLATURE AND ANALOGIES 155 lie
Page 167 and 168:
CHAPTER XII THE SIMPLEST FOUR-DIMEN
Page 169 and 170:
THE SIMPLEST FOUR-DIMENSIONAL SOLID
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Purple Red THE SIMPLEST FOUR-DIMENS
Page 187 and 188:
Light blue Gren Light purple THE SI
Page 189 and 190:
REMARKS ON THE FIGURES 179 ochre cu
Page 191 and 192:
REMARKS ON THE FIGURES 181 for it i
Page 193 and 194:
REMARKS ON THE FIGURES 183 that is
Page 195 and 196:
REMARKS ON THE FIGURES 185 yellow l
Page 197 and 198:
REMARKS ON THE FIGURES 187 As the r
Page 199 and 200:
REMARKS ON THE FIGURES 189 cubes, w
Page 201 and 202:
4 4 REMARKS ON THE FIGURES 191 The
Page 203 and 204:
REMARKS ON THE FIGURES 193 face or
Page 205 and 206:
REMARKS ON THE FIGURES 195 face in
Page 207 and 208:
REMARKS ON THE FIGURES 197 space, a
Page 209 and 210:
REMARKS ON THE FIGURES 199 Hence wh
Page 211 and 212:
REMARKS ON THE FIGURES 201 sections
Page 213 and 214:
CHAPTER XIV * A RECAPITULATION AND
Page 215 and 216:
RECAPITULATION AND EXTENSION 205 ou
Page 217 and 218:
RECAPITULATION AND EXTENSION 207 ha
Page 219 and 220:
RECAPITULATION AND EXTENSION 209 Bu
Page 221 and 222:
RECAPITULATION AND EXTENSION 211 We
Page 223 and 224:
RECAPITULATION AND EXTENSION 213 Th
Page 225 and 226:
RECAPITULATION AND EXTENSION 215 th
Page 227 and 228:
RECAPITULATION AND EXTENSION 217 In
Page 229 and 230:
Page 231 and 232:
RECAPITULATION AND EXTENSION 221 ta
Page 233 and 234:
RECAPITULATION AND EXTENSION 223 If
Page 235 and 236:
Page 237 and 238:
RECAPITULATION AND EXTENSION 227 di
Page 239 and 240:
RECAPITULATION AND EXTENSION 229 If
Page 241 and 242:
APPENDIX I THE MODELS IN Chapter XI
Page 243 and 244:
APPENDIX I: THE MODELS 233 in an op
Page 245 and 246:
APPENDIX I: THE MODELS 235 would be
Page 247 and 248:
APPENDIX I: THE MODELS 237 have to
Page 249 and 250:
APPENDIX I: THE MODELS 239 can be u
Page 251 and 252:
APPENDIX I: THE MODELS 241 The four
Page 253 and 254:
APPENDIX I: THE MODELS 243 orange f
Page 255 and 256:
APPENDIX I: THE MODELS 245 we make
Page 257 and 258:
APPENDIX I: THE MODELS 247 sponding
Page 259 and 260:
APPENDIX II: A LANGUAGE OF SPACE 24
Page 261 and 262:
Page 263 and 264:
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Sil Sit Sin Sil Sit Sin Silan Sitan
Page 277 and 278:
Page 279 and 280:
Page 281 and 282:
TRANSCRIBER’S NOTE. Do what thou
show all

Hinton - The Fourth Dimension.pdf

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?