CONTENTS

CHAP. PAGE
I. Four-Dimensional Space 1
II. The Analogy of a Plane World 6
III. The Significance of a Four-Dimensional Existence 15
IV. The First Chapter in the History of Four Space 23
V. The Second Chapter in the History Of Four Space 41
Lobatchewsky, Bolyai, and Gauss
Metageometry
VI. The Higher World 61
VII. The Evidence for a Fourth Dimension 76
VIII. The Use of Four Dimensions in Thought 85
IX. Application to Kant’s Theory of Experience 107
X. A Four-Dimensional Figure 122
XI. Nomenclature and Analogies 136
XII. The Simplest Four-Dimensional Solid 157
XIII. Remarks on the Figures 178
XIV. A Recapitulation and Extension of the Physical Argument 203
APPENDIX I.—The Models 231
APPENDIX II.—A Language of Space 248