A posteriori 43 60
A priori 38 64
A priori and the purely formal 4
A usdehnungslehre, Grassmann’s 28
Absolute, the 25
Anschauung 82 97
Anyness 46
Anyness, Space founded on 60
Apollonius 31
Apparent arbitrariness of is ideal 44
Apparent arbitrariness of the 96
Apparent arbitrariness of the constructions 112
Apparent arbitrariness of the constructions verified by experience 122
Apparent arbitrariness of the constructions, Geometries are 127
Apparent arbitrariness of the logical 54
Apparent arbitrariness of the purely 55
Apparent arbitrariness of the rigidly 54 55
Apparent arbitrariness of, Source of the 51
Apriority of different degrees 49ff
Apriority of mathematical space 121 129
Apriority, Problem of 36
Archimedes 31
Astral geometry 15
Atomic fiction 81
Ball, Sir Robert, on the nature of space 23ff
bernoulli 9
Bessel, Letter of Gauss to, 21ff
Billingsley, Sir H. 82
Bolyai, Janos 22ff 98
Bolyai, translated 27
Boundaries 78 129
Boundaries, produced by halving, Even 85 86
Boundary concepts, Utility of 74
Bridges of Konigsberg 20ff
Busch, Wilhelm 115
Carus, Paul, Fundamental Problems 3
Carus, Paul, Fundamental Problems; Kants Prolegomena 39 122
Carus, Paul, Fundamental Problems; Primer of Philosophy 41.
Causation and transformation 54
Causation, a priori 53
Causation, Kant on 40
Cayley 25
Chessboard, Problem of 101
Circle, squaring of the 104
Circle, the simplest curve 75
Classification 79
Clifford 16 32 60
Clifford, Plane constructed by 69
Common notions 2 4 128
Comte 38
Concreteness, Purely formal, absence of 60
Continuum 78ff
Curved space 106
de Morgan, Augustus 10
Definitions of Euclid 1 128
Delboeuf, B. J. 27
Determinism in mathematics 104
Dimension, definition of 85
Dimensions, Space of four 9 off.
Directions of space, Infinite 117
Discrete units 78ff
Dual number 89
Edward’s Dream 115
Egg-shaped body 33f
Elliptic geometry 25
Empiricism, Transcendentalism and 38ff
Engel, Friedrich 26
Euclid 43
Euclidean geometry, classical 31 121
Even boundaries 122
Even boundaries as standards of measurement 69 85 86
Even boundaries, produced by halving 85 86
Experience, Physiological space originates through 65
Expositionsof, rearranged 128
Faust 133
Fictitious spaces 19ff
Flatland 115
FORM 60 133
Form and reason 48
Four dimensions 109
Four-dimensional space and tridimensional beings 93
Fourth dimension 25
Fourth dimension, illustrated by mirrors 93
Geometrical construction, Definiteness of 99ff
Geometries, a priori constructions 127
God, Conception of 136
Grassmann 27
Halsted on 31
Halsted, George Bruce 4 23 26 27 2811 101
Halsted, George Bruce on Euclid 3
Helmholtz 26 83
Helmholtz on 113
Helmholtz on curved space 113
Helmholtz on two-dimensional beings 11
Hilbert’s use of “axiom” 128
Homaloidal 18 74
Homogeneity of space 66ff
Hypatia 31
Infinite directions of space 117
Infinite directions of space, division of line 117
Infinite directions of space, Infinitude 61ff
Infinite directions of space, not mysterious 118
Infinite directions of space, Space is 116 126
Infinite directions of space, Time is 116
Infinite, division of 117
Infinite, Shortest 84
Infinite, Straightest 75 127
Kant 35 40 61 84
Kant and the a priori 36 38
Kant his identification of “ideal” and “subjective” 44ff
Kant his term Anschauung 32 97
Kant his use of “transcendental” 41
Kant’s Prolegomena 39
Keyser, Cassius Jackson 77
Kinematoscope 80
Klein, Felix 25
Konigsberg, Seven bridges of 102ff
Lambert, Johann Heinrich 19
Laws of nature 132
legendre 11
Line created by construction 83
Line created by construction, independent of position 62
LITTRE 38
Lobatchevsky 10 2
Lobatchevsky, translated 27
Lobatchevsky’s Theory of Parallels 101
| Logic is static 53
Mach, Ernst 27 65
Mathematical space 63ff 67 109
Mathematical space, Apriority of 121 129
Mathematical space, priori 65
Mathematics and 82ff
Mathematics, Analogy of, to religion 134
Mathematics, Determinism in 104
Mathematics, Reality of 77
Mathematics, Teaching of 27ff
Measurement of star parallaxes 125
Measurement, Even boundaries as standards of 69
Measurement, Standards for 74
Mental activity, First rule of 79
Metageometry, History of 26
Mill, John Stuart 38
Mind develops through uniformities 52
Mirrors, Fourth dimension illustrated by 93
Monist 4 27 125
Names, Same, for parts of figures 130
Nasir eddin 7
Nature 16
Nature a continuum 78
Newcomb, Simon 25
Open Court 2
Order in life and arithmetic 80
Pangeometry 22
Pappus 31
Parallel lines in spherical space 84
Parallel lines in spherical space, theorem 4
Parallels, Axiom of 3
Path of highest intensity a straight line 58
Peirce, Charles S., on the nature of space 123
Physiological space 63
Physiological space, originates through experience 65
Plane, a zero of curvature 82
Plane, constructed by Clifford 69
Plane, created by construction 83
Plane, Nature of 73
Plane, Significance of 129
Plato 135
Plutarch 135
Poincare, H. 27
Point congruent with itself 71
Population of Great Britain determined 29f
POSITION 62
Postulates 2 128
Potentiality 63
Proclus 4 31
Pseudo-spheres 83
Pure form 63
Pure form space, Uniqueness of 61
Purely a priori, The formal, absence of concreteness 60
Question in geometry 72 73 121
Ray a final boundary 58
Reason, Form and 48
Reason, Nature of 76
Rectangular pentagon 98
Religion, Analogy of mathematics to 134
Riemann 15
Right angle created by construction 83
Right angle created by construction, Nature of 73
Right angle created by construction, Significance of 129
Russell on non-Euclidean geometry 119
Russell, Bertrand A.V. 26
Saccheri, Girolamo 8f
Schlegel, Victor 30
Schoute, P. H. 3
Schumaker, Letter of Gauss to, n.Schweikart 15
Sense-experience and space 122
Shortest line 84
significance of 129
Significance of possible 74
Space, a manifold 108
Space, a spread of motion 56
Space, Apriority of mathematical 121 129
Space, curved 126
Space, founded on “anyness 60
Space, Helmholtz on curved 113
Space, Homogeneity of 66
Space, Infinite directions of 117
Space, Mathematical 63ff 67 109
Space, Mathematical and actual 62
Space-conception, how far a priorif 59ff
Space-conception, product of pure activity 55
Space-measurement, Apriority of 109
Spaces, Fictitious 109
Squaring of the circle 104
Stackel, Paul 26
Standards of measurement 74
Standards of measurement, boundaries as 69
Star parallaxes, Measurements of 125
Straight line 69 71 112 122
Straight line a path of highest intensity 59
Straight line does not exist 72
Straight line indispensable 72
Straight line, created by construction 83
Straightest line 75 127
Subjective and ideal, Kant’s identification of 44f
Subjective and ideal, not synonyms 64
Superreal, The 76
Taurinus, Letter of Gauss to 63f
Teaching of mathematics 127
Tentamen 23
Theory of Parallels, Lobatchevsky’s 101
Thought-forms, systems of reference 61
Three, The number 88f
Time is infinite 116
Tlieon 31 32
Transcendentalism and Empiricism 35 38ff
Transformation, Causation and 54
Tridimensional beings, Four-dimensional space and 93
Tridimensionality 84
Trinity, Doctrine of the 89
Two-dimensional beings and tridimensional space 91
Units, Discrete 78
Various systems of 104
Wallis, John 71f
WHY 100
Zamberti 32
Ziwet, Professor 135
“Axiom”, Euclid avoided 1 127
“Axiom”, Hilbert’s use of 128
“Ideal” and “subjective,” Kant’s identification of 44ff
“Ideal” and “subjective,” not synonyms 64
“Transcendental”, Kant’s use of 41
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