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| Birkhoff G.D., Beatley R. — Basic Geometry |
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| Ïðåäìåòíûé óêàçàòåëü |
Algebra 38 58 60 94 165—166 192 236 240 284—288
Algebraic treatment of proportion 64—66
Altitude 74 259
Altitude on hypotenuse 86
Analysis 5 21
And no other(s) 88 246
And only one 89—90 107
Angle(s) 38 39 45 46 55 146 173—174
Angle(s) of polygon 55
Angle(s), acute 50
Angle(s), central 134
Angle(s), complementary 111
Angle(s), directed 49 235—239
Angle(s), division of 165—166 168 170—172 189—190 194—195
Angle(s), exterior 84 87 116 117
Angle(s), inscribed 145
Angle(s), interior 55 116 117
Angle(s), measure 45—54
Angle(s), negative 49 235—239
Angle(s), obtuse 50
Angle(s), positive 49 235—239
Angle(s), right 50
Angle(s), sides of 46
Angle(s), straight 46 50
Angle(s), sum of 82—85
Angle(s), supplementary 111
Angle(s), to prove equal 99 111
Angle(s), trisection of 166 171 189—190 195
Angle(s), vertex of 46
Angle(s), vertical 52
Apothem 204
Arc(s) 134
Arc(s), directed 209 234—239
Arc(s), equal 135
Arc(s), intersection of 173
Arc(s), length of 135 209 223
Arc(s), major 134
Arc(s), mid-point of 135
Arc(s), minor 134
Area 198—226 see "Rectangle" "Square" "Triangle"
Area of solids 202 206—207 215—216
Area, approximate 200 202—205 225—226
Area, notes on 222—226 279
Area, unit of 199 222
Assumption (s) 17—19 23 25 38 39 106 107 222 230 268—270 273—278 282—283
Assumption (s), concerning limits 212
Assumption (s), concerning number 284—288
Assumption (s), five fundamental 38—60 106 107 230
Assumption (s), temporary 5 71 106 198 199 278—279
Axiom(s) 19 284—288
Axis, axes of network 118—123
Axis, axes of symmetry 124—126
Axis, axes, radical 262—263
Basic assumptions 38—60 106 107 230
Basic theorems 71—93 107
Begging the question 31 32 280
Between for half-lines with common end-point 53—54
Between for points on a line 43
Betweenness 146
BISECT 44 48
Bisector of angle 48 174 182—183 251—252 256 260
Bisector of exterior angle 116 117 260
Bisector of interior angle 116 117 260
Bisector, perpendicular 63 81 88—89 172 181 250—251 255
Broken line 55
Center(s) of a circle 133
Center(s) of inversion 263
Center(s) of regular polygon 154
Center(s) of similitude 127
Center(s) of symmetry 125 126
Center(s), line of 142
Chord 136—137
Chord, common 143
circle 15 133—160 223—225
Circle of inversion 263
Circle, area of 210—213 223—225
Circle, circumference of 15 208—213 223—225
Circle, circumscribed 138 181—182
Circle, inscribed 138 182—183
Circle, tangent 143
Circumscribed, circle 138 181—182
Circumscribed, polygon 138 195
clockwise 48 235—239
Collinear 125—128
Compasses 165—196
Conclusion 22 27
concurrent 126—128 255 256 259
Congruent 59 60 135 242
Construction(s) 165—196
Construction(s), general vs. special 33
Construction(s), incorrect 32
Construction(s), misleading 33
Construction(s), possible 165—166 170—172 189—190 194—195
continuous 229
Continuous variation 60 228—240 242
Continuous variation of a point 231
Continuous variation of a quantity 230
Continuous variation of an angle 231—234
Continuous variation of directed angles 234—238
Continuous variation of directed lengths 238—240
CONVERSE 26—29 88 246—248 249—251
Convex, closed curve 204 225—226
Convex, polygon 55
Cooerdinate (s) 119—123 242
Corollary 93
counter-clockwise 48 235—239
Deduction 273—277
Definition(s) 12—15 25 39 106 270 280 282
Definition(s) for area 198 199 222—226
Definition(s) for circle 133—135 208—213 223—225
Definition(s), listed in summaries 67—68 98—99 130—131 156 220—221
Degree(s) 46 49 50 52
Diagonal 4 61 97
Diameter 15 136
Directed, angle(s) 49 235—239
Directed, arc(s) 209 234—239
Directed, distance (s) 42—43 119 238—240
Distance (s) 38 39 41
Distance (s) from point to line 95
Distance (s), directed 42—43 119 238—240
Distance (s), perpendicular 95
Distance (s), to prove equal 99
Distance (s), unit of 40—42 199
Division of angle 165—166 168 170—172 189—190 194—195
Division of line segment 166—170 176—178 192
Division, external 116 260
Division, internal 116 260
End-point(s) 45
equal 39 105 285
Equal arcs 135
Equal circles 135
Equal triangles 59 80
Equation of circle 133
Equation of line 122—124
Equiangular polygons 85
Equiangular polygons, triangles 77
Equilateral polygons 85
Equilateral polygons, triangles 77
Euclid 4
Euler's theorem 219
EXIST 105 106 154 181 182 256
External division 116 260
External tangency 143—144 184—185
Factor of proportionality 57—59
Fallacy, geometric 32 280
Geometric figures 33 55 57
Geometry exemplifies logic 283
Golden section 192
Grade 53
hadamard 222
| Half-line(s) 45—49 53—54
Hypotenuse 85
Hypothesis 22 27
If and only if 28—29 88 246
If..., then... 22 27
Included, including 14 58
Incommensurable case 4 228—230
Indirect method 33—35
Induction 273—276
Inequality 34 94 95 231—234
Inscribed, angle 145
Inscribed, circle 138 182—183
Inscribed, polygon 138 190—194
intercept 141
Internal division 116 260
Internal tangency 143—144 184—185
intersect 45
Intersection of arcs 173
Intersection of line and circle 138
Intersection of two circles 142—143
Intersection of two lines 44—45
inversion 263—266
Isosceles 75—77
Language, artificial 280—283
Laws of number 38 94 284—288
Length(s) 41 198—226
Length(s) of arc 135 209 223
Length(s) of circle 15 208—213 223—225
Length(s), directed 42—43 119 238—240
Length(s), to prove equal 99
Length(s), unit of 40—42 199
Line(s) 38—40 44 55
Line(s) of centers 142
Line(s), broken 55
Line(s), equation of 122—124
Line(s), half- 45—49 53—54
Line(s), intersection of 44—45
Line(s), inverse of 264
Line(s), measure 40—44 198—226
Line(s), parallel 105—123 108 168 174—175
Line(s), perpendicular 50 54 74 89—90 105 106 107 168 172 178—180
Line(s), segment 44 166—170 176—178 192
Line(s), skew 130
Line(s), slope of 120—123
Line(s), straight 39
Line(s), symmetry with respect to 124—126
Locus, loci 242—266
Locus, loci of a point 243
Locus, loci of all points 243
Locus, loci, construction of 253
Locus, loci, contains isolated points 244
Locus, loci, defined 242 246
Locus, loci, plotting a 245 246
Locus, loci, points not included in 252 253
Locus, loci, proof of 246—248 251 254
Locus, loci, seven standard theorems 248—254
Logical chain 278—279
Logical deduction 273—277
Logical system 12 35—36 106 268—270 273—274 280—283
Logical terms 39 280—283 285
Maxima 218—219
Mean proportional 85 86 180
Measure 40—44 45—54 166—170 198—226 230
Method of the scientist 100 273 see "Induction" "Proof" "Reasoning"
Mid-point 20 23 44
Mid-point of arc 135
Mid-point of hypotenuse 101 257
Mid-point of line segment 20 44
MIL 53
Minima 218—219
Motion 59—60 242
Network 118—123 200 202—205 225—226
Non sequitur 29
Non-Euclidean geometries 277—278
NUMBER 38 39 58 60 242 279 285
Number, integer 228
Number, irrational 4 58 228—229
Number, laws of 38 94 284—288
Number, rational 58 228—229
Number, real 4 58 228—230
Oblique 95
One and only one 89—90 107
Opposite 246—247 249—251
Opposite converse 247 252
Optional topics 6
Order 39 285
Origin 118 122—124 133
Original 100
Parallel(s) 105—123 108 168 174—175
Parallel(s), postulate 106
Parallel(s), system of 108 110 111 118
Parallelogram 113 201
Perimeter of a polygon 66 210—212
Perpendicular(s) 50 54 74 89—90 105 106 107 168 172 178—180
Perpendicular(s), bisector 63 81 88—89 172 181 250—251 255
Perpendicular(s), distance 95
Perpendicular(s), foot of 95 263
Petitio principii 31
PI 212—213 223—224
Plane 39 128—130
Plane of symmetry 125
Point (s) 38—40 43—45 55
Point (s) of contact 138
Point (s) of intersection 45 138 143
Point (s) of tangency 138
Point (s), infinitude of 266
Point (s), inverse of 263
Point (s), power of 261—263
Point (s), symmetry with respect to 125 126
Polygon(s) 55
Polygon(s), angles of 55
Polygon(s), area of 203—204 222—226 279
Polygon(s), can be reproduced 59
Polygon(s), center of regular 154
Polygon(s), circumscribed 138 195
Polygon(s), convex 55
Polygon(s), diagonal of 61
Polygon(s), equiangular 85
Polygon(s), equilateral 85
Polygon(s), exterior angle of 87
Polygon(s), inscribed 138 190—194
Polygon(s), irregular 203 222—226
Polygon(s), perimeter of 66 210—212
Polygon(s), regular 85 133—159 170—172 190—196 210—212
Polygon(s), sides of 55
Polygon(s), similar 57 205—206
Polygon(s), vertices of 55
Postulate (s) 19 23 25 38 39 106 107 222 230 268—270 273—278 282—283
Postulate (s), concerning limits 212
Postulate (s), concerning number 284—288
Postulate (s), five fundamental 38—60 106 107 230
Postulate (s), parallel 106
Postulate (s), temporary 5 71 106 198 199 278—279
Power of a point 261—263
Principle(s), five fundamental 38—60
Principle(s), listed in summaries 67—68 98—99
Principle(s), numbering of 107
Projection 265—266
Proof of a locus 246—248 251 254
Proof, indirect method of 33—35
Proof, nature of geometric 20—23
Proportion 57—59 67
Proportion, algebraic treatment of 64—66
Proportion, continued 66
Proportion, laws of 65 66
Proportional 57
Proportional fourth 167 178
Proportional mean 85 86 180
Proposition (s) 17 18
Proposition (s), converse 26—29 88 246—248 249—251
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