Preface |
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xi | |
About the author |
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xv | |
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1 | (18) |
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2 | (7) |
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9 | (4) |
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13 | (3) |
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16 | (1) |
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17 | (2) |
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19 | (34) |
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Geometry as applied mathematics |
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20 | (3) |
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23 | (3) |
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26 | (3) |
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29 | (4) |
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33 | (2) |
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35 | (2) |
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37 | (2) |
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39 | (3) |
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Geometry as pure mathematics |
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42 | (8) |
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50 | (3) |
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Elementary Euclidean geometry |
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53 | (74) |
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55 | (2) |
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Ruler axiom and its consequences |
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57 | (3) |
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Pasch's axiom and the separation theorems |
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60 | (4) |
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Angles and the protractor axioms |
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64 | (3) |
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67 | (4) |
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71 | (5) |
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Parallel axiom and related theorems |
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76 | (5) |
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Area and Pythagoras' theorem |
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81 | (8) |
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89 | (3) |
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92 | (8) |
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100 | (6) |
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106 | (4) |
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Arcs and trigonometric functions |
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110 | (9) |
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119 | (8) |
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Exercises on elementary geometry |
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127 | (30) |
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Exercises on the incidence and ruler axioms |
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128 | (2) |
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Exercises related to Pasch's axiom |
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130 | (3) |
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Exercises on congruence and perpendicularity |
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133 | (2) |
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Exercises involving the parallel axiom |
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135 | (2) |
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Exercises on similarity and Pythagoras' theorem |
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137 | (3) |
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Exercises on circles and spheres, part 1 |
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140 | (3) |
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143 | (3) |
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146 | (2) |
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Exercises on circles and spheres, part 2 |
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148 | (3) |
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Exercises on coordinate geometry |
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151 | (6) |
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Some triangle and circle geometry |
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157 | (70) |
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Four concurrence theorems |
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158 | (4) |
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162 | (3) |
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165 | (6) |
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171 | (6) |
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177 | (9) |
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186 | (7) |
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193 | (3) |
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196 | (3) |
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199 | (5) |
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Euler line and Feuerbach circle |
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204 | (7) |
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211 | (16) |
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Plane isometries and similarities |
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227 | (68) |
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232 | (8) |
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240 | (7) |
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247 | (4) |
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251 | (3) |
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254 | (4) |
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258 | (3) |
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261 | (1) |
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Isometries and orthogonal matrices |
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262 | (5) |
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267 | (9) |
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276 | (5) |
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281 | (14) |
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Three dimensional isometries and similarities |
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295 | (32) |
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296 | (6) |
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302 | (4) |
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Translations and rotations |
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306 | (3) |
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Glide and rotary reflections |
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309 | (3) |
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312 | (3) |
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315 | (2) |
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317 | (10) |
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327 | (96) |
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336 | (8) |
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344 | (11) |
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355 | (26) |
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381 | (26) |
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407 | (16) |
Appendix A Equivalence relations |
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423 | (2) |
Appendix B Least upper bound principle |
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425 | (4) |
Appendix C Vector and matrix algebra |
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429 | (14) |
Bibliography |
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443 | (20) |
Index |
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463 | |