# Continuous Symmetry: From Euclid to Klein

American Mathematical Soc. - Mathematics - 546 pages
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"This text is for a one-semester undergraduate course on geometry. It is richly illustrated and contains hundreds of exercises."--BOOK JACKET.

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### Contents

 IV 1 VI 6 VII 17 VIII 22 IX 27 X 34 XI 46 XII 56
 XXXVI 235 XXXVII 240 XXXVIII 251 XL 256 XLI 266 XLII 276 XLIII 287 XLIV 292

 XIII 62 XIV 70 XV 84 XVI 94 XVII 110 XVIII 115 XIX 119 XX 121 XXI 135 XXII 146 XXIII 156 XXIV 161 XXV 165 XXVII 181 XXVIII 188 XXIX 191 XXX 199 XXXI 206 XXXII 211 XXXIII 217 XXXIV 224 XXXV 231
 XLV 298 XLVI 309 XLVII 315 XLVIII 322 XLIX 340 L 347 LII 356 LIII 363 LIV 375 LV 376 LVI 399 LVII 416 LVIII 439 LIX 459 LXI 467 LXII 482 LXIII 487 LXIV 505 LXV 520 LXVI 531 LXVII 533 Copyright

### Popular passages

Page xiii - That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Page 58 - The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Page 48 - The SAS Postulate: Given a correspondence between two triangles (or between a triangle and itself). If two sides and the included angle of the first triangle are congruent to the corresponding parts of the second triangle, then the correspondence is a congruence.
Page 4 - the best way to explain it is to do it." (And, as you might like to try the thing yourself some winter day, I will tell you how the Dodo managed it.) First it marked out a race-course, in a sort of circle, ("the exact shape doesn't matter," it said,) and then all the party were placed along the course, here and there. There was no "One, two...
Page 61 - If two sides of one triangle are equal to two sides of a second triangle and the included angle of the first is greater than the included angle of the second, then the third side of the first triangle is greater than the third side of the second.
Page 294 - A median of a triangle is a line which joins a vertex of the triangle to the midpoint of the opposite side. Let ABC be any triangle, and let a, b and c be position vectors, of A, B and C relative to some fixed origin.
Page 114 - The radius of a circle is a line segment from the center of the circle to a point on the circle.
Page 48 - If two sides of a triangle are congruent, then the angles opposite these sides are congruent.
Page 68 - The sum of the measures of the interior angles of any triangle is 180°.
Page 120 - Suppose a correspondence between two triangles is such that two sides and the included angle of the first triangle are congruent to the corresponding parts of the second triangle.