Continuous Symmetry: From Euclid to Klein

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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
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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.

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