Non-Euclidean Geometry

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Cosimo, Inc., May 1, 2007 - Mathematics - 288 pages
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"Non-Euclidean Geometry is a history of the alternate geometries that have emerged since the rejection of Euclid s parallel postulate. Italian mathematician ROBERTO BONOLA (1874 1911) begins by surveying efforts by Greek, Arab, and Renaissance mathematicians to close the gap in Euclid s axiom. Then, starting with the 17th century, as mathematicians began to question whether it was actually possible to prove Euclid s postulate, he examines non-Euclidean predecessors Saccheri, Lambert, Legendre, W. Bolyai, Wachter, and Thibaut, and non-Euclidean founders Gauss, Schweikart, Taurinus, Lobachevski, and J. Bolyai. He concludes with a look at later developments in non-Euclidean geometry. Including five appendices and an index of authors, Bonola s Non-Euclidean Geometry is a useful reference guide for students of mathematical history."
 

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Contents

I
1
II
9
III
12
IV
22
V
44
VI
51
VII
55
VIII
60
XXVII
176
XXVIII
177
XXIX
181
XXX
184
XXXI
192
XXXII
195
XXXIII
200
XXXIV
206

IX
62
X
63
XI
64
XII
75
XIII
77
XIV
84
XV
96
XVI
113
XVII
118
XVIII
121
XIX
129
XX
130
XXI
139
XXII
151
XXIII
152
XXIV
154
XXV
164
XXVI
175
XXXV
211
XXXVI
216
XXXVII
222
XXXVIII
223
XXXIX
224
XLI
227
XLII
228
XLIII
229
XLV
231
XLVI
233
XLVII
234
XLVIII
236
XLIX
238
L
239
LI
250
LII
265
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Page 1 - That, if a straight line falling on two straight lines make 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.

References to this book

The Shape of Space
Graham Nerlich
Limited preview - 1994
Hyperbolic Geometry
James Anderson
Limited preview - 2005
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