# Non-Euclidean Geometry

Cosimo, Inc., May 1, 2007 - Mathematics - 288 pages
"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 Copyright

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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.