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Talk:Saccheri quadrilateral

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84: 74: 53: 22: 243:(in which you need to toss out both Euclid's second and fifth postulates) it can be shown that the summit angles of a Saccheri quadrilateral are obtuse. This is what the article is saying without mentioning the additional modifications needed to make the statement true. So, the answer to your question is, they both are ... but under different sets of assumptions. 239:, leads to a contradiction. Both Saccheri and Omar Khayyam were able to show this, so they talk about rejecting the assumption of the obtuse angle. When properly phrased this contradiction can be turned into a proof of the parallel postulate. This is what Kline and Coxeter are talking about. On the other hand, in 265:
According to Cooke's history of math text, Jeremy Gray calls this a Thabit quadrilateral and that it thus predates Khayyam by a few centuries. If so, perhaps some Knowledge guru could fix that; I am not familiar enough with the editing protocol and syntax to do so myself without spending more time
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I can see why you are confused. The article is not being precise enough to clarify this. The assumption of the obtuse angle,
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This new page is to direct article text links of "Saccheri quadrilateral" to the "Saccheri Quadrilateral" article.
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This article claims that in the case of obtuse angle, the quadrilateral leads to elliptical geometry, but both
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than I can devote to it. But it would be good to have the right people attributed to this concept.
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on Knowledge. If you would like to participate, please visit the project page, where you can join
248: 89: 73: 52: 218:) state (without proof) that this case leads to accept the fifth postulate. Which is correct?-- 240: 223: 212: 169: 204: 290: 244: 219: 196: 281: 252: 227: 173: 165: 102: 79: 183:
Capitalization matters in Wiki article links... perhaps to be considered a
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in the presence of the first four Euclidean postulates
101:, a collaborative effort to improve the coverage of 201:Mathematical Thought From Ancient to Modern Times 8: 19: 267: 47: 49: 7: 95:This article is within the scope of 38:It is of interest to the following 14: 302:Low-priority mathematics articles 115:Knowledge:WikiProject Mathematics 297:Start-Class mathematics articles 118:Template:WikiProject Mathematics 82: 72: 51: 20: 135:This article has been rated as 164:Added title. —Nils von Barth ( 1: 109:and see a list of open tasks. 282:13:58, 29 October 2019 (UTC) 318: 253:06:43, 10 April 2012 (UTC) 174:21:33, 19 April 2009 (UTC) 228:22:10, 9 April 2012 (UTC) 134: 67: 46: 141:project's priority scale 191:in case of obtuse angle 98:WikiProject Mathematics 209:Non-Euclidean Geometry 28:This article is rated 203:, chapter XXXVI) and 121:mathematics articles 90:Mathematics portal 34:content assessment 284: 272:comment added by 241:elliptic geometry 176: 155: 154: 151: 150: 147: 146: 309: 245:Bill Cherowitzo 211:, 1999, page 5, 163: 123: 122: 119: 116: 113: 92: 87: 86: 76: 69: 68: 63: 55: 48: 31: 25: 24: 16: 317: 316: 312: 311: 310: 308: 307: 306: 287: 286: 263: 193: 160: 120: 117: 114: 111: 110: 88: 81: 61: 32:on Knowledge's 29: 12: 11: 5: 315: 313: 305: 304: 299: 289: 288: 274:50.227.112.182 262: 259: 258: 257: 256: 255: 216:978-0883855225 205:H.S.M. Coxeter 192: 189: 178: 177: 159: 156: 153: 152: 149: 148: 145: 144: 133: 127: 126: 124: 107:the discussion 94: 93: 77: 65: 64: 56: 44: 43: 37: 26: 13: 10: 9: 6: 4: 3: 2: 314: 303: 300: 298: 295: 294: 292: 285: 283: 279: 275: 271: 260: 254: 250: 246: 242: 238: 234: 233: 232: 231: 230: 229: 225: 221: 217: 214: 210: 206: 202: 198: 190: 188: 186: 181: 175: 171: 167: 162: 161: 157: 142: 138: 132: 129: 128: 125: 108: 104: 100: 99: 91: 85: 80: 78: 75: 71: 70: 66: 60: 57: 54: 50: 45: 41: 35: 27: 23: 18: 17: 268:— Preceding 264: 236: 208: 200: 197:Morris Kline 194: 184: 182: 179: 137:Low-priority 136: 96: 62:Low‑priority 40:WikiProjects 112:Mathematics 103:mathematics 59:Mathematics 30:Start-class 291:Categories 158:(redirect) 261:Ibn Qurra 270:unsigned 185:Wikiflaw 220:Nickanc 139:on the 166:nbarth 36:scale. 278:talk 249:talk 224:talk 213:ISBN 170:talk 168:) ( 131:Low 293:: 280:) 251:) 226:) 187:. 172:) 276:( 247:( 222:( 207:( 199:( 143:. 42::

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content assessment
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Mathematics
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icon
Mathematics portal
WikiProject Mathematics
mathematics
the discussion
Low
project's priority scale
nbarth
talk
21:33, 19 April 2009 (UTC)
Morris Kline
H.S.M. Coxeter
ISBN
978-0883855225
Nickanc
talk
22:10, 9 April 2012 (UTC)
elliptic geometry
Bill Cherowitzo
talk
06:43, 10 April 2012 (UTC)
unsigned
50.227.112.182
talk

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