A commentary upon Bīruni's Kitāb tahdīd al-amākin: an 11th century treatise on mathematical geography
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| Format: | Buch |
| Sprache: | English |
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Beirut
American Univ. of Beirut
1973
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 270 S. graph. Darst. |
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| 245 | 1 | 0 | |a A commentary upon Bīruni's Kitāb tahdīd al-amākin |b an 11th century treatise on mathematical geography |c by E. S. Kennedy |
| 264 | 1 | |a Beirut |b American Univ. of Beirut |c 1973 | |
| 300 | |a XX, 270 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 600 | 1 | 4 | |a Bīrūnī, Muḥammad ibn Aḥmad <973?-1048> |t Taḥdīd nihāyāt al-amākin |
| 650 | 4 | |a Naturwissenschaft | |
| 650 | 4 | |a Science |v Early works to 1800 | |
| 650 | 4 | |a Spherical astronomy |v Early works to 1800 | |
| 700 | 1 | |a Bīrūnī, Abu-'r-Raiḥān Muḥammad Ibn-Aḥmad al- |d 973-1048 |e Sonstige |0 (DE-588)118511327 |4 oth | |
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| 940 | 1 | |q TUB-nveb | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009094765 | ||
Datensatz im Suchindex
| _version_ | 1804128110612840448 |
|---|---|
| adam_text | A COMMENTARY UPON BIRUNI S
KITAB TAHDID AL-AMAKIN
An 11th Century Treatise on Mathematical Geography
by
E S KENNEDY
American University of Beirut
Beirut, Lebanon
CONTENTS Pag
Preface x v
List of Symbols amp; Conventions xvii
Transcription of Arabic Letters on Geometric Figures xx
CHAPTER I INTRODUCTORY
1 Generalities (22:1-33:4) 1
2 Adventures of a Pilot in the China Trade (33:5 - 35:4) 2
3 First Remarks on the Qibla (35:4 - 38:19) 3
4 The Creation, Geological Change, Fossils (38:13 - 44:8) 4
5 Abu al- Abbas al-Iranshahrl (43:6, 51:4) 5
6 The Dam of Ma rib (44:9 14) 5
7 The Oxus and the Caspian (44:15 - 47:13) 6
8 Places and Peoples (44:15 - 47:13) 7
9 Earthquakes and Floods (48:1 - 49:4) • 8
10 The Ancient Nile - Red Sea Canal (49:5 - 12) 9
11 Deserts and Ancient Remains (50:11 - 55:2) 10
12 The Situation of the Southern Hemisphere (55:3 - 58:23) 11
13 Zones Permitting Habitation (51:1 - 62:13) 12
Figures A and B 14
CHAPTER II TERRESTRIAL LATITUDE A amp; LATITUDE
14 Determination of Local Latitude by Observing a Never-
Setting Star (63:1 - 65:1, 67:5-18) 16
15 Application by the Banu Musa: the Latitude of Baghdad
(66:1 - 67:5) 16
Figure Cl 17
16 Three Techniques for Determining Local Latitude when the
Observed Day-Circle Intersects the Horizon (68:1 - 72:13) 18
Figure C3 19
Figure C3A 21
17 Latitude from Two Solar Observations, Worked Examples
for Jurjaniya (72:13 - 82:9) 22
Figure C4 23
Figure C5 25
Figure C6 28
18 Difference in the Latitudes of Two Localities from Meridian
Altitudes, Three Examples (82:10 - 87:14) 29
vii
CHAPTER III OBLIQUITY OF THE ECLIPTIC
19 P to lemy s Determinat ion 88:1 - 89:21)
20 Yahya and Khalid at Baghdad and Damscus (89:22 - 91:12)
21 Reduction of the Damascus Observat ions (91:13 - 94:10)
Figure C9
Figure CIO
22 Observat ions at Samarra, Baghdad, and Raqqa (94:11 - 96:2)
23 Observat ions at Balkh, Marv, and Rayy (96:3 - 99:4)
24 Observat ions at Shiraz and Baghdad (99:5 - 100:16)
25 Al-Kuhl at Baghdad (100:17 - 101:19)
26 The Fakhr i Sextant at Rayy (101:20 - 102:10)
27 Reduction of al-Khujandi s Observat ions (102:11 - 107:6)
F igure C l l
F igure C12
28 Bi run l s Discussion of the Accident Which Befell the
Fakhri Sextant (107:7:7 - 109:3) • 48
29 BiruniTs Own Determinat ions of the Obliquity (109:4 - 111:14X 49
30 The Effect of Parallax (112:7 - 115:13) 51
Figure C15 52
31 Conclusions (116:1 - 116:14) 53
Figure Cl 6 5 3
CHAPTER IV RELATIONSHIPS BETWEEN 9,e, AND 6
32 Relations Between Meridian Solar Altitude, Declination,
and Local Latitude (117:1 - 121:9) 54
33 The Relation Between Declination, an Altitude of Azimuth
Zero , and the Local Latitude (121:10 - 122:12) 55
Figure C18 56
34 Relations Between Local Latitude, Declination, Altitude, and
Azimuth (122:13 - 127:8) 57
Figure C19 1 58
Figure C19 2 5 9
Figure C19 3 60
Figure C20 1 63
35 Solar Declination from Two Azimuths and Altitudes
(121:1-14) 64
Figure C21 65
36 A Worked Example of the Above (129:1-16) 66
37 Latitude of Jurjaniya from Symmetrically Disposed Meridian
Altitudes (129:10 - 130:12) 67
Figure C21 1 68
38 An Instrument for Local Latitude (130:13 - 131:14) 69
39 Relations Between Latitude, Solar Declination, Rising
Amplitude, and Daylight Length (] 31:15 - 133:19) 70
Figure C21 2 70
Figure C22 71
40 The Seven Iranian Keshvars (134:1 - 135:15) 73
41 Localities in the First and Fourth Keshvars (136) 75
42 Localities in the Fifth, Sixth, and Seventh Keshvars (136) 75
43 The Arctic and the Tropical Regions (135:16 - 138:12) 76
44 The Table of Climate Bounds and Its Calculation (138:13-141) 77
Figure C24
7g
45 The Surrounding Sea (142:1 - 145:10) 81
46 Daylight and Night in the Polar Regions (145:1 - 146:12) 82
47 The Methods of Ibn al-Sabbah and Abu Nasr Mansur for
Finding the Obliquity of the Ecliptic (146:13 - 155:7) 82
Figure C26 85
Figure C27 89
CHAPTER V ON THE DETERMINATION OF LONGITUDINAL DIFFERENC
48 Base Meridians (156:1 - 158:8) 91
Figure C28 92
49 Sunrise Time, Localities on the Same Meridian
(158:9-160:7) 93
50 Sunrise Difference, Localities Having the Same Latitude
(160:8 - 162:13) 93
Figure C29 94
51 Sunrise Difference, Both Coordinates Different (1 63:1-1 65: If 96
Figure C30 97
Figure C30 1 99
52 Longitude Determination from Eclipses (1 66:1 - 169:9) 100
53 A Digression on Combinatorial Analysis (169:10 - 170:14) 101
54 A Lunar Eclipse Observed from Two Localities, Both
Times with Respect to the Local Meridians
(170:15 - 174:1) 103
Figure C31 104
55 Times Observed From One Meridian and the Other Horizon
(174:2 -179:1) 105
Figure C36 106
56 Times Observed from the Two Horizons (179:2 - 185:11) 107
Figure C40 108
Figure C44 110
57 Another Digression, on the Muctazila (185:12 - 186:16) I l l
58 Various Remarks Concerning Lunar Eclipses
(186:17 - 190:17) 112
59 Time Determination from a Star s Altitude
(190:18 - 193:3) 113
Figure C47 114
60 Time Determination from a Star s Azimuth (193:4 - 194:20) 115
• Figure C48 116
61 Time Determination from a Star s Altitude and Azimuth
(195:1 - 196:6) 118
62 Solar Longitude at the Time of the Eclipse (196:7 - 196:12) 118
63 Spherical-Astronomical Nomenclature (196:13 - 198:20) 119
Figure C49 120
64 Ecliptic Degree of Culmination (199:1 - 200:11) 122
Figure C50 123
65 Avicenna Determines the Longitude of Gurgan
(201:1 - 203:9) 124
66 Al-Hashimi Determines the Longitude of Raqqa 125
(203:10 - 204:12)
67 A Rule from al-Sarakhsi1 s Zij (204:13 - 206:7) 126
Figure C51 127
68 Distance and Azimuth from the Coordinates of Two
Localities (206:8 - 211:1) 128
Figure C52 129
69 Length of a Degree Along a Meridian (211:2 - 215:6) 131
Table 2: Sexagesimal Conversion Table from Farsakhs 134
and Miles to Degrees Along the Meridian
70 Length of a Degree Along an Oblique Great Circle (218:1-18) 136
71 Radius of the Earth by Observation from a Mountain
(218:19 - 221:2) 137
Figure C53 138
72 Finding the Height of a Mountain (221:3 - 222:9) 140
Figure C55 141
Figure C56 142
73 Biruni s Observation at Nandana; Announcement of the
Final Objective (222:10 - 226:9) 143
CHAPTER VI RELATIONS BETWEEN DISTANCES, LONGITUDES, AND
LATITUDES
74 Great Circle Distances and Geographical Coordinates
(227:3 - 228:9) 1 4 4
Figure C56 1 145
Figure C57 _ 146
75 Indian Rules and Birunl s Critique (228:10 - 234:11) 146
Figure C58 149
Figure C60 150
76 Great Circle vs Road Distance, Mecca to Baghdad
(234:12 - 235:18) 151
CHAPTER VII THE MAIN LONGITUDE COMPUTATION - THE NORTHERN
TRAVERSE
77 The Longitude Difference Between Baghdad and Rayy
(236:1 - 239:11) 152
78 Longitude Difference Between Rayy and Jurjaniya
(240:1-14) 153
79 The Longitude of Jurjan from the Coordinates of Rayy
and Jurjaniya (241:1 - 245:5) 154
Figure C62 155
80 The Longitude Difference Between Bushkanz and Jurjaniya
(246:1-15) 158
81 Azimuth Difference at Jurjaniya Between Kath and
Bushkanz (246:16 - 247:19) 159
Figure C63 160
82 The Azimuth of Bushkanz from Jurjaniya (248:1-12) 1 61
83 Calculation of the Latitude of Kath (248:13 - 249:11) 162
84 The Longitude Difference Between Kath and Jurjaniya
(249:12 - 250:19) 164
85 The Longitude Difference Between Jurjaniya and Balkh
(251:1 - 252:11) 165
86 The Coordinates of Darghan from those of Jurjaniya and Balkh
(253:1 - 255:11) 166
Figure C64 167
Figure C64 1 170
87 The Coordinates of Amuya from those of Balkh and
Jurjaniya (256:1-16) 171
88 The Azimuth Difference of Amuya and Bukhara from Darghan
(257:1-17) 172
Figure C63 1 173
89 The Azimuth of Amuya from Darghan (258:1-12) 175
90 Calculation of the Latitude of Bukhara (258:13 - 259:4) 176
91 Calculation of the Longitude of Bukhara (259:5-18) 177
92 The Distance Between Balkh and Bukhara Calculated
(260:1 - 261:2) 178
93 The Coordinates of Nlshapur (261:3 - 263:18) 179
CHAPTER VIII THE SOUTHERN TRAVERSE
94 The Longitude Difference Between Baghdad and Shiraz
(263:19 - 264:11) 182
95 The Longitude Difference Between Shiraz and Zaranj
(264:12 - 266:5) 183
96 The Longitude Difference Between Balkh and Ghazna
(266:6 - 267:9) 185
97 The Longitude Difference Between Zaranj and Bust
(267:10 - 269:10) 186
98 The Longitude Difference Between Bust and Ghazna
(265:11 - 266:5) 188
99 The Longitude Difference Between Zaranj and Ghazna
(270:6 - 271:12) 189
100 The Coordinates of Bust Calculated from those of Ghazna
and Zaranj (271:13 - 272:16) 190
Figure C64 2 191
101 The Ghazna Longitude Calculated in the Canon 195
102 Critique of the Main Determination 196
CHAPTER IX CALCULATIONS OF THE QIBLA OF GHAZNA
103 The First Method (272:17 - 275:11) 198
Figure C65 199
104 The Second Method (276:1 - 279:8) 202
Figure C66 203
105 The Third Method (279:9 - 287:13) 206
Figure C67 207
106 An Analemma Construction for the Qibla (284:1-9) 209
Figure C67 1 210
107 The Third Computational Method (284:10 - 286:1) 211
Figure C68 212
108 Rational Approximations to the Qibla of Ghazna - Evaluatio
of the Results (286:2-12) 214
109 Graphical Determination of the Meridian (286:13 - 290:13) 216
Figure C70 217
Figure C70 1 218
CHAPTER X MORE LONGITUDE COMPUTATIONS;
EQUINOX OBSERVATIONS
110 Two Eclipse Observations (290:14 - 292:5) 220
111 The Longitude Difference Between Baghdad and Raqqa
(292:6 - 294:23) 221
112 The Longitude Difference Between Raqqa and Alexandria
(295:1 - 296:4) 224
113 Local Time Differences (296:5-18) 225
114 Autumnal Equinox Observations (297:1 - 302:15) 226
CHAPTER XI TOPICAL SUMMARIES
115 Computational Technique in the Tahdid 229
116 Trigonometry in the Tahdid 230
117 Calendrical Remarks 232
Bibliography 234
General Index 274
Index of Sexagesimal Parameters 264
Index of Decimal Numbers, Dates _ 267
Misprints in the English Translation of the Tahdid 269
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| language | English |
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| spelling | Kennedy, Edward S. 1912-2009 Verfasser (DE-588)122809238 aut A commentary upon Bīruni's Kitāb tahdīd al-amākin an 11th century treatise on mathematical geography by E. S. Kennedy Beirut American Univ. of Beirut 1973 XX, 270 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bīrūnī, Muḥammad ibn Aḥmad <973?-1048> Taḥdīd nihāyāt al-amākin Naturwissenschaft Science Early works to 1800 Spherical astronomy Early works to 1800 Bīrūnī, Abu-'r-Raiḥān Muḥammad Ibn-Aḥmad al- 973-1048 Sonstige (DE-588)118511327 oth HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009094765&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kennedy, Edward S. 1912-2009 A commentary upon Bīruni's Kitāb tahdīd al-amākin an 11th century treatise on mathematical geography Bīrūnī, Muḥammad ibn Aḥmad <973?-1048> Taḥdīd nihāyāt al-amākin Naturwissenschaft Science Early works to 1800 Spherical astronomy Early works to 1800 |
| title | A commentary upon Bīruni's Kitāb tahdīd al-amākin an 11th century treatise on mathematical geography |
| title_auth | A commentary upon Bīruni's Kitāb tahdīd al-amākin an 11th century treatise on mathematical geography |
| title_exact_search | A commentary upon Bīruni's Kitāb tahdīd al-amākin an 11th century treatise on mathematical geography |
| title_full | A commentary upon Bīruni's Kitāb tahdīd al-amākin an 11th century treatise on mathematical geography by E. S. Kennedy |
| title_fullStr | A commentary upon Bīruni's Kitāb tahdīd al-amākin an 11th century treatise on mathematical geography by E. S. Kennedy |
| title_full_unstemmed | A commentary upon Bīruni's Kitāb tahdīd al-amākin an 11th century treatise on mathematical geography by E. S. Kennedy |
| title_short | A commentary upon Bīruni's Kitāb tahdīd al-amākin |
| title_sort | a commentary upon biruni s kitab tahdid al amakin an 11th century treatise on mathematical geography |
| title_sub | an 11th century treatise on mathematical geography |
| topic | Bīrūnī, Muḥammad ibn Aḥmad <973?-1048> Taḥdīd nihāyāt al-amākin Naturwissenschaft Science Early works to 1800 Spherical astronomy Early works to 1800 |
| topic_facet | Bīrūnī, Muḥammad ibn Aḥmad <973?-1048> Taḥdīd nihāyāt al-amākin Naturwissenschaft Science Early works to 1800 Spherical astronomy Early works to 1800 |
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