Aristarchus of Samos: On the sizes and distances of the sun and moon: Greek text, translation, analysis, and relevant scholia
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| Other Authors: | , |
| Format: | Book |
| Language: | Ancient Greek English |
| Published: |
London ; New York
Routledge, Taylor & Francis Group
2023
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| Series: | Scientific writings from the ancient and medieval world
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvi, 307 Seiten Illustrationen, Diagramme 24 cm |
| ISBN: | 9781032026732 |
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| adam_text | Contents 1 List offigures Preface Acknowledgements xi xv xvii Preliminary study 1 Aristarchus ofSamos 1 The calculation of the distances and sizes of the Sun and the Moon from Antiquity to the early modern period 3 The values before Aristarchus 3 Aristarchus ’s calculation 4 Aristarchus ’s methods in Antiquity and the Middle Ages 10 The calculation of the distances and sizes in the early modern period 15 History of the text and introduction to the translation 20 History of the text and description of the editions 20 Our translation 38 2 Greek text and translation 3 Analysis of On the Sizes and Distances of the Sun and Moon Comprehension difficulties for a modern reader 182 The general structure of On Sizes 183 Analysis of the hypotheses 185 First hypothesis: that the Moon receives its light from the Sun 185 Second hypothesis: that the Earth has a ratio ofa point and a center with respect to the sphere of the Moon 186 44 182
viii Contents Third hypothesis: that when the Moon appears to us halved, the great circle delimiting the dark and the bright parts of the Moon is inclined to our eye 187 Fourth hypothesis: that when the Moon appears to us halved, its distance from the Sun is one quadrant minus one-thirtieth part ofa quadrant 190 Fifth hypothesis: that the width of the shadow (of the Earth) is two Moons 192 Sixth hypothesis: that the Moon subtends one-fifteenth part ofa sign of the zodiac 194 Observation and theory in obtaining the values of the hypotheses 196 Toward the ratio between the distances (propositions 1 to 7) 197 Conceptual introduction 197 Proposition 3 200 Proposition 4 202 Proposition 5 206 Proposition 6 206 Proposition 7 208 Introduction 208 Proposition 7a minimum limit 209 Proposition 7b maximum limit 212 Conclusion 215 Conclusion to this section 215 Towards the ratio between the sizes of the Sun and the Moon 215 Conceptual introduction 215 Proposition 8 216 Proposition 9 218 Proposition 10 219 The conclusion to this section 219 Towards the ratio between the sizes of the Sun and the Earth 219 Conceptual introduction 219 Unwanted simplifications 220 The reason for the first simplification: the radius of the base ofthe cone is not equal to the radius ofthe sphere 221 The reason for the second and third simplifications: the circle dividing the visible and the invisible parts of the Moon 221 Propositions 11 to 14: Aristarchus ’s calculations to avoid simplifications 227 Proposition 11 228 Proposition 12 231 Proposition 13 232
Contents ix Proposition 13a: the upper limit of the ratio between the shadow line and the lunar diameter 233 Proposition 13b: the upper limit of the ratio between the shadow line and a lunar diameter 234 Proposition 13c: the upper limit of the ratio between the shadow line and the diameter of the Sun 234 Proposition 13d: the lower limit of the ratio between the shadow line and the diameter of the Sun 235 Proposition 13e: the lower limit of the ratio between the shadow line and the base of the cone 235 Proposition 14 237 Proposition 15 240 Proposition 16 243 Conclusion to this section 243 Towards the ratio between the sizes of the Moon and the Earth 243 Introduction 243 Proposition 17 243 Proposition 18 244 Conclusion 244 4 Scholia General introduction 246 Scholion 3(5) 247 Scholion 5(4) 248 Scholion 13(8) 248 Scholion 14(9) 249 Scholion 19(11) 250 Scholion 21(13) 250 Scholion 32(16) 251 Scholion 37(18) 251 Scholion 45(23) 252 Scholion 47(30) 252 Scholion 50(27) 252 Scholion 52(28) 253 Scholion 54(29) 253 Scholion 59 254 Scholion 60(33) 254 Scholion 77(47) 254 Scholion 83 254 Scholion 99(66) 255 Translation of the scholia 25 7 246
x Contents Appendix 1: Mathematical tools Proto-trigonometric relationships 292 Geometrical theorem 1 292 Geometrical theorem 2 294 Geometrical theorem 3 294 Geometrical theorem 4 294 Operations with quotients 295 Appendix 2: List ofmanuscripts References Editions of On Sizes 298 General bibliography 299 292 297 298
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| adam_txt |
Contents 1 List offigures Preface Acknowledgements xi xv xvii Preliminary study 1 Aristarchus ofSamos 1 The calculation of the distances and sizes of the Sun and the Moon from Antiquity to the early modern period 3 The values before Aristarchus 3 Aristarchus ’s calculation 4 Aristarchus ’s methods in Antiquity and the Middle Ages 10 The calculation of the distances and sizes in the early modern period 15 History of the text and introduction to the translation 20 History of the text and description of the editions 20 Our translation 38 2 Greek text and translation 3 Analysis of On the Sizes and Distances of the Sun and Moon Comprehension difficulties for a modern reader 182 The general structure of On Sizes 183 Analysis of the hypotheses 185 First hypothesis: that the Moon receives its light from the Sun 185 Second hypothesis: that the Earth has a ratio ofa point and a center with respect to the sphere of the Moon 186 44 182
viii Contents Third hypothesis: that when the Moon appears to us halved, the great circle delimiting the dark and the bright parts of the Moon is inclined to our eye 187 Fourth hypothesis: that when the Moon appears to us halved, its distance from the Sun is one quadrant minus one-thirtieth part ofa quadrant 190 Fifth hypothesis: that the width of the shadow (of the Earth) is two Moons 192 Sixth hypothesis: that the Moon subtends one-fifteenth part ofa sign of the zodiac 194 Observation and theory in obtaining the values of the hypotheses 196 Toward the ratio between the distances (propositions 1 to 7) 197 Conceptual introduction 197 Proposition 3 200 Proposition 4 202 Proposition 5 206 Proposition 6 206 Proposition 7 208 Introduction 208 Proposition 7a minimum limit 209 Proposition 7b maximum limit 212 Conclusion 215 Conclusion to this section 215 Towards the ratio between the sizes of the Sun and the Moon 215 Conceptual introduction 215 Proposition 8 216 Proposition 9 218 Proposition 10 219 The conclusion to this section 219 Towards the ratio between the sizes of the Sun and the Earth 219 Conceptual introduction 219 Unwanted simplifications 220 The reason for the first simplification: the radius of the base ofthe cone is not equal to the radius ofthe sphere 221 The reason for the second and third simplifications: the circle dividing the visible and the invisible parts of the Moon 221 Propositions 11 to 14: Aristarchus ’s calculations to avoid simplifications 227 Proposition 11 228 Proposition 12 231 Proposition 13 232
Contents ix Proposition 13a: the upper limit of the ratio between the shadow line and the lunar diameter 233 Proposition 13b: the upper limit of the ratio between the shadow line and a lunar diameter 234 Proposition 13c: the upper limit of the ratio between the shadow line and the diameter of the Sun 234 Proposition 13d: the lower limit of the ratio between the shadow line and the diameter of the Sun 235 Proposition 13e: the lower limit of the ratio between the shadow line and the base of the cone 235 Proposition 14 237 Proposition 15 240 Proposition 16 243 Conclusion to this section 243 Towards the ratio between the sizes of the Moon and the Earth 243 Introduction 243 Proposition 17 243 Proposition 18 244 Conclusion 244 4 Scholia General introduction 246 Scholion 3(5) 247 Scholion 5(4) 248 Scholion 13(8) 248 Scholion 14(9) 249 Scholion 19(11) 250 Scholion 21(13) 250 Scholion 32(16) 251 Scholion 37(18) 251 Scholion 45(23) 252 Scholion 47(30) 252 Scholion 50(27) 252 Scholion 52(28) 253 Scholion 54(29) 253 Scholion 59 254 Scholion 60(33) 254 Scholion 77(47) 254 Scholion 83 254 Scholion 99(66) 255 Translation of the scholia 25 7 246
x Contents Appendix 1: Mathematical tools Proto-trigonometric relationships 292 Geometrical theorem 1 292 Geometrical theorem 2 294 Geometrical theorem 3 294 Geometrical theorem 4 294 Operations with quotients 295 Appendix 2: List ofmanuscripts References Editions of On Sizes 298 General bibliography 299 292 297 298 |
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| spelling | Aristarchus Samius v310-v230 Verfasser (DE-588)118645714 aut (DE-588)4312889-0 De magnitudinibus et distantiis solis et lunae Aristarchus of Samos: On the sizes and distances of the sun and moon Greek text, translation, analysis, and relevant scholia edited and translated by Christián C. Carman and Rodolfo P. Buzón On the sizes and distances of the sun and moon London ; New York Routledge, Taylor & Francis Group 2023 xvi, 307 Seiten Illustrationen, Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Scientific writings from the ancient and medieval world Original Greek text with English translation Aristarchus Samius v310-v230 De magnitudinibus et distantiis solis et lunae (DE-588)4312889-0 gnd rswk-swf Astronomy, Greek / Early works to 1800 Astronomy, Greek Early works Aristarc / de Samos / aproximadament 310 aC-aproximadament 230 aC. Astronomia antiga Aristarchus Samius TLG 1181 (DE-2581)TH000000293 gbd Astronomie (DE-2581)TH000007322 gbd Mond (DE-2581)TH000007323 gbd Aristarchus Samius v310-v230 De magnitudinibus et distantiis solis et lunae (DE-588)4312889-0 u DE-604 Carman, Christián C. (DE-588)1307253067 edt trl Buzón, Rodolfo 1942- (DE-588)1307253512 edt trl Äquivalent Druck-Ausgabe, Paperback 978-1-03-202676-3 Erscheint auch als Online-Ausgabe 978-1-00-086992-7 Digitalisierung BSB München - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034570586&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aristarchus Samius v310-v230 Aristarchus of Samos: On the sizes and distances of the sun and moon Greek text, translation, analysis, and relevant scholia Aristarchus Samius v310-v230 De magnitudinibus et distantiis solis et lunae (DE-588)4312889-0 gnd |
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| title | Aristarchus of Samos: On the sizes and distances of the sun and moon Greek text, translation, analysis, and relevant scholia |
| title_GND | (DE-588)4312889-0 |
| title_alt | De magnitudinibus et distantiis solis et lunae On the sizes and distances of the sun and moon |
| title_auth | Aristarchus of Samos: On the sizes and distances of the sun and moon Greek text, translation, analysis, and relevant scholia |
| title_exact_search | Aristarchus of Samos: On the sizes and distances of the sun and moon Greek text, translation, analysis, and relevant scholia |
| title_exact_search_txtP | Aristarchus of Samos: On the sizes and distances of the sun and moon Greek text, translation, analysis, and relevant scholia |
| title_full | Aristarchus of Samos: On the sizes and distances of the sun and moon Greek text, translation, analysis, and relevant scholia edited and translated by Christián C. Carman and Rodolfo P. Buzón |
| title_fullStr | Aristarchus of Samos: On the sizes and distances of the sun and moon Greek text, translation, analysis, and relevant scholia edited and translated by Christián C. Carman and Rodolfo P. Buzón |
| title_full_unstemmed | Aristarchus of Samos: On the sizes and distances of the sun and moon Greek text, translation, analysis, and relevant scholia edited and translated by Christián C. Carman and Rodolfo P. Buzón |
| title_short | Aristarchus of Samos: On the sizes and distances of the sun and moon |
| title_sort | aristarchus of samos on the sizes and distances of the sun and moon greek text translation analysis and relevant scholia |
| title_sub | Greek text, translation, analysis, and relevant scholia |
| topic | Aristarchus Samius v310-v230 De magnitudinibus et distantiis solis et lunae (DE-588)4312889-0 gnd |
| topic_facet | Aristarchus Samius v310-v230 De magnitudinibus et distantiis solis et lunae |
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