| Title | Simplicius’s Proof of Euclid’s Parallels Postulate |
| Type | Article |
| Language | English |
| Date | 1969 |
| Journal | Journal of the Warburg and Courtauld Institutes |
| Volume | 32 |
| Pages | 1-24 |
| Categories | no categories |
| Author(s) | Sabra, A. I. |
| Editor(s) | |
| Translator(s) |
| A commentary by Simplicius on the premisses to Book I of Euclid’s Elements survives in an Arabic translation of which the author and the exact date of execution are unknown. The translation is reproduced by the ninth-century mathematician al-Fadl ibn Hâtim al-Nayrïzï in the course of his own com mentary on the Elements. Of Nayrïzî’s commentary, which is based on the earlier translation of the Elements by al-Hajjâj ibn Yûsuf ibn Matar, we have only one manuscript copy at Leiden and Gerard of Cremona’s Latin trans lation, both of which have been published.1The passages quoted by Nayrïzï, owing to their extensiveness and con secutive order, would strongly lead one to assume that they together make up the whole of Simplicius’s text. In what follows, however, I shall argue that they suffer from at least one important omission : a proof by Simplicius himself of Euclid’s parallels postulate. Since the omission occurs both in the Leiden manuscript and in Gerard’s translation, it cannot simply be an accidental feature of the former. My argument will consist in (i) citing evidence (Document I) to the effect that such a proof was known to some Arabic mathematicians, and (2) producing a hitherto unnoticed text (Document II) which, in the light of the evidence cited, may well be taken to be the missing proof. In addition, I shall show how Simplicius’s proof entered Arabic discussions on parallels, first, by being made subject to criticism (Document I), and then by being incorporated into a new proof which was designed to take that criticism into account (Document III). [p. 1] |
| Online Resources | https://uni-koeln.sciebo.de/s/yyXlDjNP3t7ipML |
{"_index":"sire","_type":"_doc","_id":"1055","_score":null,"_source":{"id":1055,"authors_free":[{"id":1602,"entry_id":1055,"agent_type":null,"is_normalised":null,"person_id":396,"institution_id":null,"role":{"id":1,"role_name":"author"},"free_name":"Sabra, A. I.","free_first_name":"A. I.","free_last_name":"Sabra","norm_person":{"id":396,"first_name":"A. I.","last_name":"Sabra","full_name":"Sabra, A. I.","short_ident":"","is_classical_name":null,"dnb_url":"http:\/\/d-nb.info\/gnd\/1023667843","viaf_url":"","db_url":"","from_claudius":null}}],"entry_title":"Simplicius\u2019s Proof of Euclid\u2019s Parallels Postulate","main_title":{"title":"Simplicius\u2019s Proof of Euclid\u2019s Parallels Postulate"},"abstract":"A commentary by Simplicius on the premisses to Book I of Euclid\u2019s Elements \r\nsurvives in an Arabic translation of which the author and the exact date \r\nof execution are unknown. The translation is reproduced by the ninth-century \r\nmathematician al-Fadl ibn H\u00e2tim al-Nayr\u00efz\u00ef in the course of his own com\u00ad\r\nmentary on the Elements. Of Nayr\u00efz\u00ee\u2019s commentary, which is based on the \r\nearlier translation of the Elements by al-Hajj\u00e2j ibn Y\u00fbsuf ibn Matar, we have \r\nonly one manuscript copy at Leiden and Gerard of Cremona\u2019s Latin trans\u00ad\r\nlation, both of which have been published.1The passages quoted by Nayr\u00efz\u00ef, owing to their extensiveness and con\u00ad\r\nsecutive order, would strongly lead one to assume that they together make \r\nup the whole of Simplicius\u2019s text. In what follows, however, I shall argue that \r\nthey suffer from at least one important omission : a proof by Simplicius himself \r\nof Euclid\u2019s parallels postulate. Since the omission occurs both in the Leiden \r\nmanuscript and in Gerard\u2019s translation, it cannot simply be an accidental \r\nfeature of the former. My argument will consist in (i) citing evidence \r\n(Document I) to the effect that such a proof was known to some Arabic \r\nmathematicians, and (2) producing a hitherto unnoticed text (Document \r\nII) which, in the light of the evidence cited, may well be taken to be the \r\nmissing proof. In addition, I shall show how Simplicius\u2019s proof entered Arabic \r\ndiscussions on parallels, first, by being made subject to criticism (Document I), \r\nand then by being incorporated into a new proof which was designed to take \r\nthat criticism into account (Document III). [p. 1]","btype":3,"date":"1969","language":"English","online_url":"","online_resources":"https:\/\/uni-koeln.sciebo.de\/s\/yyXlDjNP3t7ipML","doi_url":null,"categories":[],"authors":[{"id":396,"full_name":"Sabra, A. I.","role":{"id":1,"role_name":"author"}}],"book":null,"booksection":null,"article":{"id":1055,"journal_id":null,"journal_name":"Journal of the Warburg and Courtauld Institutes","volume":"32","issue":"","pages":"1-24"}},"sort":[1969]}
| Title | Simplicius’s Proof of Euclid’s Parallels Postulate |
| Type | Article |
| Language | English |
| Date | 1969 |
| Journal | Journal of the Warburg and Courtauld Institutes |
| Volume | 32 |
| Pages | 1-24 |
| Categories | no categories |
| Author(s) | Sabra, A. I. |
| Editor(s) | |
| Translator(s) |
A commentary by Simplicius on the premisses to Book I of Euclid’s Elements survives in an Arabic translation of which the author and the exact date of execution are unknown. The translation is reproduced by the ninth-century mathematician al-Fadl ibn Hâtim al-Nayrïzï in the course of his own com mentary on the Elements. Of Nayrïzî’s commentary, which is based on the earlier translation of the Elements by al-Hajjâj ibn Yûsuf ibn Matar, we have only one manuscript copy at Leiden and Gerard of Cremona’s Latin trans lation, both of which have been published.1The passages quoted by Nayrïzï, owing to their extensiveness and con secutive order, would strongly lead one to assume that they together make up the whole of Simplicius’s text. In what follows, however, I shall argue that they suffer from at least one important omission : a proof by Simplicius himself of Euclid’s parallels postulate. Since the omission occurs both in the Leiden manuscript and in Gerard’s translation, it cannot simply be an accidental feature of the former. My argument will consist in (i) citing evidence (Document I) to the effect that such a proof was known to some Arabic mathematicians, and (2) producing a hitherto unnoticed text (Document II) which, in the light of the evidence cited, may well be taken to be the missing proof. In addition, I shall show how Simplicius’s proof entered Arabic discussions on parallels, first, by being made subject to criticism (Document I), and then by being incorporated into a new proof which was designed to take that criticism into account (Document III). [p. 1] |
| Online Resources | https://uni-koeln.sciebo.de/s/yyXlDjNP3t7ipML |
{"_index":"sire","_type":"_doc","_id":"1055","_score":null,"_source":{"id":1055,"authors_free":[{"id":1602,"entry_id":1055,"agent_type":null,"is_normalised":null,"person_id":396,"institution_id":null,"role":{"id":1,"role_name":"author"},"free_name":"Sabra, A. I.","free_first_name":"A. I.","free_last_name":"Sabra","norm_person":{"id":396,"first_name":"A. I.","last_name":"Sabra","full_name":"Sabra, A. I.","short_ident":"","is_classical_name":null,"dnb_url":"http:\/\/d-nb.info\/gnd\/1023667843","viaf_url":"","db_url":"","from_claudius":null}}],"entry_title":"Simplicius\u2019s Proof of Euclid\u2019s Parallels Postulate","main_title":{"title":"Simplicius\u2019s Proof of Euclid\u2019s Parallels Postulate"},"abstract":"A commentary by Simplicius on the premisses to Book I of Euclid\u2019s Elements \r\nsurvives in an Arabic translation of which the author and the exact date \r\nof execution are unknown. The translation is reproduced by the ninth-century \r\nmathematician al-Fadl ibn H\u00e2tim al-Nayr\u00efz\u00ef in the course of his own com\u00ad\r\nmentary on the Elements. Of Nayr\u00efz\u00ee\u2019s commentary, which is based on the \r\nearlier translation of the Elements by al-Hajj\u00e2j ibn Y\u00fbsuf ibn Matar, we have \r\nonly one manuscript copy at Leiden and Gerard of Cremona\u2019s Latin trans\u00ad\r\nlation, both of which have been published.1The passages quoted by Nayr\u00efz\u00ef, owing to their extensiveness and con\u00ad\r\nsecutive order, would strongly lead one to assume that they together make \r\nup the whole of Simplicius\u2019s text. In what follows, however, I shall argue that \r\nthey suffer from at least one important omission : a proof by Simplicius himself \r\nof Euclid\u2019s parallels postulate. Since the omission occurs both in the Leiden \r\nmanuscript and in Gerard\u2019s translation, it cannot simply be an accidental \r\nfeature of the former. My argument will consist in (i) citing evidence \r\n(Document I) to the effect that such a proof was known to some Arabic \r\nmathematicians, and (2) producing a hitherto unnoticed text (Document \r\nII) which, in the light of the evidence cited, may well be taken to be the \r\nmissing proof. In addition, I shall show how Simplicius\u2019s proof entered Arabic \r\ndiscussions on parallels, first, by being made subject to criticism (Document I), \r\nand then by being incorporated into a new proof which was designed to take \r\nthat criticism into account (Document III). [p. 1]","btype":3,"date":"1969","language":"English","online_url":"","online_resources":"https:\/\/uni-koeln.sciebo.de\/s\/yyXlDjNP3t7ipML","doi_url":null,"categories":[],"authors":[{"id":396,"full_name":"Sabra, A. I.","role":{"id":1,"role_name":"author"}}],"book":null,"booksection":null,"article":{"id":1055,"journal_id":null,"journal_name":"Journal of the Warburg and Courtauld Institutes","volume":"32","issue":"","pages":"1-24"}},"sort":["Simplicius\u2019s Proof of Euclid\u2019s Parallels Postulate"]}