A history of Arabic sciences and mathematics: Volume 5 Ibn Al-Haytham's geometrical methods and the philosophy of mathematics
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Weitere beteiligte Personen: | |
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
London ; New York
Routledge
2017
|
| Schriftenreihe: | Culture and civilization in the Middle East
55 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027167177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverzeichnis Seite [639]-648 |
| Umfang: | xiv, 664 Seiten Diagramme |
| ISBN: | 9780415582193 |
Internformat
MARC
| LEADER | 00000nam a2200000 cc4500 | ||
|---|---|---|---|
| 001 | BV041720184 | ||
| 003 | DE-604 | ||
| 005 | 20250306 | ||
| 007 | t| | ||
| 008 | 140305s2017 xx |||| |||| 00||| eng d | ||
| 020 | |a 9780415582193 |c hardback |9 978-0-415-58219-3 | ||
| 035 | |a (OCoLC)915422768 | ||
| 035 | |a (DE-599)BVBBV041720184 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-11 |a DE-12 |a DE-473 | ||
| 100 | 1 | |a Rashed, Roshdi |d 1936- |e Verfasser |0 (DE-588)120250446 |4 aut | |
| 245 | 1 | 0 | |a A history of Arabic sciences and mathematics |n Volume 5 |p Ibn Al-Haytham's geometrical methods and the philosophy of mathematics |c Roshdi Rashed ; translated by J.V. Field |
| 264 | 1 | |a London ; New York |b Routledge |c 2017 | |
| 300 | |a xiv, 664 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Culture and civilization in the Middle East |v 55 | |
| 490 | 0 | |a Culture and civilization in the Middle East | |
| 500 | |a Literaturverzeichnis Seite [639]-648 | ||
| 600 | 1 | 7 | |a Ibn-al-Haiṯam, al-Ḥasan Ibn-al-Ḥasan |d 965-1039 |0 (DE-588)118648160 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Araber |0 (DE-588)4002528-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Ibn-al-Haiṯam, al-Ḥasan Ibn-al-Ḥasan |d 965-1039 |0 (DE-588)118648160 |D p |
| 689 | 0 | 1 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 0 | 2 | |a Araber |0 (DE-588)4002528-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Field, Judith Veronica |d 1943- |0 (DE-588)123499259 |4 trl | |
| 773 | 0 | 8 | |w (DE-604)BV039699811 |g 5 |
| 775 | 0 | 8 | |i Äquivalent |n Druck-Ausgabe, Paperback |z 978-0-367-86529-0 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-315-16845-6 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-351-68600-6 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-351-68601-3 |
| 830 | 0 | |a Culture and civilization in the Middle East |v 55 |w (DE-604)BV022955619 |9 55 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bamberg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027167177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 940 | 1 | |q gbd_1 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027167177 | |
Datensatz im Suchindex
| _version_ | 1826400989467377664 |
|---|---|
| adam_text |
CONTENTS Foreword. Preface . ix xi INTRODUCTION: MOTION AND TRANSFORMATIONS IN GEOMETRY. 1 CHAPTER I: THE PROPERTIES OF THE CIRCLE INTRODUCTION. 1. The concept of homothety. 2. Euclid, Pappus and Ibn al-Haytham: on homothety . 3. Ibn al-Haytham and homothety as a point by point transformation . 4. History of the text . MATHEMATICAL COMMENTARY. 17 19 23 27 32 35 TRANSLATED TEXT: On the Properties of Circles . 85 CHAPTER II: THE ANALYTICAL ART IN THE TENTH TO ELEVENTH CENTURIES INTRODUCTION. 1. The rebirth of a subject. 2. Analytical art: discipline and method. 3. The analytical art and the new discipline: ‘The Knowns’
. .". 4. History of the texts. On Analysis and Synthesis . The Knowns. 131 131 138 142 151 151 153 I. ANALYSIS AND SYNTHESIS: MATHEMATICAL METHOD AND DISCIPLINE MATHEMATICAL COMMENTARY. 157 1. The double classification of Analysis and Synthesis . Preliminary propositions . Analysis and synthesis in arithmetic. Analysis and synthesis in geometry. Analysis and synthesis in astronomy . Analysis in music . 2. Applications of analysis and synthesis in number theory and in geometry. Number theory . Perfect numbers. Two indeterminate systems of equations of the first degree. Geometrical
problems . Problem in plane geometry. Problem solved with the help of transformations. Construction of a circle to touch three given circles. 157 157 162 166 171 173 174 175 175 178 182 182 185 187
VI CONTENTS Auxiliary problem. 199 Geometrical commentary on the problem. 207 Algebraic commentary on the auxiliary problem. 214 TRANSLATED TEXT: On Analysis and Synthesis . 219 II. THE KNOWNS: A NEW GEOMETRICAL DISCIPLINE. 305 INTRODUCTION. 305 MATHEMATICAL COMMENTARY. 308 1. Properties of position and of form and geometrical transformations . 308 2. Invariant properties of geometrical loci and geometrical transformations. 329 TRANSLATED TEXT: On the Knowns. 361 III: ANALYSIS AND SYNTHESIS: EXAMPLES OF THE GEOMETRY OF TRIANGLES . 1. On a geometrical problem: Ibn Sahl, al-Sijzï and Ibn al-Haytham . 2. Distances from a point of a triangle to its sides. 3. History of the texts. 3.1. On a Geometrical Problem . 3.2.
On the Properties of the Triangle . 435 436 453 471 471 473 TRANSLATED TEXTS: On a Geometrical Problem. 477 On the Properties of the Triangle in Regard to Height. 485 CHAPTER III: IBN AL-HAYTHAM AND THE GEOMETRISATION OF PLACE . 495 HISTORY OF THE TEXT. 505 TRANSLATED TEXT: On Place. 507 APPENDIX: THE ARS INVENIENDI·. THÄBIT IBN QURRA AND AL-SIJZl 517 I. THÄBIT IBN QURRA: AXIOMATIC METHOD AND INVENTION. 517 II. AL-SIJZI: THE IDEA OF AN ARS INVENIENDI. 1. Introduction. 2. A propaedeutic to the ars inveniendi . 3. The methods of the ars inveniendi and their applications . 3.1. Analysis and point-to-point transformation. 3.2. Analysis and variation of one element of the figure . 3.3. Analysis and variation of two methods of solution of a single problem . 3.4.
Analysis and variation of lemmas. 3.5. Analysis and variation of constructions carried out using the same figure 3.6. Variations on a problem from Ptolemy. 521 521 523 528 530 533 534 537 537 543
CONTENTS vii 3.7. Variations on the same problem from Ptolemy in other writings by al-Sijzï. 560 4. Analysis and synthesis: variation of the auxiliary constructions. 566 5. Two principal methods of the ars inveniendi . 568 III. HISTORY OF THE TEXTS. 572 3.1. Book by Thäbit ibn Qurrafor Ibn Wahb on the Means ofArriving at Determining the Construction of Geometrical Problems . 572 3.2. To Smooth the Paths for Determining Geometrical Propositions, by al-Sijzï . 575 3.3. Letter of al-Sijzï to Ibn Yumn on the Construction of an Acute-angled Triangle. 577 3.4. Two Propositions from the Ancients on the Property ofHeights of an Equilateral Triangle: Ps-Archimedes, Aqätun, Menelaus . 577 TRANSLATED TEXTS: 1. Book ofAbii al-Hasan Thäbit ibn Qurrafor Ibn Wahb on the Means of Arriving at Determining the Construction of Geometrical Problems . 581 2. Book ofAhmad ibn Muhammad ibn ‘Abd al-Jalïl al-Sijzï to Smooth the Paths for Determining Geometrical Propositions . 591 3. Letter ofAhmad ibn Muhammad ibn ‘Abd al-Jalïl al-Sijzï to the Physician Abü ‘Alï Nazïf ibn Yumn on the Construction of
the Acute-angled Triangle from Two Unequal Straight Lines. 623 4. Two Propositions of the Ancients on the Property of the Heights of an Equilateral Triangle: Pseudo-Archimedes, Aqâtun, Menelaus. 627 SUPPLEMENTARY NOTES I. Fakhr al-DTn al-Râzï: Ibn al-Haytham’s critique of the notion of place as envelope. 633 II. Al-Hasan ibn al-Haytham and Muhammad ibn al-Haytham: the mathematician and the philosopher - On place. 634 BIBLIOGRAPHY . 639 INDEXES Index of names. Subject index. Index of works . Index of manuscripts. 649 652 659 664 |
| any_adam_object | 1 |
| author | Rashed, Roshdi 1936- |
| author2 | Field, Judith Veronica 1943- |
| author2_role | trl |
| author2_variant | j v f jv jvf |
| author_GND | (DE-588)120250446 (DE-588)123499259 |
| author_facet | Rashed, Roshdi 1936- Field, Judith Veronica 1943- |
| author_role | aut |
| author_sort | Rashed, Roshdi 1936- |
| author_variant | r r rr |
| building | Verbundindex |
| bvnumber | BV041720184 |
| ctrlnum | (OCoLC)915422768 (DE-599)BVBBV041720184 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cc4500</leader><controlfield tag="001">BV041720184</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20250306</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">140305s2017 xx |||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780415582193</subfield><subfield code="c">hardback</subfield><subfield code="9">978-0-415-58219-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)915422768</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV041720184</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-11</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-473</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rashed, Roshdi</subfield><subfield code="d">1936-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)120250446</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A history of Arabic sciences and mathematics</subfield><subfield code="n">Volume 5</subfield><subfield code="p">Ibn Al-Haytham's geometrical methods and the philosophy of mathematics</subfield><subfield code="c">Roshdi Rashed ; translated by J.V. Field</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">London ; New York</subfield><subfield code="b">Routledge</subfield><subfield code="c">2017</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xiv, 664 Seiten</subfield><subfield code="b">Diagramme</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Culture and civilization in the Middle East</subfield><subfield code="v">55</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Culture and civilization in the Middle East</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverzeichnis Seite [639]-648</subfield></datafield><datafield tag="600" ind1="1" ind2="7"><subfield code="a">Ibn-al-Haiṯam, al-Ḥasan Ibn-al-Ḥasan</subfield><subfield code="d">965-1039</subfield><subfield code="0">(DE-588)118648160</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Araber</subfield><subfield code="0">(DE-588)4002528-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Ibn-al-Haiṯam, al-Ḥasan Ibn-al-Ḥasan</subfield><subfield code="d">965-1039</subfield><subfield code="0">(DE-588)118648160</subfield><subfield code="D">p</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Araber</subfield><subfield code="0">(DE-588)4002528-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Field, Judith Veronica</subfield><subfield code="d">1943-</subfield><subfield code="0">(DE-588)123499259</subfield><subfield code="4">trl</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="w">(DE-604)BV039699811</subfield><subfield code="g">5</subfield></datafield><datafield tag="775" ind1="0" ind2="8"><subfield code="i">Äquivalent</subfield><subfield code="n">Druck-Ausgabe, Paperback</subfield><subfield code="z">978-0-367-86529-0</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-315-16845-6</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-351-68600-6</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-351-68601-3</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Culture and civilization in the Middle East</subfield><subfield code="v">55</subfield><subfield code="w">(DE-604)BV022955619</subfield><subfield code="9">55</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bamberg - ADAM Catalogue Enrichment</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027167177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">gbd_1</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027167177</subfield></datafield></record></collection> |
| id | DE-604.BV041720184 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-12T15:01:54Z |
| institution | BVB |
| isbn | 9780415582193 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027167177 |
| oclc_num | 915422768 |
| open_access_boolean | |
| owner | DE-11 DE-12 DE-473 DE-BY-UBG |
| owner_facet | DE-11 DE-12 DE-473 DE-BY-UBG |
| physical | xiv, 664 Seiten Diagramme |
| psigel | gbd_1 |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Routledge |
| record_format | marc |
| series | Culture and civilization in the Middle East |
| series2 | Culture and civilization in the Middle East |
| spelling | Rashed, Roshdi 1936- Verfasser (DE-588)120250446 aut A history of Arabic sciences and mathematics Volume 5 Ibn Al-Haytham's geometrical methods and the philosophy of mathematics Roshdi Rashed ; translated by J.V. Field London ; New York Routledge 2017 xiv, 664 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Culture and civilization in the Middle East 55 Culture and civilization in the Middle East Literaturverzeichnis Seite [639]-648 Ibn-al-Haiṯam, al-Ḥasan Ibn-al-Ḥasan 965-1039 (DE-588)118648160 gnd rswk-swf Araber (DE-588)4002528-7 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Ibn-al-Haiṯam, al-Ḥasan Ibn-al-Ḥasan 965-1039 (DE-588)118648160 p Mathematik (DE-588)4037944-9 s Araber (DE-588)4002528-7 s DE-604 Field, Judith Veronica 1943- (DE-588)123499259 trl (DE-604)BV039699811 5 Äquivalent Druck-Ausgabe, Paperback 978-0-367-86529-0 Erscheint auch als Online-Ausgabe 978-1-315-16845-6 Erscheint auch als Online-Ausgabe 978-1-351-68600-6 Erscheint auch als Online-Ausgabe 978-1-351-68601-3 Culture and civilization in the Middle East 55 (DE-604)BV022955619 55 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027167177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rashed, Roshdi 1936- A history of Arabic sciences and mathematics Culture and civilization in the Middle East Ibn-al-Haiṯam, al-Ḥasan Ibn-al-Ḥasan 965-1039 (DE-588)118648160 gnd Araber (DE-588)4002528-7 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)118648160 (DE-588)4002528-7 (DE-588)4037944-9 |
| title | A history of Arabic sciences and mathematics |
| title_auth | A history of Arabic sciences and mathematics |
| title_exact_search | A history of Arabic sciences and mathematics |
| title_full | A history of Arabic sciences and mathematics Volume 5 Ibn Al-Haytham's geometrical methods and the philosophy of mathematics Roshdi Rashed ; translated by J.V. Field |
| title_fullStr | A history of Arabic sciences and mathematics Volume 5 Ibn Al-Haytham's geometrical methods and the philosophy of mathematics Roshdi Rashed ; translated by J.V. Field |
| title_full_unstemmed | A history of Arabic sciences and mathematics Volume 5 Ibn Al-Haytham's geometrical methods and the philosophy of mathematics Roshdi Rashed ; translated by J.V. Field |
| title_short | A history of Arabic sciences and mathematics |
| title_sort | a history of arabic sciences and mathematics ibn al haytham s geometrical methods and the philosophy of mathematics |
| topic | Ibn-al-Haiṯam, al-Ḥasan Ibn-al-Ḥasan 965-1039 (DE-588)118648160 gnd Araber (DE-588)4002528-7 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Ibn-al-Haiṯam, al-Ḥasan Ibn-al-Ḥasan 965-1039 Araber Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027167177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV039699811 (DE-604)BV022955619 |
| work_keys_str_mv | AT rashedroshdi ahistoryofarabicsciencesandmathematicsvolume5 AT fieldjudithveronica ahistoryofarabicsciencesandmathematicsvolume5 |