The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations: Gerolamo Cardano's De Regula Aliza
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Wiesbaden
Springer Fachmedien Wiesbaden GmbH
2015
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XX, 443 S. 34 schw.-w. Ill., 10 schw.-w. Tab. 210 mm x 148 mm |
| ISBN: | 9783658092740 3658092742 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042472439 | ||
| 003 | DE-604 | ||
| 005 | 20150519 | ||
| 007 | t | ||
| 008 | 150326s2015 gw ad|| m||| 00||| eng d | ||
| 015 | |a 15,N10 |2 dnb | ||
| 016 | 7 | |a 1067324488 |2 DE-101 | |
| 020 | |a 9783658092740 |c Pb. : EUR 79.99 (DE) (freier Pr.), EUR 82.24 (AT) (freier Pr.), sfr 100.00 (freier Pr.) |9 978-3-658-09274-0 | ||
| 020 | |a 3658092742 |9 3-658-09274-2 | ||
| 024 | 3 | |a 9783658092740 | |
| 028 | 5 | 2 | |a Best.-Nr.: 978-3-658-09274-0 |
| 035 | |a (OCoLC)915635529 | ||
| 035 | |a (DE-599)DNB1067324488 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-HE | ||
| 049 | |a DE-11 | ||
| 082 | 0 | |a 100 | |
| 084 | |a CE 5400 |0 (DE-625)17986: |2 rvk | ||
| 084 | |a 100 |2 sdnb | ||
| 100 | 1 | |a Confalonieri, Sara |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations |b Gerolamo Cardano's De Regula Aliza |c Sara Confalonieri |
| 263 | |a 201504 | ||
| 264 | 1 | |a Wiesbaden |b Springer Fachmedien Wiesbaden GmbH |c 2015 | |
| 300 | |a XX, 443 S. |b 34 schw.-w. Ill., 10 schw.-w. Tab. |c 210 mm x 148 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a Zugl.: Paris, Univ., Diss., 2013 | ||
| 600 | 1 | 7 | |a Cardano, Girolamo |d 1501-1576 |0 (DE-588)11863822X |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kubische Gleichung |0 (DE-588)4455887-9 |2 gnd |9 rswk-swf |
| 653 | |a Research | ||
| 653 | |a Gerolamo Cardano | ||
| 653 | |a cubic equations | ||
| 653 | |a renaissance algebra | ||
| 653 | |a cubic formula | ||
| 653 | |a casus irreducibilis | ||
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Kubische Gleichung |0 (DE-588)4455887-9 |D s |
| 689 | 0 | 1 | |a Cardano, Girolamo |d 1501-1576 |0 (DE-588)11863822X |D p |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m X:MVB |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=5158063&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027907574&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027907574 | |
Datensatz im Suchindex
| _version_ | 1806330881831337984 |
|---|---|
| adam_text |
CONTENTS
FOREWORD V
NOTATIONS AND MORE VII
1. INTRODUCTION 1
2. PUTTING IN CONTEXT CARDANO'S WORKS AND MATHEMATICS 5
2.1. CARDANO AS A MATHEMATICAL WRITER 5
2.2. A PUZZLING BOOK 13
2.3. FROM THE "ALIZA PROBLEM" TO THE DE REGULA ALIZA . 18
2.4. THE READERS OF THE DE REGULA ALIZA 26
2.5. THE MATHEMATICAL CONTEXT NOWADAYS 30
2.5.1. SOLVING QUADRATIC EQUATIONS 31
2.5.2. QUADRATIC EQUATIONS WITH REAL COEFFICIENTS . 32
2.5.3. SOLVING CUBIC EQUATIONS 33
2.5.4. CUBIC EQUATIONS WITH REAL COEFFICIENTS 37
2.5.5. CUBIC EQUATIONS WITH REAL COEFFICIENTS SOLVED IN
A TRIGONOMETRICAL WAY 40
2.5.6. WHAT GALOIS THEORY CAN SAY ABOUT CUBIC EQUATIONS 41
2.5.7. PARADIGMATIC EXAMPLES FOR CUBIC EQUATIONS . . 43
2.5.8. SOLVING QUARTIC EQUATIONS 45
2.5.9. QUARTIC EQUATIONS WITH REAL COEFFICIENTS 49
3. CARDANO SOLVES EQUATIONS IN THE ARS MAGNA 53
3.1. MISCELLANEOUS CONSIDERATIONS REGARDING EQUATIONS . 56
3.1.1. SOLVING LINEAR, QUADRATIC, AND OTHER SIMPLE EQUA
TIONS. COMING ACROSS THE SQUARE ROOTS OF NEGAT
IVE NUMBERS 56
HTTP://D-NB.INFO/1067324488
XVIII
CONTENTS
3.1.2. TRANSFORMATIONS OF EQUATIONS 60
3.1.3. CARDANO SOLVES "MIDDLE POWER EQUAL TO THE
HIGHEST POWER AND A NUMBER" IN "GENERAL" . 73
3.1.4. "PARTICULAR" VERSUS "GENERAL" 79
3.1.5. CARDANO'S "ROYAL ROAD" . . . 100
3.1.6. SUMMING UP 103
3.2. SOLVING DEPRESSED CUBIC EQUATIONS 105
3.2.1. "ON THE CUBE AND SOME THINGS EQUAL TO A NUMBER"105
3.2.2. "ON THE CUBE EQUAL TO SOME THINGS AND A NUMBER"110
3.2.3. "ON THE CUBE AND A NUMBER EQUAL TO SOME THINGS" 115
3.2.4. SUMMING UP 121
3.3. SOLVING CUBIC EQUATION LACKING IN THE FIRST DEGREE TERM 122
3.3.1. "ON THE CUBE EQUAL TO SOME SQUARES AND A NUMBER" 122
3.3.2. "ON THE CUBE AND SOME SQUARES EQUAL TO A NUMBER" 125
3.3.3. "ON THE CUBE AND A NUMBER EQUAL TO SOME SQUARES" 130
3.3.4. SUMMING UP 134
3.4. SOLVING COMPLETE EQUATIONS 135
3.4.1. "ON THE CUBE, SOME SQUARES, AND SOME THINGS
EQUAL TO A NUMBER" 135
3.4.2. "ON THE CUBE AND SOME THINGS EQUAL TO SOME
SQUARES AND A NUMBER" 141
3.4.3. "ON THE CUBE AND SOME SQUARES EQUAL TO SOME
THINGS AND A NUMBER" 150
3.4.4. "ON THE CUBE EQUAL TO SOME SQUARES, SOME
THINGS, AND A NUMBER" 151
3.4.5. "ON THE CUBE AND A NUMBER EQUAL TO SOME
SQUARES AND SOME THINGS" 153
3.4.6. "ON THE CUBE, SOME THINGS, AND A NUMBER EQUAL
TO SOME SQUARES" 156
3.4.7. "ON THE CUBE, SOME SQUARES, AND A NUMBER
EQUAL TO SOME THINGS" 158
3.4.8. SUMMING UP 161
3.5. INTERDEPENDENCES AND CASUS IRREDUCIBILIS 161
CONTENTS
XIX
3.6. SOLVING QUARTIC EQUATIONS 165
3.6.1. CARDANO'S LIST OF THE "MOST GENERAL" QUARTIC
EQUATIONS 165
3.6.2. SOLVING "THE SQUARE SQUARE, SOME SQUARES, AND
A NUMBER EQUAL TO SOME THINGS" 169
3.6.3. WHAT ABOUT THE OTHER QUARTIC EQUATIONS? . . . 172
3.6.4. SUMMING UP 177
4. EARLIER ENCOUNTERS WITH GENERAL TREATMENTS OF EQUATIONS 179
4.1. VARIOUS ENCOUNTERS IN THE PRACTICA ARITHMETIC#; .
179
4.1.1. THE APPENDIX DEVOTED TO EQUATIONS 180
4.1.2. SUMMING UP 184
4.2. APPROACHES TO CUBICS IN THE /IRS MAGNA ARITHMETICAL . 185
4.2.1. SHORTLY AGAIN ON THE SQUARE ROOTS OF NEGATIVE
NUMBERS 187
4.2.2. METHODS THAT LEAD TO THE SOLUTION OF NEW CASES 188
4.2.3. TRANSFORMATIONS OF EQUATIONS 192
4.2.4. "GENERAL" SHAPES FOR IRRATIONAL SOLUTIONS . 196
4.2.5. THE CUBIC FORMULAE, OR WHAT GETS CLOSER TO THEM 214
4.2.6. "PARTICULAR" SOLVING METHODS 232
4.2.7. SUMMING UP 238
5. STRATEGIES TO POSSIBLY OVERCOME THE CASUS IRRIDUCIBILIS:
THE DE REGULA ALIZA 243
5.1. GETTING ACQUAINTED WITH THE DE REGULA ALIZA 243
5.1.1. OVERVIEW OF THE DE REGULA ALIZA'S CONTENTS . . 247
5.1.2. AGAIN ON DATING THE ALIZA'S MISCELLANY 263
5.2. THE METHOD OF THE SPLITTINGS IN ALIZA, CHAPTER I . 264
5.2.1. THE SPLITTING (A 1.1) 268
5.2.2. THE SPLITTING (A I.2)-(A 1.7) 273
5.2.3. THE REMAINING SPLITTINGS 284
5.2.4. SUMMING UP 290
5.3. ANALYSING THE SPLITTINGS 291
5.3.1. ON THE ORIGIN OF THE SUBSTITUTION X = Y + Z: A
HYPOTHESIS ON THE GENERAL SHAPES FOR IRRATIONAL
SOLUTIONS 291
XX
CONTENTS
5.3.2. ON THE ORIGIN OF THE SPLITTINGS: A HYPOTHESIS IN
RELATION WITH ARS MAGNA, CHAPTER XXV . 323
5.3.3. CARDANO'S LAST SAY ON THE ORIGIN OF THE SPLITTINGS 334
5.3.4. STUDYING THE SPLITTINGS BY THEMSELVES 339
5.3.5. SUMMING UP 349
5.4. SOME TECHNICAL SUPPLEMENTS 351
5.4.1. PRELIMINARY STUDY OF IRRATIONAL NUMBERS . 352
5.4.2. AGAIN ON PROPOSITION (AM VIII.2) 354
5.5. HOW FAR GOES GEOMETRY IN THE ALIZA? 361
5.5.1. CARDANO'S PROOF OF THE EXISTENCE OF A SOLUTION
FOR
X
3
+ AO = A2X
2
361
5.5.2. COMPARING CARDANO'S PROOF WITH HIS FORERUN
NERS' ONE 367
5.5.3. SUMMING UP 377
5.6. TRYING FOR AN ARITHMETIC OF NASTY NUMBERS 378
CONCLUSIONS 389
A. A SHORT HISTORY OF CARDANO'S LIFE 395
A.L. CHRONICLE OF A CONTROVERSY 398
A.2. TARTAGLIA'S POEM 405
B. LIST OF REFERENCES IN AND TO THE DE REGULA ALIZA 407
C. LIST OF CARDANO'S NUMERICAL CUBIC EQUATIONS 413
BIBLIOGRAPHY 431
1. SOURCES 431
2. SECONDARY LITERATURE 438 |
| any_adam_object | 1 |
| author | Confalonieri, Sara |
| author_facet | Confalonieri, Sara |
| author_role | aut |
| author_sort | Confalonieri, Sara |
| author_variant | s c sc |
| building | Verbundindex |
| bvnumber | BV042472439 |
| classification_rvk | CE 5400 |
| ctrlnum | (OCoLC)915635529 (DE-599)DNB1067324488 |
| dewey-full | 100 |
| dewey-hundreds | 100 - Philosophy & psychology |
| dewey-ones | 100 - Philosophy & psychology |
| dewey-raw | 100 |
| dewey-search | 100 |
| dewey-sort | 3100 |
| dewey-tens | 100 - Philosophy & psychology |
| discipline | Philosophie |
| format | Thesis Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000zc 4500</leader><controlfield tag="001">BV042472439</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20150519</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">150326s2015 gw ad|| m||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">15,N10</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">1067324488</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783658092740</subfield><subfield code="c">Pb. : EUR 79.99 (DE) (freier Pr.), EUR 82.24 (AT) (freier Pr.), sfr 100.00 (freier Pr.)</subfield><subfield code="9">978-3-658-09274-0</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3658092742</subfield><subfield code="9">3-658-09274-2</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9783658092740</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">Best.-Nr.: 978-3-658-09274-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)915635529</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB1067324488</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE-HE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-11</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">100</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">CE 5400</subfield><subfield code="0">(DE-625)17986:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">100</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Confalonieri, Sara</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations</subfield><subfield code="b">Gerolamo Cardano's De Regula Aliza</subfield><subfield code="c">Sara Confalonieri</subfield></datafield><datafield tag="263" ind1=" " ind2=" "><subfield code="a">201504</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Wiesbaden</subfield><subfield code="b">Springer Fachmedien Wiesbaden GmbH</subfield><subfield code="c">2015</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XX, 443 S.</subfield><subfield code="b">34 schw.-w. Ill., 10 schw.-w. Tab.</subfield><subfield code="c">210 mm x 148 mm</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="502" ind1=" " ind2=" "><subfield code="a">Zugl.: Paris, Univ., Diss., 2013</subfield></datafield><datafield tag="600" ind1="1" ind2="7"><subfield code="a">Cardano, Girolamo</subfield><subfield code="d">1501-1576</subfield><subfield code="0">(DE-588)11863822X</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kubische Gleichung</subfield><subfield code="0">(DE-588)4455887-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Research</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Gerolamo Cardano</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">cubic equations</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">renaissance algebra</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">cubic formula</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">casus irreducibilis</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4113937-9</subfield><subfield code="a">Hochschulschrift</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Kubische Gleichung</subfield><subfield code="0">(DE-588)4455887-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Cardano, Girolamo</subfield><subfield code="d">1501-1576</subfield><subfield code="0">(DE-588)11863822X</subfield><subfield code="D">p</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">X:MVB</subfield><subfield code="q">text/html</subfield><subfield code="u">http://deposit.dnb.de/cgi-bin/dokserv?id=5158063&prov=M&dok_var=1&dok_ext=htm</subfield><subfield code="3">Inhaltstext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</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=027907574&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027907574</subfield></datafield></record></collection> |
| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV042472439 |
| illustrated | Illustrated |
| indexdate | 2024-08-03T02:16:08Z |
| institution | BVB |
| isbn | 9783658092740 3658092742 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027907574 |
| oclc_num | 915635529 |
| open_access_boolean | |
| owner | DE-11 |
| owner_facet | DE-11 |
| physical | XX, 443 S. 34 schw.-w. Ill., 10 schw.-w. Tab. 210 mm x 148 mm |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Springer Fachmedien Wiesbaden GmbH |
| record_format | marc |
| spelling | Confalonieri, Sara Verfasser aut The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations Gerolamo Cardano's De Regula Aliza Sara Confalonieri 201504 Wiesbaden Springer Fachmedien Wiesbaden GmbH 2015 XX, 443 S. 34 schw.-w. Ill., 10 schw.-w. Tab. 210 mm x 148 mm txt rdacontent n rdamedia nc rdacarrier Zugl.: Paris, Univ., Diss., 2013 Cardano, Girolamo 1501-1576 (DE-588)11863822X gnd rswk-swf Kubische Gleichung (DE-588)4455887-9 gnd rswk-swf Research Gerolamo Cardano cubic equations renaissance algebra cubic formula casus irreducibilis (DE-588)4113937-9 Hochschulschrift gnd-content Kubische Gleichung (DE-588)4455887-9 s Cardano, Girolamo 1501-1576 (DE-588)11863822X p DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=5158063&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027907574&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Confalonieri, Sara The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations Gerolamo Cardano's De Regula Aliza Cardano, Girolamo 1501-1576 (DE-588)11863822X gnd Kubische Gleichung (DE-588)4455887-9 gnd |
| subject_GND | (DE-588)11863822X (DE-588)4455887-9 (DE-588)4113937-9 |
| title | The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations Gerolamo Cardano's De Regula Aliza |
| title_auth | The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations Gerolamo Cardano's De Regula Aliza |
| title_exact_search | The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations Gerolamo Cardano's De Regula Aliza |
| title_full | The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations Gerolamo Cardano's De Regula Aliza Sara Confalonieri |
| title_fullStr | The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations Gerolamo Cardano's De Regula Aliza Sara Confalonieri |
| title_full_unstemmed | The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations Gerolamo Cardano's De Regula Aliza Sara Confalonieri |
| title_short | The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations |
| title_sort | the unattainable attempt to avoid the casus irreducibilis for cubic equations gerolamo cardano s de regula aliza |
| title_sub | Gerolamo Cardano's De Regula Aliza |
| topic | Cardano, Girolamo 1501-1576 (DE-588)11863822X gnd Kubische Gleichung (DE-588)4455887-9 gnd |
| topic_facet | Cardano, Girolamo 1501-1576 Kubische Gleichung Hochschulschrift |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=5158063&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027907574&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT confalonierisara theunattainableattempttoavoidthecasusirreducibilisforcubicequationsgerolamocardanosderegulaaliza |