{"id":"https://openalex.org/W2355059404","doi":null,"title":"Cardano\u2032s erroneous rule for the transformation between two equations","display_name":"Cardano\u2032s erroneous rule for the transformation between two equations","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2355059404","mag":"2355059404"},"language":"en","primary_location":{"id":"mag:2355059404","doi":null,"is_oa":false,"landing_page_url":"http://en.cnki.com.cn/Article_en/CJFDTOTAL-XBDZ200901050.htm","pdf_url":null,"source":{"id":"https://openalex.org/S2764424372","display_name":"Journal of Northwest University","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4323237962","host_organization_name":"Northwest University","host_organization_lineage":["https://openalex.org/P4323237962"],"host_organization_lineage_names":["Northwest University"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Journal of Northwest University","raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083969121","display_name":"Jiwei Zhao","orcid":"https://orcid.org/0000-0002-9298-9412","observed_orcids":["https://orcid.org/0000-0002-9298-9412"]},"institutions":[{"id":"https://openalex.org/I37802460","display_name":"Northwest University","ror":"https://ror.org/00z3td547","country_code":"CN","type":"education","lineage":["https://openalex.org/I37802460"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiwei Zhao","raw_affiliation_strings":["Centre for History of Mathematics and Sciences,Northwest University,Xi'an 710127,China)"],"raw_orcid":"https://orcid.org/0000-0002-9298-9412","affiliations":[{"raw_affiliation_string":"Centre for History of Mathematics and Sciences,Northwest University,Xi'an 710127,China)","institution_ids":["https://openalex.org/I37802460"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5083969121"],"corresponding_institution_ids":["https://openalex.org/I37802460"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.42391304,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11137","display_name":"Historical Philosophy and Science","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cardano","display_name":"Cardano","score":0.7699999809265137},{"id":"https://openalex.org/keywords/transformation-of-equations","display_name":"transformation of equations","score":0.6779999732971191},{"id":"https://openalex.org/keywords/history-of-algebra","display_name":"history of algebra","score":0.8980000019073486},{"id":"https://openalex.org/keywords/renaissance-mathematics","display_name":"Renaissance mathematics","score":0.5640000104904175},{"id":"https://openalex.org/keywords/synthesis-methods","display_name":"synthesis methods","score":0.3070000112056732},{"id":"https://openalex.org/keywords/cubic-equations","display_name":"cubic equations","score":0.3149999976158142}],"concepts":[{"id":"https://openalex.org/C2777179996","wikidata":"https://www.wikidata.org/wiki/Q911222","display_name":"Mistake","level":2,"score":0.7895017862319946},{"id":"https://openalex.org/C2778732403","wikidata":"https://www.wikidata.org/wiki/Q815577","display_name":"Ignorance","level":2,"score":0.7092500329017639},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7056947350502014},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6585845351219177},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5385794043540955},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.45013678073883057},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35185134410858154},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2605413794517517},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.252109557390213},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.2461041808128357},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.13270169496536255},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05074608325958252},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2355059404","doi":null,"is_oa":false,"landing_page_url":"http://en.cnki.com.cn/Article_en/CJFDTOTAL-XBDZ200901050.htm","pdf_url":null,"source":{"id":"https://openalex.org/S2764424372","display_name":"Journal of Northwest University","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4323237962","host_organization_name":"Northwest University","host_organization_lineage":["https://openalex.org/P4323237962"],"host_organization_lineage_names":["Northwest University"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Journal of Northwest University","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2386749186","https://openalex.org/W2387542153","https://openalex.org/W2349526272","https://openalex.org/W630381407","https://openalex.org/W2795959920","https://openalex.org/W2182514476","https://openalex.org/W1993259158","https://openalex.org/W2480699313","https://openalex.org/W4415267309","https://openalex.org/W2752341745"],"abstract_inverted_index":{"Aim":[0],"To":[1],"reconstruct":[2],"Cardano\u2032s":[3,37,66],"creating":[4,67],"of":[5,18,23,25,43,50,53,65,68,79,85,98],"an":[6],"erroneous":[7],"rule,i.e.,rule":[8],"7.13,for":[9],"transformation":[10],"between":[11],"two":[12],"equations":[13],"in":[14,40,92],"the":[15,51,54,77,80,83,90],"seventh":[16],"chapter":[17],"Artis":[19],"Magnae.Methods":[20],"By":[21],"means":[22],"principles":[24],"reconstructing":[26],"ancient":[27],"proofs":[28],"and":[29,87],"mathematical":[30,63],"analysis.Results":[31],"It":[32],"is":[33,71,104],"pointed":[34],"out":[35],"that":[36,47],"mistake":[38],"lies":[39],"his":[41,48,60],"ignorance":[42],"a":[44,93],"latent":[45],"supposition,and":[46],"underestimation":[49],"complexity":[52],"rule":[55,69,81,91,99],"prevents":[56],"him":[57],"from":[58,82],"checking":[59],"examples.Conclusion":[61],"The":[62],"idea":[64],"7.13":[70,100],"revealed":[72],"as":[73],"thus:he":[74],"initially":[75],"gets":[76],"suppositions":[78],"conclusion":[84],"it":[86],"then":[88],"expresses":[89],"synthetic":[94],"way.Finally,the":[95],"correct":[96],"form":[97],"with":[101],"its":[102],"examples":[103],"given.":[105]},"counts_by_year":[],"updated_date":"2025-10-10T17:16:08.811792","created_date":"2016-06-24T00:00:00"}