{"created":"2023-05-15T12:20:22.049477+00:00","id":10915,"links":{},"metadata":{"_buckets":{"deposit":"97cffcf4-c73d-4ffa-8e10-67bf91b20f85"},"_deposit":{"created_by":1,"id":"10915","owners":[1],"pid":{"revision_id":0,"type":"depid","value":"10915"},"status":"published"},"_oai":{"id":"oai:kansai-u.repo.nii.ac.jp:00010915","sets":["528:1538:1541:1561"]},"author_link":["23172","23171"],"item_10_alternative_title_20":{"attribute_name":"その他のタイトル","attribute_value_mlt":[{"subitem_alternative_title":"Proof of Cavarieli's Proposition on the Quadrature of the General Parabola"}]},"item_10_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2007-01-10","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"72","bibliographicPageStart":"55","bibliographicVolumeNumber":"26","bibliographic_titles":[{"bibliographic_title":"情報研究 : 関西大学総合情報学部紀要"}]}]},"item_10_description_4":{"attribute_name":"概要","attribute_value_mlt":[{"subitem_description":"本論では,17世紀初頭に活躍したB.カヴァリエリの不可分量の概念を用いて,一般放物線(y=x^nでnが任意の自然数の曲線)の下の面積を求める.まず,不可分量の概念と不可分法による楕円と球の求積を述べる.また,不可分量と密接な関係にあるアルキメデスの発見法を述べる.さらに,低次放物線(y=x^nでnが1桁の自然数の曲線)の下の求積に関するカヴァリエリの業績を述べる.次に,不可分量の概念を目に見える形で用いて,低次放物線の下の面積を求める.さらに,一般放物線の下の面積を与える定理を,ほぼ同時代の研究者であるB.パスカルが開発した数学的帰納法を用いて証明する.これは,カヴァリエリが推測するだけに終わった命題である.","subitem_description_type":"Other"},{"subitem_description":"In this paper, the quadrature of a general parabola y=x^n is described, based on the concept of indivisibles developed by B. Cavarieli in the early 17th century. First, the area of an ellipse and the volume of a sphere are calculated using indivisibles. Next, the Archimedean heuristic having relationships with indivisibles is described. Second, Cavarieli's researches on the areas of parabolas having low degrees are investigated, and formulas of these areas are derived faithfully based on the concept of indivisibles. Last, Cavarieli's proposition on the area of a general parabola is proven using the mathematical induction developed by B. Pascal in the contemporary era.","subitem_description_type":"Other"}]},"item_10_full_name_3":{"attribute_name":"著者別名","attribute_value_mlt":[{"nameIdentifiers":[{"nameIdentifier":"23172","nameIdentifierScheme":"WEKO"}],"names":[{"name":"Fukada, Youji"}]}]},"item_10_publisher_34":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"関西大学"}]},"item_10_source_id_10":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AN10484636","subitem_source_identifier_type":"NCID"}]},"item_10_source_id_8":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"1341156X","subitem_source_identifier_type":"ISSN"}]},"item_10_version_type_17":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"深田, 陽司"}],"nameIdentifiers":[{"nameIdentifier":"23171","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2019-05-22"}],"displaytype":"detail","filename":"KU-1100-20070110-04.pdf","filesize":[{"value":"1.0 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"KU-1100-20070110-04.pdf","url":"https://kansai-u.repo.nii.ac.jp/record/10915/files/KU-1100-20070110-04.pdf"},"version_id":"492b838e-dd33-4892-80bf-c08bb0a7a0b6"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"関西大学","subitem_subject_scheme":"Other"},{"subitem_subject":"Kansai University","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"一般放物線の求積に関するカヴァリエリの命題の証明","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"一般放物線の求積に関するカヴァリエリの命題の証明"}]},"item_type_id":"10","owner":"1","path":["1561"],"pubdate":{"attribute_name":"公開日","attribute_value":"2018-02-01"},"publish_date":"2018-02-01","publish_status":"0","recid":"10915","relation_version_is_last":true,"title":["一般放物線の求積に関するカヴァリエリの命題の証明"],"weko_creator_id":"1","weko_shared_id":1},"updated":"2023-05-17T02:03:02.036478+00:00"}