Historia Mathematica最新文献

{"title":"Paris, BULAC Ara 606 and its relation to the Arabic Euclidean transmission attributed to al-Ḥajjāj","authors":"Gregg De Young","doi":"10.1016/j.hm.2025.04.002","DOIUrl":"10.1016/j.hm.2025.04.002","url":null,"abstract":"<div><div>I introduce a recently discovered Arabic manuscript containing a version of Euclid's <em>Elements</em>: Paris, BULAC, Ara 606. In an attempt to situate Ara 606 within the Arabic Euclidean tradition, I survey the manuscript evidence currently known to me reporting characteristics of the tradition ascribed by medieval authors to al-Ḥajjāj and show that Ara 606 includes all the formulations explicitly attributed to al-Ḥajjāj. These features suggest that Ara 606 belongs to the Ḥajjāj tradition, along with Mumbai, Mullā Fīrūz, R.I.6 studied by <span><span>Brentjes</span></span> (<span><span>2006</span></span>, <span><span>2018</span></span>).</div><div>Another surprising result is that St. Petersburg, Akad. Nauk, S-2145 appears to be a hybrid manuscript, containing a traditional Isḥāq-Thābit version in books I–VI but containing a version very similar to Ara 606 in books VII–XIII. These two manuscripts thus provide an important complement to the Mumbai manuscript because they contain a Ḥajjāj-related version similar to that found in Mumbai but extending beyond book IX, where the Mumbai manuscript breaks off.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"71 ","pages":"Pages 87-126"},"PeriodicalIF":0.5,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144264110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"In memoriam: Jim Bennett (1947-2023)","authors":"Stephen Johnston","doi":"10.1016/j.hm.2025.03.003","DOIUrl":"10.1016/j.hm.2025.03.003","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"71 ","pages":"Pages 74-77"},"PeriodicalIF":0.5,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144264108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Overspecification, indifference to visual accuracy, and other characteristics in the transmission of the diagrams of Copernicus’ De Revolutionibus","authors":"Christián C. Carman ,&nbsp;Diego Pelegrin","doi":"10.1016/j.hm.2025.03.001","DOIUrl":"10.1016/j.hm.2025.03.001","url":null,"abstract":"<div><div>This paper investigates the transmission of diagrams in Copernicus' <em>De Revolutionibus</em>, focusing on the phenomena of overspecification and indifference to visual accuracy. Unlike previous studies that assumed the original diagrams, this research uses source diagrams to analyze how these features emerge and persist through various editions and manuscripts. The study demonstrates the gradual and independent development of overspecification and visual inaccuracies during transmission, highlighting their stability over multiple copies. Additionally, it explores errors in labeling and the introduction of spurious elements in diagrams, reinforcing the belief that these characteristics arise during the transmission process. The findings challenge the notion that these diagrammatic features were common practices confined to ancient and medieval times, showing that they persist into the 21st century.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"71 ","pages":"Pages 34-58"},"PeriodicalIF":0.5,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144264106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Linguistics as method in German histories of numeracy, 1780–1840","authors":"Tuska Benes","doi":"10.1016/j.hm.2025.03.002","DOIUrl":"10.1016/j.hm.2025.03.002","url":null,"abstract":"<div><div>A late eighteenth-century linguistic turn in German intellectual life transformed language study into a method significant for the history of mathematics. Theologically inspired recognition of language's role in cognition encouraged Hamann to curtail the epistemological importance Kant and rationalists like Wolff bestowed on the symbolic forms of mathematics. Scholars within the tradition of general grammar, including Abel-Rémusat had upheld mathematics as a model of precision; in a debate over Chinese, Wilhelm von Humboldt insisted that historically contingent grammatical structures decisively shaped thought. Alexander von Humboldt interpreted the origins of the Indian positional method using his brother Wilhelm's typology of language structure, as linguistic such as Franz Bopp applied etymology to the history of number systems.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"71 ","pages":"Pages 59-73"},"PeriodicalIF":0.5,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144264107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The difficulty of bringing Gauss's Disquisitiones Arithmeticae in the hands of readers (1801-1804)","authors":"Maarten Bullynck","doi":"10.1016/j.hm.2025.04.001","DOIUrl":"10.1016/j.hm.2025.04.001","url":null,"abstract":"<div><div>Some new facts and a reconstruction are presented on how C.F. Gauss's book <em>Disquisitiones Arithmeticae</em> (1801) was distributed and found its way to its first readers. These include a hitherto unknown contemporary German review of the <em>Disquisitiones Arithmeticae</em> (1802) and a reconstruction on how Gauss's book finally arrived in the book shops of Paris.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"71 ","pages":"Pages 78-86"},"PeriodicalIF":0.5,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144264109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Graphs and lattices in the early versions of Ramon Llull's Art","authors":"A. Bonner,&nbsp;P.J. Planas Mulet,&nbsp;L. Badia","doi":"10.1016/j.hm.2025.02.001","DOIUrl":"10.1016/j.hm.2025.02.001","url":null,"abstract":"<div><div>Even though Ramon Llull (c. 1232–1316) made poor use of explicit mathematical formulations, since the times of G.W. Leibniz his Art of finding and demonstrating the truth has been considered an intellectual tool forerunning varied mathematical deployments, from combinatorics, to voting theory and even to computing sciences. This article shows how Llull used implicitly two mathematical formulations, graph theory and lattice theory, not known to have made their appearance before the 20th century: <em>Ars demonstrativa</em> (c.1283) displays some devices of graph theory and <em>Liber principiorum medicinae</em> (c.1274–1283) develops lattice theory in the context of the University of Montpellier.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"70 ","pages":"Pages 31-52"},"PeriodicalIF":0.5,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143609591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical imagination in 14th-century natural philosophy. The case of the endless, infinite helix line","authors":"Elżbieta Jung,&nbsp;Robert Podkoński","doi":"10.1016/j.hm.2025.02.005","DOIUrl":"10.1016/j.hm.2025.02.005","url":null,"abstract":"<div><h3>Résumé</h3><div>Dans cet article, nous listons et discutons en détail les exemples géométriques apparaissant dans des textes de philosophie naturelle du XIVe siècle dans le contexte des débats relatifs à l'infini, au continu et à l'existence d'entités indivisibles. Dans la première partie de l'article, nous concentrons sur les propriétés de la spirale 'proportionnelle' (<em>linea girativa</em>) inventée par Richard Kilvington, qui décrit clairement cette ligne comme une entité géométrique infiniment longue. Beaucoup de ses contemporains et d'auteurs scolastiques plus tardifs tentèrent ardemment de rejeter cette conclusion, en dépit de sa cohérence mathématique. Dans la seconde partie de l'article, nous présentons les arguments géométriques employés contre les théories atomistes apparues dans la philosophie naturelle oxfordienne du début du XIVe siècle. Ces arguments géométriques furent utilisés par leurs auteurs en raison de leur plus grande efficacité, comparée aux arguments logiques ou philosophiques, pour réfuter l'atomisme. Sur la base de ces discussions, nous présentons enfin quelques conclusions à propos de l'attitude des penseurs de la fin du Moyen Âge concernant l'utilité des preuves mathématiques dans le contexte de la philosophie naturelle aristotélicienne.</div></div><div><h3>Summary</h3><div>In the present paper we compile and discuss in detail the geometrical examples presented in fourteenth-century natural philosophical texts in the context of discussions on infinity, continuity, and the existence of indivisible entities. In the first part of this article we focus on the controversies over the properties of the “proportional” helix line (<em>linea girativa</em>), invented by Richard Kilvington, who unambiguously described this line as an actually infinitely long geometrical entity. Many of his contemporary as well as later scholastic authors tried fervently to deny that conclusion, in spite of its mathematical consistency. In the second part of the article we present the geometrical arguments used against the atomistic theories appearing in Oxford natural philosophy at the beginning of the fourteenth century. These geometrical arguments were recognized by their authors as “more efficacious” in proving atomism false than logical or philosophical ones. On the basis of these discussions we finally present a few conclusions concerning the attitude of later medieval scholars about the usefulness of mathematical proofs in the context of Aristotelian natural philosophy.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"70 ","pages":"Pages 53-72"},"PeriodicalIF":0.5,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143609592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"","authors":"Alain Bernard","doi":"10.1016/j.hm.2025.02.003","DOIUrl":"10.1016/j.hm.2025.02.003","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"70 ","pages":"Pages 3-6"},"PeriodicalIF":0.5,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143609588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Euclidean proof for the Fourth Postulate","authors":"José Gil-Férez ,&nbsp;Piotr Błaszczyk ,&nbsp;M. Andrew Moshier ,&nbsp;Alberto Naibo ,&nbsp;Marco Panza ,&nbsp;Jean-Michel Salanskis","doi":"10.1016/j.hm.2024.12.001","DOIUrl":"10.1016/j.hm.2024.12.001","url":null,"abstract":"<div><div>We discuss some classical conundrums about Euclid's Fourth Postulate. Our inquire sheds lights on the role the postulate is playing within the deductive structure of Book I of the <em>Elements</em> and provides a proof of it fully admissible within Euclid's original setting.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"70 ","pages":"Pages 10-30"},"PeriodicalIF":0.5,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143609590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"","authors":"Helena Durnová","doi":"10.1016/j.hm.2025.02.004","DOIUrl":"10.1016/j.hm.2025.02.004","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"70 ","pages":"Pages 7-9"},"PeriodicalIF":0.5,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143609589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}