{"title":"L'ipocicloide tricuspide: Il duplice approccio di Luigi Cremona ed Eugenio Beltrami","authors":"M. A. Vaccaro, N. Palladino","doi":"10.19272/201809201003","DOIUrl":"https://doi.org/10.19272/201809201003","url":null,"abstract":"","PeriodicalId":55343,"journal":{"name":"Bollettino di Storia delle Scienze Matematiche","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2017-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43697859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Tra matematica e fisica : François Jacquier in Italia e le sue Institutiones philosophicae","authors":"Luigi Pepe","doi":"10.19272/201609202004","DOIUrl":"https://doi.org/10.19272/201609202004","url":null,"abstract":"","PeriodicalId":55343,"journal":{"name":"Bollettino di Storia delle Scienze Matematiche","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68126887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Su Maestro Grazia dei Castellani teologo e matematico del XIV secolo","authors":"E. Ulivi","doi":"10.1400/232280","DOIUrl":"https://doi.org/10.1400/232280","url":null,"abstract":"","PeriodicalId":55343,"journal":{"name":"Bollettino di Storia delle Scienze Matematiche","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66622855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Arithmetic, geometric and harmonic means in music theory","authors":"Fabio Bellissima","doi":"10.1400/227130","DOIUrl":"https://doi.org/10.1400/227130","url":null,"abstract":"","PeriodicalId":55343,"journal":{"name":"Bollettino di Storia delle Scienze Matematiche","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66622379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Antanairesis, literally «successive subtractions», is the method to-day known as Euclidean algorithm. In the Elements it is applied to numbers, for computing the GCD, and also to generic magnitudes, to determine if they are commensurable or not. The oldest example of an antanairetic procedure, described in a fragment of Philolaus, regards the construction of the musical intervals in the Pythagorean scale. These intervals ― fourth, tone, diesis, comma ― are in fact obtained from octave and fifth by successive subtractions. Since octave and fifth are incommensurable, such antanairesis is infinite; therefore does not exist an interval by which all the others can be measured (a passage from Plato's Republic is possibly a reference to that). In order to approximate this interval, the musical antanairesis has been forced to stop, an operation which corresponds to finding a convergent of a continued fraction. Those, as the Phytagoreans, who did not accept this kind of intervals, solved the problem by using two incommensurable measures. This suggests an alternative usage of the cut of an antanairesis, that we analyze in the second part of the paper.
{"title":"L'antanairesi e la teoria armonica greca","authors":"Fabio Bellissima","doi":"10.1400/171695","DOIUrl":"https://doi.org/10.1400/171695","url":null,"abstract":"Antanairesis, literally «successive subtractions», is the method to-day known as Euclidean algorithm. In the Elements it is applied to numbers, for computing the GCD, and also to generic magnitudes, to determine if they are commensurable or not. The oldest example of an antanairetic procedure, described in a fragment of Philolaus, regards the construction of the musical intervals in the Pythagorean scale. These intervals ― fourth, tone, diesis, comma ― are in fact obtained from octave and fifth by successive subtractions. Since octave and fifth are incommensurable, such antanairesis is infinite; therefore does not exist an interval by which all the others can be measured (a passage from Plato's Republic is possibly a reference to that). In order to approximate this interval, the musical antanairesis has been forced to stop, an operation which corresponds to finding a convergent of a continued fraction. Those, as the Phytagoreans, who did not accept this kind of intervals, solved the problem by using two incommensurable measures. This suggests an alternative usage of the cut of an antanairesis, that we analyze in the second part of the paper.","PeriodicalId":55343,"journal":{"name":"Bollettino di Storia delle Scienze Matematiche","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66610550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article is dedicated to the algebraic theory of equations, presented by Jean Prestet in the two editions of his Elemens de mathematiques. Jean Prestet develops there an innovative idea: the association of algebra and combinatorial analysis; he underlines the novelty of his approach by registering his resolution of equations in a new way: the «voie mixte». This mixed way, he tells us, rests on the two already existing ways: the analytical way (the algebra for Jean Prestet) and the synthetic way (illustrated by the combinatorial analysis in Elemens de mathematiques).
{"title":"JEAN PRESTET: ALGÈBRE ET COMBINATOIRE DANS LA RÉSOLUTION DES ÉQUATIONS","authors":"Katia Asselah","doi":"10.1400/171693","DOIUrl":"https://doi.org/10.1400/171693","url":null,"abstract":"This article is dedicated to the algebraic theory of equations, presented by Jean Prestet in the two editions of his Elemens de mathematiques. Jean Prestet develops there an innovative idea: the association of algebra and combinatorial analysis; he underlines the novelty of his approach by registering his resolution of equations in a new way: the «voie mixte». This mixed way, he tells us, rests on the two already existing ways: the analytical way (the algebra for Jean Prestet) and the synthetic way (illustrated by the combinatorial analysis in Elemens de mathematiques).","PeriodicalId":55343,"journal":{"name":"Bollettino di Storia delle Scienze Matematiche","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66610543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper presents the transcription of the chapters devoted to astronomy/astrology in the abbacus treatise contained in the manuscript Magl. Cl. XI, 119 (Florence National Library) written in the first half of the 15 th century. The treatment of this subject in the manuscript differs in many interesting aspects from that in the others so far studied. Among the subjects presented we find: tables to find month to month the day and the hour of the moonrise, a method to calculate the initial day of a month, a rule to build a sundial, lunar prognostica, a table for sailing (tavoletta da navigare). The presence of the last subject is very interesting, its presence in abbacus treatises is in fact very unusual.
本文介绍了手稿Magl中abbacus论文中专门讨论天文学/占星术的章节的抄写。Cl。11, 119(佛罗伦萨国家图书馆)，写于15世纪上半叶。手稿中对这一主题的处理在许多有趣的方面与迄今为止所研究的其他问题不同。在提出的主题中，我们发现:找出月出的日期和时间的表格，计算一个月开始一天的方法，制作日晷的规则，月球预测，航海表(tavoletta da navigare)。最后一个主题的出现是非常有趣的，它在abbacus论文中的出现实际上是非常不寻常的。
{"title":"Astronomia/astrologia in un trattato d'abaco della prima metà del QUattrocento (Ms. Mag. Cl XI, 119 della Biblioteca Nazionale di Firenze)","authors":"R. Franci","doi":"10.1400/157161","DOIUrl":"https://doi.org/10.1400/157161","url":null,"abstract":"The paper presents the transcription of the chapters devoted to astronomy/astrology in the abbacus treatise contained in the manuscript Magl. Cl. XI, 119 (Florence National Library) written in the first half of the 15 th century. The treatment of this subject in the manuscript differs in many interesting aspects from that in the others so far studied. Among the subjects presented we find: tables to find month to month the day and the hour of the moonrise, a method to calculate the initial day of a month, a rule to build a sundial, lunar prognostica, a table for sailing (tavoletta da navigare). The presence of the last subject is very interesting, its presence in abbacus treatises is in fact very unusual.","PeriodicalId":55343,"journal":{"name":"Bollettino di Storia delle Scienze Matematiche","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66595551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper I try to prove that the tendency of Luca Valerio to generalize definitions and results is not limited to the few rightly famous examples, but is one of the characteristic features of all his mathematical work. This is particularly evident for the limiting procedures widely used in De centro gravitatis solidorum that I compare with analogues procedures in the Subtilium indagationum liber, an early treatise by Valerio where he seems to approach infinitesimal mathematics concepts from a physical point of view. I also compare some passages of Valerio's treatises with analogous Archimedean passages, underlining where Valerio diverges in a significant way from the classical source. Moreover I draw reader's attention to a theorem where Valerio compares two different figures with the same height and with the bases on the same plane or straight line, by means of their sections with planes or straight lines parallel to the bases using the corpus of propositions which allow him to deal with abstract properties of a class of figures.
{"title":"TEMI GENERALI NELL'OPERA DI LUCA VALERIO","authors":"Loredana Biacino","doi":"10.1400/157162","DOIUrl":"https://doi.org/10.1400/157162","url":null,"abstract":"In this paper I try to prove that the tendency of Luca Valerio to generalize definitions and results is not limited to the few rightly famous examples, but is one of the characteristic features of all his mathematical work. This is particularly evident for the limiting procedures widely used in De centro gravitatis solidorum that I compare with analogues procedures in the Subtilium indagationum liber, an early treatise by Valerio where he seems to approach infinitesimal mathematics concepts from a physical point of view. I also compare some passages of Valerio's treatises with analogous Archimedean passages, underlining where Valerio diverges in a significant way from the classical source. Moreover I draw reader's attention to a theorem where Valerio compares two different figures with the same height and with the bases on the same plane or straight line, by means of their sections with planes or straight lines parallel to the bases using the corpus of propositions which allow him to deal with abstract properties of a class of figures.","PeriodicalId":55343,"journal":{"name":"Bollettino di Storia delle Scienze Matematiche","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66595562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In proposition 14 of the second book of his Conics, Apollonius proves that the asymptotes and the hyperbola approach one another indefinitely without meeting. This proposition appeals to the notion of infinity and of infinite construction of the sequences of distances between the curve and its asymptote. But this notion of 'infinity' was bound to create problems for both mathematicians and philosophers, since Geminus and Proclus. These problems were taken anew by al-Sijzī (second half of 10 th century) and his followers. In this article, the reader will find an outline of the history of this question, an analysis of the work of al-Qummī (a successor of al-Sijzī), as well as a critical edition and translation of new materials concerning the study of asymptotic behaviour.
{"title":"L'Asymptote : Apollonius et ses lecteurs.","authors":"R. Rashed","doi":"10.1400/157163","DOIUrl":"https://doi.org/10.1400/157163","url":null,"abstract":"In proposition 14 of the second book of his Conics, Apollonius proves that the asymptotes and the hyperbola approach one another indefinitely without meeting. This proposition appeals to the notion of infinity and of infinite construction of the sequences of distances between the curve and its asymptote. But this notion of 'infinity' was bound to create problems for both mathematicians and philosophers, since Geminus and Proclus. These problems were taken anew by al-Sijzī (second half of 10 th century) and his followers. In this article, the reader will find an outline of the history of this question, an analysis of the work of al-Qummī (a successor of al-Sijzī), as well as a critical edition and translation of new materials concerning the study of asymptotic behaviour.","PeriodicalId":55343,"journal":{"name":"Bollettino di Storia delle Scienze Matematiche","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66595588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The work brings together numerous previously unpublished documents on Luca Pacioli, Leonardo da Vinci, Piero della Francesca and their families. The documents are first explained and commented on in detail, and then transcribed in the respective Appendices. The first, and more substantial, part contains information on Pacioli, the periods he spent in the town of his birth, Sanse-polcro, and his relations with Piero and Leonardo; the second, along with documents concerning Leonardo directly, chiefly provides unpublished information on his relatives, updating one of our earlier publications on the Da Vinci family. The documents include three autographs by Luca Pacioli and one by Piero della Francesca.
{"title":"Documenti inediti su Luca Pacioli, Piero della Francesca e Leonardo da Vinci, con alcuni autografi","authors":"E. Ulivi","doi":"10.1400/116043","DOIUrl":"https://doi.org/10.1400/116043","url":null,"abstract":"The work brings together numerous previously unpublished documents on Luca Pacioli, Leonardo da Vinci, Piero della Francesca and their families. The documents are first explained and commented on in detail, and then transcribed in the respective Appendices. The first, and more substantial, part contains information on Pacioli, the periods he spent in the town of his birth, Sanse-polcro, and his relations with Piero and Leonardo; the second, along with documents concerning Leonardo directly, chiefly provides unpublished information on his relatives, updating one of our earlier publications on the Da Vinci family. The documents include three autographs by Luca Pacioli and one by Piero della Francesca.","PeriodicalId":55343,"journal":{"name":"Bollettino di Storia delle Scienze Matematiche","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66582766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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