Geometry and arithmetic in the medieval traditions of Euclid’s Elements: a view from Book II

Corry, Leo

doi:10.1007/s00407-013-0121-5

Cited by 31 publications

(10 citation statements)

References 40 publications

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“…During the 1970s there was a debate within the historiography of mathematics concerning whether it is correct to claim that Euclid was a geometric algebraist, in the sense that he was handling geometrical notions but was actually practicing common algebra (Corry 2013). Within the research field of history of mathematics, this debate is sometimes referred to as the Unguru debate: did the Greeks have an algebra?…”

Section: History Of Mathematics or Heritage Of Mathematics?mentioning

confidence: 99%

Handbook of the Mathematics of the Arts and Sciences

2020

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In the present chapter, interpretations of the mathematics of the past are problematized, based on examples such as archeological artifacts, as well as written sources from the ancient Egyptian, Babylonian, and Greek civilizations. The distinction between history and heritage is considered in relation to Euler's function concept, Cauchy's sum theorem, and the Unguru debate. Also, the distinction between the historical past and the practical past, as well as the distinction between the historical and the nonhistorical relations to the past, are made concrete based on Torricelli's result on an infinitely long solid from the seventeenth century. Two complementary but different ways of analyzing

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Section: History Of Mathematics or Heritage Of Mathematics?mentioning

confidence: 99%

Handbook of the Mathematics of the Arts and Sciences

2020

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“…Besides the several methods, the figure was used in different stages of design, which will be described within the scope of this paper, with pentagonal forms detected in medieval buildings throughout Europe (for example, England, France, Germany, Bohemia, Hungary) from the Early Middle Ages to Late Gothic times (Fehér et al 2018a, b;Pentagons: 305-315). The correct construction of the regular pentagon was commonly known (Scriba et al 2015: 62-63;Corry 2013), but seems to have been rather ignored in the architectural practice of the Middle Ages (Kidson 2008: 10). According to the few remaining medieval graphic sources of architecture, master masons had invented or learnt methods for the geometrical approximation of the figure.…”

Section: Introductionmentioning

confidence: 99%

Pentagons in Medieval Sources and Architecture

Fehér¹,

Szilágyi²,

Bölcskei³

et al. 2019

Nexus Netw J

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A range of entirely different pentagon approximations are known from textual and graphic sources related to the architecture of the Middle Ages. Analysis of the mathematical logic behind them highlights the scientific knowledge of master masons who directly calculated constructional methods according to their practical needs. From the examination of these pentagon approximations, their mathematical features, such as the initial data of the construction or precision of side lengths and angles, the range of architectural design problems they would have been able to solve can be determined. This paper provides an accurate comparison of mathematical and geometrical features of pentagon constructions from medieval sources, studying their applicability from an architectural aspect.

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“…post-Vietan) algebra 8 was either altogether ignored, or it was considered as merely a question of the extent to which a homogeneous – and, thus, largely ahistorical – “algebraic essence” was manifested in a particular historical period (cf. Corry 2013, 639).…”

Section: Introduction: a Critical Examination Of The Debate On “Geomementioning

confidence: 99%

“…A direct consequence of the algebraic interpretation of Heron's proofs is that they are still largely considered as a unique, un-contextualized, and thus unexplained phaenomenon in the history of mathematical ideas (cf. Corry 2013, 654).…”

Section: Introduction: a Critical Examination Of The Debate On “Geomementioning

confidence: 99%

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Situating the Debate on “Geometrical Algebra” within the Framework of Premodern Algebra

Sialaros¹,

Christianidis²

2016

Sci Context

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Argument The aim of this paper is to employ the newly contextualized historiographical category of "premodern algebra" in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on "geometrical algebra." Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related to Elem. II.5 as a case study, we discuss Euclid's geometrical proofs, the so-called "semi-algebraic" alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron's practice, highlights the significance of contextualizing "premodern algebra," and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition.

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Geometry and arithmetic in the medieval traditions of Euclid’s Elements: a view from Book II

Cited by 31 publications

References 40 publications

Handbook of the Mathematics of the Arts and Sciences

Handbook of the Mathematics of the Arts and Sciences

Pentagons in Medieval Sources and Architecture

Situating the Debate on “Geometrical Algebra” within the Framework of Premodern Algebra

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