Journal Article•
Linee Larghe: Un’ ambiguità geometrica dimenticata
01 Jan 1995-Bollettino Di Storia Delle Scienze Matematiche (Max-Planck-Institut für Wissenschaftsgeschichte)-Vol. 22, pp 84-87
About: This article is published in Bollettino Di Storia Delle Scienze Matematiche.The article was published on 1995-01-01 and is currently open access. It has received 17 citations till now.
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TL;DR: The difference between these two approaches is discussed in this paper, with examples exhibited; these will include Euclid, set theory, limits, and applied mathematics in general, and examples of the difference between them are discussed.
89 citations
Cites background from "Linee Larghe: Un’ ambiguità geometr..."
...Not coincidentally, his edition of Euclid was much 6 Again, Euclid defined lines as “breadthless” (Book 1, Definition 2); often criticized by inheritors, he made clear an of his own history, in replacing the Babylonian use of “lines”a objects with width [Høyrup, 1995; and 2002,passim]....
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01 Jan 1996
17 citations
08 Sep 2010
TL;DR: The message inherent in the second portrait is not very different: if mathematics is not of the type we know, and whose roots we customarily trace to the Greeks, it is just a collection of mindless recipes (a type we also know, indeed, from teaching of those social classes that are not supposed to possess or exercise reason) - tertium as discussed by the authors.
Abstract: Until recently, Old Babylonian “algebra” (mostly identified simply as “Babylonian) either looked very much like recent equation algebra in presentations of the history of mathematics, or it was characterized as “empirical”, a collection of rules found by trial and error or other (unidentified) methods not based on reasoning. In the former case, the implicit message was a confirmation of the status of our present type of mathematics as mathematics itself. The message inherent in the second portrait is not very different: if mathematics is not of the type we know, and whose roots we customarily trace to the Greeks, it is just a collection of mindless recipes (a type we also know, indeed, from teaching of those social classes that are not supposed to possess or exercise reason) – tertium
11 citations
TL;DR: In this paper, it is argued that the discussion of notational imperfection versus conceptual divergence is none the less too simplistic, since differences may also be due to deliberate choices and exclusions on the part of the authors of the ancient texts, or as a result of a critique in the Kantian sense, an elimination of expressions and forms of reasoning that are found theoretically incoherent.
11 citations
Additional excerpts
...22 See the discussion in [Høyrup 1995]....
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01 Jan 2005
11 citations