On Comparison, Equivalence and Addition of Magnitudes
DOI:
https://doi.org/10.5007/1808-1711.2019v23n2p153Resumen
A theory of magnitudes involves criteria for their comparison, equivalence and addition. We examine these aspects from an abstract viewpoint, stressing independence and definability. These considerations are triggered by the so-called De Zolt’s principle in the theory of equivalence of plane polygons.
Citas
CLIFFORD, A. (1958). Totally Ordered Commutative Semigroups. Bulletin of the American Mathematical Society 64: 305–316.
EHRLICH, P. (2006). The Rise of non-Archimedean Mathematics and the Roots of a Misconception I: The Emergence of non–Archimedean Systems of Magnitudes. Archive for History of Exact Sciences 60: 1–121.
GIOVANNINI, E., Lassalle Casanave, A. and Veloso, P. (2017). De la práctica euclideana a la práctica hilbertiana: las teorías del área plana. Revista Portuguesa de Filosofía 73 (2): 1263–1294.
HADWIGER, H. (1957). Vorlesungen über Inhalt, Oberfläche und Isometrie. Heidelberg: Springer.
HALE, B. (2000). Reals by Abstraction. Philosophia Mathematica 8 (3): 100–123.
HILBERT, D. (1971). Foundations of Geometry. La Salle: Open Court. Translated by L. Unger from the 10th German Edition.
HÖLDER, O. (1901). Die Axiome der Quantität und die Lehre vom Mass. Berichten der mathematisch–physischen Classe der Königl. Sächs. Gesellschaft der Wissenschaften zu Leipzig 53: 1–64.
HUNTINGTON, E. (1902). A Complete Set of Postulates for the Theory of Absolute Continuous Magnitude. Transactions of the American Mathematical Society 3 (2): 264–279; (3): 280–284.
ŁOMNICKI, A. (1922). O zasadzie dysjunkcyi w logistyce i matematyce. Ruch filozoficzny 6 (1921–1922): 144–146. The title means, “On the principle of disjunction in logic and mathematic”. Unpublished English translation by Andrew McFarland.
McFARLAND, A., McFarland, J. and Smith, J. (Eds.). (2014). Alfred Tarski. Early Work in Poland – Geometry and Teaching. Berlin: Birhäuser.
SATYANARAYANA, M. (1979). Positively Ordered Semigroups. New York: Marcel Dekker Inc.
STEIN, H. (1990). Eudoxos and Dedekind: on the ancient Greek theory of ratios and its relation to the modern mathematics. Synthese 84, 163–211.
STOLZ, O. (1883). Zur Geometrie der Alten, insbesondere über ein Axiom des Archimedes. Mathematische Annalen 22: 504–519.
STOLZ, O. (1885). Vorlesungen über allgemeine Arithmetik. Erster Theil: Allgemeines und Arithmetik der reellen Zahlen. Leipzig: Teubner.
ZOLT, A. (1881). Principii della eguaglianza di poligoni preceduti da alcuni cenni critici sulla teoria della equivalenza geometrica. Milano: Briola.
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