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On the relationships between the geometric and the algebraic ideas in Duhre’s textbooks of mathematics, as reflected via Book II of Euclid’s Elements

Conference paper
Authors Johanna Pejlare
Published in “DIG WHERE YOU STAND” 4. Proceedings of the Fourth International Conference on the History of Mathematics Education. 23-26 September, 2015. Torino, Italy
ISBN 9788868128647
Publisher Edizioni Nuova Cultura
Place of publication Roma
Publication year 2017
Published at Department of Mathematical Sciences
Language en
Keywords History of mathematics; Anders Gabriel Duhre; geometry; algebra; Euclid's Elements
Subject categories Geometry, Algebra and geometry, Other Mathematics, Mathematics, History of science


The present article explores the relationships between the geometric and algebraic ideas presented in Anders Gabriel Duhre’s mathematics textbooks. Of particular interest is Book II of Euclid’s Elements as presented by Duhre in his textbook on geometry from 1721. We consider in detail Duhre’s two versions of Proposition II.5, dealing with straight lines cut into equal and unequal parts, as well as the two proofs of the propositions that he presents. Duhre’s formulations are slightly different from traditional geometric formulations, as he moved away from a purely geometrical context towards an algebraic one. Duhre established Proposition II.5 using algebra in Descartes’ notation as well as in the notation of Wallis and Oughtred. Duhre ́s reason for introducing algebra in Book II of Euclid’s Elements was to obtain convenience in calculations, as well as the possibility to generalize results to different kinds of quantities.

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