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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

Paper i proceeding
Författare Johanna Pejlare
Publicerad i “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
Förlag Edizioni Nuova Cultura
Förlagsort Roma
Publiceringsår 2017
Publicerad vid Institutionen för matematiska vetenskaper
Språk en
Länkar https://doi.org/10.4458/8647
https://www.researchgate.net/public...
https://gup.ub.gu.se/file/207048
Ämnesord History of mathematics; Anders Gabriel Duhre; geometry; algebra; Euclid's Elements
Ämneskategorier Geometri, Algebra och geometri, Annan matematik, Matematik, Vetenskapshistoria

Sammanfattning

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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