- Tytuł:
- Decoding Book II of the Elements
- Autorzy:
-
Błaszczyk, Piotr
Mrówka, Kazimierz
Petiurenko, Anna - Powiązania:
- https://bibliotekanauki.pl/articles/1789252.pdf
- Data publikacji:
- 2020-12-31
- Wydawca:
- Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
- Tematy:
-
Euclid’s diagrams
Visual evidence
Renaming
Substitution rules
Geometric algebra
Common Notions
Euclidean fields
Pythagorean fields - Opis:
- The paper is a commentary to the Polish translation of the Elements Book II, included in this volume.We focus on relations between figures represented and not represented on diagrams and identify rules which enable Euclid to bridge these two kinds of objects. Also, we argue that the main mathematical problem addressed in Book II is constructing a leg of a rightangled triangle, given its hypotenuse and the other leg. In proposition II.14, Euclid solves it through the construction called the geometric mean. We trace the problem in Book III and beyond the Elements: in Heron’s Metrica, Descartes’ La Géométrie, and modern foundations of mathematics. We show that Descartes, by novel interpretation of the Pythagorean theorem, provides a modern solution to this problem.
- Źródło:
-
Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2020, 12; 39-88
2080-9751
2450-341X - Pojawia się w:
- Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
- Dostawca treści:
- Biblioteka Nauki
Artykuł