1977/03/01 by Stuart Robertson · 1 citation
Arts and Humanities · Social Sciences · Mathematics · Engineering · #Classical Philosophy and Thought #Historical and Literary Studies #History and Theory of Mathematics #Isosceles triangle #Quadrilateral #Equilateral triangle #Combinatorics #Mathematics #Geometry #Engineering #Structural engineering
paper · doi:10.2307/3617441
openalex publication_date 1977/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
Among the definitions at the beginning of Book I in Euclid’s Elements [1] there are several that pick out special kinds of triangles and quadrilaterals. In his commentary [2] on Book I, Proclus observes that Euclid classifies triangles in two ways: firstly ‘by sides’ into equilateral, isosceles and scalene triangles; and secondly ‘by angles’ into right-angled, obtuse-angled and acute-angled triangles. With regard to quadrilaterals, Proclus ([2], p. 134) attributes to Posidonius the classification scheme on p. 39, which is to be found in Heath’s edition of the Elements ([1], p. 189). Thus the ancient classification of triangles and quadrilaterals produces three (or six) species of triangles and seven species of quadrilaterals.