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Classifying triangles and quadrilaterals

Published online by Cambridge University Press:  22 September 2016

S. A. Robertson
S. A. Robertson*
Affiliation:
The University, Southampton SO9 5NH
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Extract

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.

Type
Research Article
Information
The Mathematical Gazette , Volume 61 , Issue 415 , March 1977 , pp. 38 - 49
Copyright
Copyright © Mathematical Association 1977

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References

1. Heath, T. L., The thirteen books of Euclid’s Elements (2nd edition), Vol I. Cambridge University Press (1925), re-issued by Dover (New York, 1956).Google Scholar
2. Morrow, G. L., Proclus: A commentary on the first book of Euclid’s Elements. Princeton University Press (1970).Google Scholar
3. Robertson, S. A., Carter, S. and Morton, H. L., Finite orthogonal symmetry, Topology 9, 79–95 (1970).CrossRefGoogle Scholar
4. Robertson, S. A. and Carter, S., On the Platonic and Archimedean solids, J. Lond. Math. Soc. (2), 2, 125–132 (1970).CrossRefGoogle Scholar
5. The universal encyclopedia of mathematics. Allen, and Unwin, (1964), re-issued by Pan, (1976).Google Scholar