Abstract
The configurations and the mathematical content of the propositions, as well as the argumentative means, are reminiscent of pre-Euclidean mathematics, as exemplified in the Hippocrates fragment 1: circles with inscribed triangles, geometry of the circle (presented in III/IV of the Elements), and argumentation via congruent angles in extended configurations. All this gives Props. 11 and 12 an old-fashioned character. On the other hand, no sources are known for Props. 11 and 12. Language and style show no signs of archaism. Props. 11 and 12 were probably constructed by Pappus. What was their purpose? They could be an illustration of what the operation with the technique of analysis-synthesis originally looked like. For Prop. 12, this surely is the case, whereas the situation is less clear for Prop. 11, and only a tentative thesis can be formulated.
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Notes
- 1.
On the Hippocrates fragment see Simpl. in Phys. 61–68 Diels, Heath (1921, Vol. I, p. 183 and pp.195–196), Knorr (1986, pp. 32–34), and Netz (2004).
- 2.
Prop. 12 has been read this way by Mahoney (1968), e.g.
- 3.
See the introduction to Props. 4–12.
- 4.
For a very different assessment, cf. Mahoney (1968).
- 5.
Note that the resolutio is minimal here.
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Sefrin-Weis, H. (2010). Plane Geometry, Archaic Style. In: Sefrin-Weis, H. (eds) Pappus of Alexandria: Book 4 of the Collection . Sources and Studies in the History of Mathematics and Physical Sciences. Springer, London. https://doi.org/10.1007/978-1-84996-005-2_5
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