Abstract
This second set of problems of the third kind exemplifies mathematics when the problem is “linear” by nature. Props. 39–41, like Props. 35–38, belong to the second path of development for the mathematics of motion curves, the analytical track. The analysis focuses on reduction to the symptoma of the quadratrix, and to the rectification property in Prop. 26. A certain tendency for setting out the quadratrix in a separate auxiliary figure and arguing “parallel” can be detected, but with the slim observation basis we have, we cannot be certain that this is typical.
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Notes
- 1.
My assessment differs slightly from Knorr’s, who mentions these propositions in passing and connects them to the angle division property of the quadratrix (Knorr 1989, p. 214).
- 2.
cf. Co p. 108/109 F
- 3.
One has to appeal to the proposition used already in Props. 26, 36, and 39: XII,2, Circ. mens I, V, 15: arcs in the same ratio as radii. Then consider similar triangles, half-chords, perpendicular on chord; the ratio of radii can be replaced with the ratio of half-chords. Cf. * in the proof protocol of Prop. 26.
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Sefrin-Weis, H. (2010). Quadratrix, Rectification Property. 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_11
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