an:02202710
Zbl 1096.01005
Robadey, Anne
Exploration of a way of expressing generality: Poincar??'s 1905 paper on geodesics on convex surfaces
FR
Rev. Hist. Math. 10, No. 2, 257-318 (2004).
00114512
2004
j
01A55 01A85 53-03 01A60
celestial mechanics; analytical continuity; connectedness; compactness; Ren?? Garnier; paradigm (in the French sense)
Poincar??'s ``M??thodes nouvelles de la m??canique c??leste'' (1892--1899) are indeed a precursor of his paper of 1905 ``Sur les lignes g??odesiques des surfaces convexes''. The main theorem there is: On an arbitrary convex surface there is always at least one closed geodesic without any double point, the number of the geodesics is always odd. In 1905 Poincar?? presented two proofs, the first one can be traced back to his ``M??canique c??leste''. In the following chapter Poincar??'s proof is interpreted as a paradigm in the French sense, there are given furtherreaching epistemological reflections. In form of appendices considerations are made according to passages with geometrical interpretation, about the principle of analytical continuity, connectedness, continuity, compactness, multiplicity and continuous families.
Karin Reich (Wentorf)
JFM 36.0669.01