Talk:homology

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Replication of definitions from homologous[edit]

In general, homology could be defined only in terms of homologous. I do not see whether it is a good idea; a replication of the definitions stated in homologous seems better. Why it seems better and whether it indeed is better remains unanalyzed at this point. --Daniel Polansky 17:55, 12 March 2008 (UTC)

Mathematical etymology[edit]

The following definition from OED seems to predate and underly the modern use in math. The note about Poincare is thus incomplete. "4. Mod. Geom. The relation of two figures in the same plane, such that every point in each corresponds to a point in the other, and collinear points in one correspond to collinear points in the other; every straight line joining a pair of corresponding points passes through a fixed point called the centre of homology, and every pair of corresponding straight lines in the two figures intersect on a fixed straight line called the axis of homology. 1863 G. Salmon Conic Sections (ed. 4) iv. 59 Two triangles are said to be homologous, when the intersections of the corresponding sides lie on the same right line called the axis of homology: prove that the lines joining the corresponding vertices meet in a point. 1885 C. Leudesdorf tr. L. Cremona Elements Projective Geom. 11 Two corresponding straight lines therefore always intersect on a fixed straight line, which we may call s; thus the given figures are in homology, O being the centre, and s the axis, of homology."--Zekelayla (talk) 00:33, 13 January 2018 (UTC)