On Neighborhoods (1875-1899)

"The separate atoms of a molecule are not connected all with all, or all with one, but, on the contrary, each one is connected only with one or with a few neighbouring atoms, just as in a chain link is connected with link." (Friedrich A Kekulé, "The Scientific Aims and Achievements of Chemistry", Nature 18, 1878)

"The best grouping, therefore, for the purposes of science is that which collects together all those facts and reasonings which are similar to one another in nature: so that the study of each may throw light on its neighbour. By working thus for a long time at one set of considerations, we get gradually nearer to those fundamental unities which are called nature's laws: we trace their action first singly, and then in combination; and thus make progress slowly but surely. The practical uses of economic studies should never be out of the mind of the economist, but his special business is to study and interpret facts and to find out what are the effects of different causes acting singly and in combination." (Alfred Marshall, "Principles of Economics", 1890)

"Analytic functions are those that can be represented by a power series, convergent within a certain region bounded by the so-called circle of convergence. Outside of this region the analytic function is not regarded as given a priori ; its continuation into wider regions remains a matter of special investigation and may give very different results, according to the particular case considered." (Felix Klein, "Sophus Lie", [lecture] 1893)

"If, in the very intense electric field in the neighbourhood of the cathode, the molecules of the gas are dissociated and are split up, not into the ordinary chemical atoms, but into these primordial atoms, which we shall for brevity call corpuscles; and if these corpuscles are charged with electricity and projected from the cathode by the electric field, they would behave exactly like the cathode rays." (Joseph J Thomson, "Cathode rays", Philosophical Magazine 44, 1897)

"The analogy between the results of the theory of algebraic functions of one variable and those of the theory of algebraic numbers suggested to me many years ago the idea of replacing the decomposition of algebraic numbers, with the help of ideal prime factors, by a more convenient procedure that fully corresponds to the expansion of an algebraic function in power series in the neighborhood of an arbitrary point." (Richard Dedekind, "New foundations of the theory of algebraic numbers", 1899)