The history and development of nomography

Abstract

That body of knowledge which has the name Nomography consists of the theory and practice by which the results of Geometry are used to facilitate numerical calculation. The subject existed under various titles before 1891 when d'Ocagne coined its present name. Methods in use before 1840 are examined to determine the foundations on which the subsequent structure was erected. In particular, the development of analytical geometry and of the concept of level curves, or contours, are noted for the main period of development, up to 1900, the works of lalanne, Massau and d'Ocagne are examined with that of other less important contributors. Lalanne published his ideas in 1843 giving the first indication of a related theoretical problem, that of anamorphosis or the replacement of curves difficult to construct by others more regular, preferably straight lines. Massau published many important results in 1884 including the form of a determinant equation which must be satisfied by components of a function of three variables if that function is to be represented by three systems of straight lines. Also in 1884, d'Ocagne described a new type of nomogram depending on the alignment of points; previous nomograms had depended on the intersection of curves. The possibility of alignment in the case of three variables is seen to be related to Massau's determinant equation and thus to the problem of anamorphosi for the period from 1900 two main themes are followed. The major theme examines the attempts to solve the problem of anamorphosis for functions of three variables. Surprisingly, this requires the examination of comparatively recent material and it is found that there is no neat and tidy solution; at least not one that has yet been found. The second theme considers the propagation and USB of nomographic ideas with special reference to Britain, where they were not readily adopted. finally, some recent developments in the subject are examined.