On the influence of signs in mathematical reasoning / by Charles Babbage.

  • Babbage, Charles, 1791-1871.
Date:
1826
Catalogue details

Licence: Public Domain Mark

Credit: On the influence of signs in mathematical reasoning / by Charles Babbage. Source: Wellcome Collection.

Provider: This material has been provided by The Royal College of Surgeons of England. The original may be consulted at The Royal College of Surgeons of England.

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    and - . That combination is in this mode of expressing it left oc arbitrary and undefined. The same function >/' may at the same time be a function of X® + 1 X + 1 X ’ x^ +1 ’ X® * or of a thousand other quantities; all which circumstances al- though deducible from the original expression, are not presented to the eye, because in the consequences which it is proposed to deduce, they are entirely immaterial. If two circumstances in the nature of the function are jointly the ground on which any of its properties depend, they may be separated from the rest and made prominent by several methods. Thus the index n subjoined to a function ^ y)n may be defined to mean that it is homogeneous with respect to X and y and of the dimensions n: these two circumstances are the causes on which the truth of the following property depends. xt being substituted for y ^ (x, x^)„ = x”^|.(F, l)„. In all our attempts at mathematical generalization, it is of great importance to discover and distinguish these immediate causes of successful operations; in almost all cases they lead us at once to the highest point of generality, and very frequently contribute in no inconsiderable degree to simplify the processes of the investigation. This advantage so peculiar to algebraic signs, has been remarked by M. Degerando, from whose writings I have derived much satisfaction by observing the support which many of those views that I had taken previous to my acquaintance with them, received from the reflections of that distinguished philoso-