326 Mr. BaspaGe on the Influence of Signs 
nearly a century has been required to fix permanently the foun- 
dations on which the calculus of Newton and. of Leibnitz shall 
rest. 
Time which has at length developed the various bearings of 
the differential calculus, has also accumulated a mass of materials: 
of a very heterogeneous nature, comprehending fragments of un- 
finished theories, contrivances adapted to peculiar purposes, views 
perhaps sufficiently general, enveloped in notation sufficiently ob- 
scure, a multitude of methods leading to one result, and beunded 
by the same difficulties, and what is worse than all, a profusion. 
of notations (when we regard the whele science) which threaten, 
if not duly corrected, to multiply our difficulties instead of pro- 
moting our progress. 
As a remedy to the inconveniences which must inevitably 
result from the continued accumulation of new materials, as well 
as from the various dress in which the old may be exhibited, 
nothing appears so likely to succeed as a revision of the language 
in which all the results of the science are expressed, and the 
establishment of general principles which shall curtail its exu- 
berance, and regulate that which has hitherto been considered as 
arbitrary—the contrivance of a notation to express new relations. 
Previous however to this, some observations on the nature of that 
assistance which signs lend to our reasoning faculties, and on 
the causes which give such certainty to the conclusions of analysis, 
may render our future enquiries more intelligible. 
The nature of the quantities with which the mathematical 
sciences are conversant, is undoubtedly one of the first of those 
causes: in Geometry it has been well remarked* that its founda- 
tions rest on definition, and if this do not altogether hold in alge- 
braical enquiries, at least the meaning of the symbols employed 
* Elements of the Philosophy of the Human Mind, Vol. II. p. 150.. 
