C 85 3 
V. On the Independence of the analytical and geometrical Methods 
of Investigation ; and on the Advantages to be derived from 
their Separation. By Robert Woodhouse, A. M. Fellow of 
Cains College , Cambridge. Communicated by Joseph Planta, 
Esq. Sec. R. * S. 
Read January 14, 1802. 
One of the objects of the paper which last year I had the 
honour of presenting to the Royal Society, was to shew the in- 
sufficiency in mathematical reasoning, of a principle of analogy, 
by which the properties demonstrated for one figure were to be 
transferred to another, to which the former was supposed to 
bear a resemblance; and the argument for the insufficiency of 
the principle was this, that the analogy between the two figures 
was neither antecedent to calculation, nor independent of it, 
and consequently could not regulate it ; that analogy was the 
object of investigation, not the guide ; the result of demonstra- 
tion, riot its directing principle. 
Having shewn that analogy could not establish the truth of 
certain mathematical conclusions, I next endeavoured to shew 
why such conclusions had been rightly inferred ; not by pro- 
posing any new excogitated principle, nor by pointing out an 
hitherto unobserved intellectual process ; but I conceived they 
might be obtained by operations conducted in a manner similar 
to that by which all reasoning with general terms is conducted. 
