analy tical and geometrical Methods of Investigation . 1 1 9 
more abstruse, it was found necessary to improve more and 
more the means or instrument of investigation. 
XXVII. As the question concerning the respective advan- 
tages of the ancient geometry and modern analysis, is not foreign 
to the subject of this Paper, I shall briefly state it, and endea- 
vour to afford the means of arriving therein at something like a 
precise determination. 
The superiority of one method above another, must consist 
in being either more logically strict in its deductions^ or more 
luminous, or more commodious for investigation. The discus- 
sion concerning the strictness and accuracy may, I conceive, 
be immediately put aside, since no method of deduction is essen- 
tially inaccurate ; and, if in geometry the inferences are more 
strictly deduced than in the algebraic Calculus, the advantage 
is to be reckoned an accidental one, and arising from the great 
attention with which the former science has been cultivated. 
One method may, however, be essentially more perspicuous 
and more commodious for investigation than another; or, in 
other words, the perspicuity and commodiousness of a method 
may depend on circumstances inherent in its nature and plan. 
Now, a person not sensible of the superior perspicuity of the 
geometrical method, would demand these circumstances, the 
necessary causes of perspicuity, to be pointed Out to him ; which 
might be done, by stating that geometry, instead of a generic 
term, employs, as a particular individual, the sign or represen- 
tative of a genus; and that, as in algebra, the signs are alto- 
gether arbitrary, in geometry, they bear a. resemblance to the 
things signified, and are called natural signs, since the figure of 
a triangle, or square, suggests to the mind the same tangible 
figure, in Europe, that it does in America : and this resemblance. 
