376 Mr. BaBpace on the Influence of Signs 
the want of such a previous course of instruction, as that which 
I have now pointed out. I would however guard myself from 
being supposed to imagine, that this is by any means the sole 
obstacle; I mention it as one, which appears to me of some 
weight, and which might, without much difficulty, be removed. 
The other, and more general, acceptation of the word symme- 
try, applies to the position, as well as the choice of the letters, 
employed in an enquiry: in this sense, it can scarcely exist, with- 
out a previous attention to that which has just been explained, for 
however regularly and analogously two series of quantities may 
be arranged, unless the signs, by which they are represented, are 
so constructed, as mutually to excite the idea of their correlatives, 
it is impossible, that the symmetry can be apparent to the eye. 
By employing the first species of symmetry, we assist the memory 
in remembering the ideas indicated by signs; by the use of the 
second, we enable it more easily to retain the form in which our 
investigation has arranged those signs, as well as facilitate the pro- 
cesses, by which that final arrangement was accomplished. By 
the happy union of the two, our formule acquire that wonderful 
property of conveying to the mind, almost at a single glance, the 
most complicated relations of quantity, exciting a succession of 
ideas, with a rapidity and accuracy, which would baffle the powers 
of the most copious language. 
The mode of expressing an angle of a triangle, in terms of 
the radii of three circles, which touch respectively each side, and 
the other two prolonged, will furnish the first example. Calling 
a, b,c those radii, and @ the angle opposite a, we have 
6 
ig ates 
an unsymmetrical expression. This can be improved by a very 
trifling change, for it is equivalent to 
