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analytical and geometrical Methods of Investigation . 125 
ctence as I dare assume, knowing how fallaciously we judge of 
our own performances, I affirm to be strict and direct ; estab- 
lished without artifices, and without foreign aid drawn from 
geometrical theorems and the properties of curves. In some 
parts of this paper, the subjects, for their importance, may be 
thought to be too slightly discussed ; the fear of appearing 
prolix, has perhaps driven me into brevity and obscurity. In 
other parts, what I have advanced may be remote from com- 
mon apprehension, or contrary to received opinion : but here 
I make no apology ; for, what I have written, has been written 
only after long meditation, and from no love of singularity. 
“ If I cannot add to truth/' I do not desire distinction from “ the 
** heresies of paradox/' 
