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weakness, if it be weakness, is constantly presenting itself. 
Our sense of exactitude is not quite borne out by such alge- 
braic formulae as the following : something multiplied by 
nothing is nothing ; something divided by nothing is infinite ; 
and nothing divided by nothing is almost anything. And yet 
these are the utterances of pure science. Or, to glance at 
higher branches, the differential or integral calculus, not only 
the calculi themselves, but some of their most vaunted theorems, 
rest on principles and are couched in language barely as in- 
telligible as the foregoing, and far more conflicting. And if, 
from the region of pure we pass to mixed mathematics, noting 
the necessary connection which subsists between them, and 
the dependence, so far, of the latter upon the former, and only 
glance, for instance, at the laws of motion, and how these laws 
enter into and modify, if they do not determine, some of the 
highest problems of perhaps our noblest, and certainly our 
most exact, of all physical sciences, astronomy, surely the 
weakness, if it be weakness, does not vanish. And yet scien- 
tific men accept mathematical processes and conclusions, and 
consider the various propositions proved. Now, if a weak- 
ness or obscurity, or even the absence of absolute exactness, be 
enough whereon to reject a definition, and the fault of either 
kind so vitiate such definition that the process depending upon 
it fails, — and the process failing the conclusion is untenable, — 
and if, further, the grafting such conclusions into some kindred 
science or branch, this latter, too, must be eliminated ; and, 
pursuing the same course, every branch resting upon it directly 
or indirectly, must be rejected, it would seem that mathe- 
matical science, with its vast and magnificent coil of connected 
sciences, is like a cone resting upon its apex, in danger of 
being overturned, and the whole series, with all else of 
kindred uselessness, swept into the limbo of discarded systems. 
But I have no fear of this result. The definition and expressions 
in question suffice for the purposes to which they are applied, 
and are accounted valid for the processes in which they find 
place ; and if this be so — if a fundamental definition, which 
simply tells us what the thing defined is not, suffice, as it does, 
where we find it, what defect or want of exactitude impairs 
the truths which I have ventured to instance as the kind of 
definitions which theological science offers ? A point is that 
which hath no parts, or which hath no magnitude.” Granted ; 
but who can exhibit it ? who perceive it ? Side by side with 
this, and in the light of the created universe, read f f God is ; ” 
and where is it not depicted, and who sees it not ? “ A line 
is length without breadth,” and “ a straight line is that which 
lies evenly between its extreme points.” Granted; but who 
