rule does. As to insertions, they may be restricted, without
losing any result which they could bring about, to
the insertion unenclosed of a scroll with the same graph
in its two areas. Suppose, for example, you have the
graph g and you wish to introduce a spot a. You
have only to write


The putting a double cut
about the outer a, you get


Then by twice iterating g you get

This is precisely the 5th Operation of our rule. Now, then,
is there any further difficulty? Yes there is. What
is it? It is that half of the operations, those of insertion,
iteration, and adding a double cut, complicate
the graph, and thus lead to a result [??who] possibility
or impossibility is, less evident even harder to make out, than was that
of the original graph. The cure for this is carefully

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