22

16

then if H were scribed on the bottom of a cut,
it could be transformed into G without fear danger of
introducing falsity. For if G is transformable into
H, it is that we know that it cannot be that
G is true while H is false. But if If then

is on the sheet of assertion, that is, if
H is on the bottom of a cut, G cannot be true
and therefore we may scribe

That is
H on the bottom of a cut can be transformed
into G. This is called the principle of contraposition.
From all this it follows that

Any graph on the sheet of assertion
or within an even number of cuts
can be erased. While within an odd
number of cuts already made, any
graph can be inserted. This does not
justify us in making any new cut within
an even number of cuts. That, then is
the first rule, called the rule of erasure and insertion.

[note here: Skip to p. 17]

The second is that a pair of cuts one within
the other with no graph between them [????]

16

then if H were scribed on the bottom of a cut,
it could be transformed into G without fear danger of
introducing falsity. For if G is transformable into
H, it is that we know that it cannot be that
G is true while H is false. But if If then
is on the sheet of assertion, that is, if
H is on the bottom of a cut, G cannot be true
and therefore we may scribe . That is
H on the bottom of a cut can be transformed
into G. This is called the principle of contraposition.
From all this it follows that

Any graph on the sheet of assertion
or within an even number of cuts
can be erased. While within an odd
number of cuts already made, any
graph can be inserted. This does not
justify us in making any new cut within
an even number of cuts. That, then is
the first rule, called the rule of erasure and insertion.

[note here: Skip to p. 17]

The second is that a pair of cuts one within
the other with no graph between them [????]