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Henry Bushby Transcription pages

VM533B94v4-p091.jpg

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Current Page Transcription [history]

91
The Rule of Rings is this in all
cases:^[cannot read pencil notation] 1 must not be joined to
M2 (GCM of B&n)=
M2 (GCM of C/n-1+^&n)
or y must not be joined to y-1
+ M2(GCM of B&n)=
y-1+M2(GCM of C/n-1+n)
But by XIV. (ii.267) the GCM of
B & n = z.
Therefore the Rule of rings is ^?[1m?] S2 ^only 2 bights being cut 1 must
not be joined to M2Z, or, generally,
y must not be joined to y-1+M2Z.
If it is so joined Z becomes Z+1
Problems: Rule for reducing 2 to 1
Rule for further exclusions ^or additions so that C may
remain the same
In S34b/8c join 1 to 4 (=M2Z ie. 2x2x1)
no rings result - Yes they do, & so they
do when joined to 6

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Current Page Discussion [history]

Please note that I feel that where the lowercase letter "n" appears in any of the equations may actually be an italicized lowercase lambda instead. I've been over and over it and have considered the letters "u" and "z" as well. I settled on the "n" simply because the way it was written in Bushby's hand most closely resembled how he wrote his n's. MMurray ---