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Henry Bushby Transcription Pages

VM533B94v6_268.jpg

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268
Formula of Reduction.
x being less than n, then
Kn xax(n-1)c = Kx nan(x-1)c
(or shortly, “Kn a⁄ gives Ka x⁄ ” : the rest follows.)
Further
[Note: The following 6 expressions are annotated in pencil: seq 2, seq 0, seq 3, seq 1, seq 4, seq 2, respectively]
K3 1a2c = K1 3a2c
K4 2a6c = K2 4a4c
K5 3a12c = K3 5a10c
& these were established by experiment,
after which a general formula was
substituted, containing “d”.
The reduced knot is the knot of its series
immediately following, & the reducible knot -
is that of its series immediately preceding -

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