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Henry Bushby Transcription Pages

VM533B94v2-p268.jpg

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268(follows p273.)
(xvii.) Given C & z (a no. of cords greater than
unity) : how many regular knots are there with C
on z cords ?
By x & xvi the highest value of n in this
case must be less than C + 1. (indicating a
twist knot on 1 cord.)
By] xiii [?symbol] = 1 + a measure of C
By xiv [?symbol] = G.C.H. of [?symbol] & C
[symbol of therefore] n = any factor measure of C [less than C] which, increased by 1,
is divisible by [symbol?].
Set out the factormeasure of C : increase them
by 1
& strike out all not divisible by z
Thus let C = 10 & z = 2
Measures of 10 are 1, 2, 5, (10)
Augmented by 1, 2, 3, 6, (11)
Strike out 11 ([?-C+1]) leaving
2,3,6.
Strike out 3 (not divisible by 2.)
Indices of series are 2,6 & no others.
(see pp 233, 250 for diagrams.)
[This completes the theory of Regular Knots.]

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