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Henry Bushby Transcription Pages

VM533B94v2-p259.jpg

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259
(ii.) The number of knots is infinite.
[the entire following paragraph (i.e iii) is struck through by an oblique line] (iii.) Every knot is, or may be reduced to,
a knot with alternate crossings: i.e.
one in which no part crosses over itself
or itself & other parts, or other parts
twice over or under in succession.
(iv) Knots so reduced are regular or ir-
regular, and cannot have any different
no. of alternate crossings.
(v.) Regular knots ^ are such as, reduced knots as can be represented on
an endless cord or cords laid round the
centre of a circle of which any radius
will cross the same number of parts
formed by the cord or cords. * All the
diagrams on pp230 ff. are of regular knots.
Such knots, if the radius really cut the
parts where it traverses them, would
be ordinary plaits or twists, and in their
circular form are ^ really nothing more than circular plaits or
twists.

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