Given a string S
Conj(S) is the partition Me (Meizonos and Elassoon)
The individual focusses on one or the other of these parts.
Adj(S) is Adj(Conj(S)) that is M+e
Without conjugation we do not define the conjugates which are the adjugates which are gathered or synthesised to cover or equate to S
The next thing Euclid did was use the focus region or conjugate to compare with the other conjugate. For a string , this was done by using the circular arc to compare the parts. Using these arcs Euclid defined the factor algorithm geometrically.
This geometrical sequence of arcs constructed on S visually displayed the factorisation process. It portrays factorisation and scale as geometrically linked to conjugation. This image alone reveals the logarithmic relationship between conjugations in nested sequences.
By picking out the segmented string as a notational device for rectilinear forms, Euclid kept this connection between the sphere and every rectilinear form sysnthesisable!