...it is the presentation of universal ideas by means of universal types, and it is in the combination of these types -if anywhere - that it presents Secret Doctrine. That combination may, ex hypothesi, reside in the numbered sequence of its series or in their fortuitous assemblage by shuffling, cutting and dealing, as in ordinary games of chance played with cards. Two writers have adopted the first view without prejudice to the second...
It's not really possible for me to comment on just the passages that have been posted without going ahead a bit. In summary, what I noted is Waite is talking about the combination of the trumps in 2 methods, in sequence and random by chance. He likes the first, doesn't like the 2nd.
First. -in sequence:
Mathers - 22 majors in numeric order make a sentence- gave individual trumps specific characteristics- no reason to republish all that again...
Papus - also put them in sequence, Waite says he's on the right tract but lacks insight.
Second. - chance/cartomancy
Fortune, shuffling, dealing - the use of divination for "whatsoever" purpose or intention implies things Waite "disposes" of -- Waite says the meanings are "real" - proof positive that "obvious natural moralities" can't explain the "sequence."
Trumps have been used for fortune telling but don't belong there.
The divinatory meanings Waite assigns them later he considers arbitrary, uninstructed, and at best beneath the original intention. If fortune telling had been the real intention, it wouldn't be of the secret doctrine but of (black) witchcraft.
He later says "I am not denying the possibility of divination, but I take exception as a mystic to the dedications which bring people into these paths, as if they had any relation to the Mystic Quest."