In TM:RE, the Fraternity of Samos have as one of their final initiations, the opportunity to learn Potent Magic (Artes Liberales and Philosophiae).
Since I'm thrashing out a write up of the cult I'm wondering what on earth this would cover? I'm guessing it wouldn't cover all ritual magic (which of course uses those two virtues). So what would/could it cover?
Spells designed to be always cast with Artes Liberales and Philosophiae can also be designed as Potent, thus must be cast with specific Casting Items and get an extra +6 to Lab Totals and Casting Score. To me this looks OK for a Major Virtue - especially because "only one Potent Magic Virtue applies to any single activity", and ritual spells can gain oodles of casting bonuses anyway.
Since Potent Magic covers the same areas as Magical Focus, that would mean you could have a Major Magical Focus that covers those same spells, and I think the general consensus here on the forums has been that a Magical Focus in Rituals is too broad.
I wouldn't conclude, that for every type of Potent Magic considered in an example there must also be an allowed Major or Minor Magical Focus.
Only a (TMRE p.129) Pythagorean or True Initiate, who passed "a strenuous series of Initiatory Quests and Sacrifices", might be initiated to Potent Magic (Artes Liberales and Philosophiae) - and an alternative initiation is to Ascendancy to the Hall of Heroes.
For PCs, such top level initiations of the Fraternity of Samos are also strictly decided by SG or troupe: TMRE certainly does not mandate any initiation for True Initiates, but stays with "it is said".
I would.
"Minor Potent Magic covers the same
narrow fields as a Minor Magical Focus"
TM:RE p31
"Major Potent Magic covers the same
wide fields as a Major Magical Focus,"
TM:RE p31
"Potent Magic is defined
as covering the same possible areas as
a Magical Focus."
TM:RE p36
You should certainly bring up your quotes, if the SG attempts to flesh out the TMRE p.129 "some say".
He might then answer, that these "some" were not full Pythagoreans and didn't really know what they were speaking of, while true top dog Pythagoreans speak instead of Potent Pythagorean Magic (Artes Liberales and Philosophy). 
I also concur that a potent magic / magical focus that incorporates every possible spell cast using ritual or ceremonial magic is way too broad. Instead, I'd like to offer an alternative explanation. Potent Magic (Artes Liberales and Philosophae) should not be read as Potent Magic into any spells using those abilities as part of the casting total; but as Potent Magic into any spells replicating the use of Artes Liberales and Philosophae skills through magic. This would include some new guidelines in TMRE:
It would also include the A&A guidelines for Creo/Rego Craft magic used to create a Reagent (A&A p.70).
I think this would be sufficiently narrow to fall into the scope we would naturally expect for a magical focus / potent magic.
Feedback?
This is certainly possible, since we know all the initiations of Pythagoreans only by hearsay.
But after a vow of silence to be kept for 5 years - hearsay only - and a "strenuous series of Initiatory Quests and Sacrifices", as the crowning achievement of a Pythagorean this looks pretty lame to me.
In that case a SG would have to argue with her player, that "the journey was the reward". 
I agree it could be on the weak side for a Major Potent Magic virtue. That being said, one rarely undergoes an Ordeal for the sake of gaining a single virtue, when the bonus applies to the next three initiation. I would tend to lean towards including several initiation at that level anyway.
True, however, this is supposed to be the initiation for the final rank of the order, albeit there are supposed to maybe be up to 12 initiations within that ranks. As I'm the one writing up the cult right now, I'm going to keep it simple at around 6 initiations and anything else the players may want they will need to self initiate into, although they might well be able to find previous scripts in the cult libraries.
I'm not thrilled with the ideas behind Potent Magic (Artes Liberales and Philosophae) and I don't think my players would think highly of it either, its either too powerful (all rituals and ceremonial magic) or near useless (the counting spells are very niche). I'll probably swap out the last initiation for something else. I want to avoid the theurgy and ascendency to the hall of heroes as those are both present (theurgy massively so) in several other of the cults I'm putting together and would like something that fits better into the mathematics side of things. Any ideas?
Perhaps Divination&Augury with the Numerology method would be suitable?
I think the cult as is written spreads itself too much in too many directions. If I had to redesign, I would incorporate everything in the Arithmetic Magic chapter, some Planetary Magic and Sorcerous Music but I would discard anything theurgy, great talisman, spirit magic. I might add mystical choreography from House Jerbiton, due to it being used in a specially prepared space. I could see optional initiations into things like Puissant Artes & Puissant Philosophae. I would probably add a magical focus in an area TBD but that would include as a minimum hermetic architecture within its scope, since the mystery virtue is begging for that to become useful. Unaging would make sense to me as well and maybe a capstone allowing a form of reincarnation rather than ascencion. Perhaps even a virtue granting Duration 19 years from Ancient Magic. I also like ErikT's suggestion on Numerology.
So it is a lone capstone Virtue in the end, after years of silence and a "strenuous series of Initiatory Quests and Sacrifices" to achieve it.
Then p.82ff Ascendancy to the Hall of Heroes fits verrry well to historical Pythagorean ambitions like those from the last phrase of the Chrysea Epē:
And when, after having deprived yourself of your mortal body, you arrived at the most pure Aither,
You shall be a God, immortal, incorruptible, and Death shall have no more dominion over you.
It shouldn't be something remote from Hermetic magic and bringing in a further Supernatural Ability eating xp like TMRE p.58ff Divination & Augury.
If it is a kind of Potent Magic (TMRE p.31f), it needs to be powerful.
Tying it to Artes Liberales and Philosophiae, key Abilities of a Brother or Sister of Samos, makes also sense.
Potent Magic for Rituals and Ceremonial Magic is far less powerful than a Magical Focus (Ritual Magic): it limits general bonuses to Lab Totals and Casting Scores to +6.
It requires reinvention of powerful Rituals as Potent before getting bonuses from Casting items. They basically compete with supporters with TtA p.137 box Day of Communion, which a teaching Pythagorean attracts anyway. Put all together, it is very useful, but not overpowered.
There is no need to word this Virtue in a way, that it implies a Magical Focus for Rituals in your saga.
I'm not sure I agree about potent magic that covers all rituals being weak.
The bonuses to spell casting for major potent magic are ok, +6. Much weaker than a focus for a powerful magos. But the benefit of being to invent potent spells in your area, in this case, all rituals, is REALLY powerful. Imagine the tradability of lab notes for ritual spells that all have a bonus of +5 to cast? That's exceedingly valuable to other magi. Hell you could make even more powerful rituals as trade goods for those magi with good magic theory. And they are really easy to make too. Get a copy of the lab notes for a ritual, spend a single season re-inventing it, and BAM, its suddenly massively more valuable.
Might this include Ceremonial Casting of Spontaneous spells?
It is not. It is a capstone Virtue to a centenarian Pythagorean.
I wouldn't believe, that a magus at the very top of his Cult has even the time for this kind of "cottage industry".
Potent spells can only be Formulaic - including Rituals. This is, because (TMRE p.31f Potent Spells):
Potency applies only to Formulaic spells - Spontaneous Magic allows Ceremonial Casting to produce similar results, and enchanted devices use Shape and Material Bonuses during enchantment.
But the +6 bonus to Casting Score provided by Major Potent Magic might also apply to Ceremonial Casting of Spontaneous spells with Potent Pythagorean Magic (Artes Liberales and Philosophy).
Ok, I know this is not how potent magic works, but could it be that the intent was for this to be potent natural magic?
That is, have the bonus apply to all the stuff in A&A done with Philosophiae or AL?
While comparatively weak compared to hermetic magic, this would be a massive boost to these abilities, and might be fitting thematically.
Should it work the same way as all other Potent Magic (x) or Magical Focus (x), it would affect spells and lab totals for effects that work on Artes Liberales or Philosophiae. Just as Major Potent Magic (Metals) does not give you a bonus for metals in general, or when you use metals, but only for spells and effects that affect metals.
Otherwise it is misnamed.