It would take 10 seasons to invent a formula using a Lab Total of 11, but one may be learned from a book or teacher that can convey a Study Quality of 5+. I'd assume this to be a failed medical student.
Also, there was an Herbalism ability in one book or another that was non-Academic and allowed for it to be used in place of Medicine for making Theriacs. It's all a bit of a thought experiment, anyway.
I do like this idea! Something similar to the Training seasonal activity, where you're doing a season's work and training a student in a craft or something. That would even fit with how Inceptions would likely work, since once the astrologer knows the Inception formula it's only a day or something to apply it to someone's nativity horoscope.
I'd wish it were that simple, but [A&A:69] has
Creating one of these products is a two-stage process. The philosopher must first research the formula — either learning or inventing the formula by accumulating experience points. Second, the philosopher spends one or more seasons in his laboratory concocting the product described by his formula.
To invent the formula, you spend 5xp one way or another, and your lab total is irrelevant. Then you concoct using the lab total as described on page 70f.
The example textbox on p71 contradicts this, though. In it Berenger learns a formula from a Lab Text, apparently in one season since it states "Without the Laboratory Text he would have accumulated 3 (8-5) points per season and thus taken two seasons instead."
And it seems that Berenger creates his empirica in the season that he concocts the formula, since it states he only creates two doses because of his lower Lab Total.
That's the interpretation we used for my game; otherwise it would be absurdly punitive on top of a subsystem that's already so punitive that the consensus here seems to be that most games ignore experimental philosophy altogether.
You are right that you may get lab texts which speeds this up, but these are rare.
Philosophers jealously guard the formulae that they have invented themselves, but even more jealously guard their precious Laboratory Texts.
Even with the laboratory text, it is a two-stage process, as is clear also in the example. First you have to spend 5xp be learn the spell, and then you need a season in the lab, and you get more doses than you would by concocting it without the lab text. In the example, Martin produced two texts, the tractatus and the lab text.
I assumed that only the tractatus to learn the formula would be available in game, and that laboratory texts would simply be out of reach, but if you want to make experimental philosophy commonplace, that may well change.
With a medicine score of 5 a doctor may add +5 to a healing role as an attending physician. While not directly stated in art & academe the patterns of healer's clients therein strongly imply this can be done for up to 5 patients. Similarly teh doctor could provide a +1 living bonus for 25 people. It seems to me that either of these services would be of far greater value than producing 3 mustard plasters for his regular work routine.