well, let's go to the origin of your question ...
... actually you don't know, why the Minchiate has 16-17-18-19 filled with 3 theological virtues and Prudentia, and you assume or will research, if there had been a philosophical text before about Prudenti.
I've no fun to search your philosophical text. First you should look, where the problem starts.
That's card 16 Hope, and there we have crown. Hope already earlier had some iconographical relation to star, ... for instance here:
... there's a light (star) shining in from one of the corners.
Further observation: the Minchiate is ordered in the following way:
1-15 ... a sort of "begin of older Trionfi"
16-35 ... a special Florentine input, 20 cards, which changes the "form of older Trionfi" to Minchiate
36-40 ... a sort of "end of older Trionfi", unnumbered
16 Hope is at the begin of the Florentine input, a position, which is usually filled by 16 Star (older Tarot). The star itself is moved by the operation to position 36.
A man with a crown and a star at the top. So, there's twice a crown, at somehow related positions. Now, we look for the crown.
A man is crowned at the love card at position 5. The position 5 mirrors position 36, cause "5+36 = 41". The cards 1-5 and 36-40 have special function in the versicole system (this are part of the Minchiate rules). So the first 5 cards (papi) lead to a ceremonial crowning, and the last 5 cards (aries) open with a man with a crown on a journey.
Further we have 5 other crowns at ...
Position 2 as part of the papi
Position 3 as part of the papi
Position 4 as part of the papi
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Position 39 as part of the aries
Position 40 as part of the aries
... from which I show only the last two cards:
(if you wish more details:
http://a.trionfi.eu/WWPCM/decks07/d05113/d05115.htm )
... from which the last shows a Medici crown and Medici heraldic. I think, this deck was made 1725, and in the year 1724 we had a new Medici ruler, usually rather drunken.
http://en.wikipedia.org/wiki/Gian_Gasto ... of_Tuscany
As there was a real crowning in 1724, possibly the crown details in this deck are not in original version of Minchiate ... anyway, we see, that specific games rules details could influence the iconography.
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So back to your problem:
Why Prudentia in the group of the theological virtue?
16 - 35 are 20 positions
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12 zodiac signs
4 elements
3 theological virtues
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19 positions, one was missing
Well they wanted 20, cause there are ...
2 sets with 10 cards (suit-numbers) are going from 1-10 ; totally 20
2 sets with 10 cards (suit-numbers) are going from 10-1 ; totally 20
... and they wanted, that these structure was mirrored in the trumps. For some ideological reasons they couldn't
chose the "perhaps normal" way
20 (1+20) + 20 (21-40)
or something like
10 (1-10 ... begin old Trionfi) + 20 (11-30 .. new input) + 10 (31-40 ... end old trionfi)
... but the chosen alternative is simple and elegant enough to be recognized.
So there were 19 elements and they did need a 20th ... the choice was Prudentia.
Which likely means, that a book, that describes a philosophical reason doesn't exist. The reason is likely more in the chosen system.
And 16 Hope likely explains by the similarity of this motive to the Star (No. 36).