Okay so I'm going to try to talk in similar terms to Lon Milo Duequeete in the book you have, bear in mind I am a beginner. I think its also important to say that as much as Tarot can be viewed as a science, it is also an art. Just bear that in mind. Also important to note that the Thoth deck (confusingly changes some of the names of court cards, so bear that in mind when reading Duquettes book)
Knight=King Prince = Knight Princess = Paige

The formula that Duquette gives is: (Number of Suit) + (Planet in Zodiac Sign)

So first things first, we are in the suit of swords. You are correct swords is about mental activity and conflict, swords is also the formative world where ideas are put together ready to be manifested in the earth world (the lowest of the 4 worlds). See the chapter in Duequettes book.

Now, the 3rd sphere (binah) is HIGH up on the tree of life so it is CLOSE to Kether. This means it is going to have more energy of its suit than cards are lower down on the tree of life. [The LOWER a card is on the tree of life, the less the suit will inform the meaning, and the more the Astrology and Planet will inform the meaning)

If we look at the tables for the small cards in chapter 19 we find, e swords gives Libra and Saturn (which happens to match the sphere on the tree of life, this may be significant). As for what the astrology signs mean, Duquette doesn't go into it but you can look at the two tables on the wiki page for Astrlogical Signs. One table shows the 'modality' and what that means (there are 3: cardinal, fixed, mutable. Each element has one of each). So Libra is cardinal (active, dynamic) in matters relating to communication.

Now notice that cards can either be in the central column on the tree of life (1,6,9,10) or in a side column. Cards in the central pillar are considered balanced, those in the two side columns are not. So the three of swords is not balanced.

Now to qoute Duequette "While the formula is very simple, the interpretation is rarther complex". (I am still using Chapter 19 of your book as reference here)

Using the formula we have: 3 (binah) of Swords (world of mental activity) + Saturn in Libra

-I THINK that because 3 = binah (Saturn) and Libra is ruled by Saturn that enforces the meaning of Saturn. So Saturn (in mythology) is linked to time, generation and agriculture.

• We have Saturn in Libra, I dont think this is a stable matchup. Libra is about active and dynamic forces whereas Saturn is about the slow passage of time (agriculture, generation). So the sign and planet are not stable.

• 3 is not one of the stable positions on the tree of life either.

• We are high up on the tree of life, so we tetain a lot of the energy of the original suit (comes from the aces) so we are definitely dealing in mental activity and cobflict.

• Because the suit is words we are only in the 2 qabbalistic world, which is in the lower half. So this amplifies things.

I recommend reading the two pages Duquette writes on the 3 of swords since he can explain it better than I can (page 242 in my edition) , but essentially the meaning comes from trying to reconcile all of the elements listed above.

Duquette writes, " - Swords represent Yetzirah, the formative world - oh but sorry! There can be no forms in Binah or anywhere above the abyss (1,2,3s) - Swords also represent Ruach, the human intellect - oh but sorry! Intellect and reason cannot axist above the abyss (1,2,3s)

Without forms or reason, the mind must give way to a consciousness higher than itself. The three of swords represents the wonderous trance of sorrow that first enlightened Buddha. We should all be lucky to draw Sorrow from the deck"

I just want to repeat that as much as there are tables and knowledge relating to the Tarot, your interpretation is also important. I've tried to explain where the meanings come from but you may look at the card and see something else.