The third decan of Libra runs from 20 to 30 degrees of the sign and is ruled, in the scheme this atlas records, by Jupiter.
The card on the decan
In the Golden Dawn's assignment this decan carries the Four of Swords. The mapping is one to one and exhaustive: the thirty-six small cards numbered two to ten across the four suits match the thirty-six decans exactly, taken in order from the Two of Wands at the first decan of Aries. The suit follows the sign's element, so Libra is a Air sign and takes a card of Swords, and the rank follows the position in the sequence, which puts the four here.
Why the rulers carry over between signs
The thirty-six rulers run in the Chaldean order, the seven planets arranged from slowest to fastest as Saturn, Jupiter, Mars, Sun, Venus, Mercury and Moon, applied one after another right round the circle beginning with Mars at the first degree of Aries. Because thirty-six is not divisible by seven, the sequence does not restart at each sign. It runs straight through the boundaries, which is why the rulers of a sign's three decans are not the sign's own planets and why the pattern only closes after the whole zodiac.
What the atlas is recording
The degrees and the ruler are the attributions this atlas holds for this decan, and the card is the Golden Dawn's. All of them are traditions with variants rather than settled facts, and the decan itself, as a ten degree segment of a sign, is the only part that is simply arithmetic.