The assignment of the arms and hands to Gemini is one of the places where melothesia's reasoning is easiest to see, because the reasoning is the sign's own image. Gemini is the Twins, and the parts of the body that come in pairs and work together are given to it. The same logic recurs elsewhere in the scheme and is worth naming, since it explains attributions that otherwise look arbitrary.
The scheme has three kinds of argument in it, layered rather than consistent. There is the positional argument, which simply runs the twelve signs down the body from head to feet and is the backbone of the whole thing. There is the iconographic argument, which reads the sign's image, so Gemini takes the paired limbs and Virgo the process of sorting. And there is the planetary argument, which imports the ruling planet's associations, so Gemini's rulership by Mercury pulls the lungs and the breath into its territory in many versions.
Where the three agree, the assignment is stable across sources. Where they conflict, the sources disagree with each other, which is why the stomach appears under both Cancer and Virgo and the kidneys under both Libra and Venus in this atlas.
Recognising the three arguments is the most useful thing a reader can take from the doctrine, because it shows the scheme being constructed rather than received.