Hi. I think it has to do with the notion of 'half-sums with a common axis' which is discussed on page 22. As far as I can see, it's like Arabian Parts or Lots. For example, the Part of Fortune is found by the equation PoF-ASC=Moon-Sun, therefore PoF=Moon+ASC-Sun.
So the equation Saturn+Uranus-Sun gives you the position of a point on the ecliptic which forms a planetary picture with Saturn, Uranus and the Sun. Three distinct types of planetary picture are defined on pages 21 and 22, and this is an example of type 2).
The best book I have seen on using midpoints in both mundane and psychological astrology is Working with Astrology, by Harding and Harvey.
Best wishes
Miquar