Because a few posters have indicated that this thread is way too technical for them, let me try to rephrase the most important part.
A round brilliant is a rather simple geometrical shape, and a big part of the cut-information can be deducted from a minimal number of proportions, being table size, average main pavilion angle, average main crown angle, girdle thickness and total depth. Even if one only has total depth and table size, this already gives us a minimum of info, not sufficient to judge, but sometimes sufficient to reject.
A princess-cut is more complicated in shape, and works with two main pavilion angles and two main crown angles. So, if we are looking for the full info, we definitely need to have all these angles.
The original question however was whether one could also deduct info from the basic info (table, depth, girdle), similarly like in rounds, and if this works according to the same rules. In other words, if one is looking for a table of around 60% in rounds, and a depth not higher than 61.5%, do the same rules and figures apply to a princess-cut?
The difference between ''rules'' and ''figures'' is the origin of a complicated matter.
If we talk about rules, we are talking about the interaction of light and diamond, and the basic rules are the same for a round and a princess. So, if we look at the most important proportion, the pavilion angle, I am not surprised to see that a P2-angle around 41° yields a very good result in a princess-cut, just as it is a very good target in a round.
However, when talking about figures, the whole thing becomes very complicated. Depth-percentages in a round are percentages of the average diameter of the stone. In a princess-cut, depth-percentages are percentages of the smallest diameter. Because the system of notation is different, the figures cannot be compared.
In this way, with the same pavilion-angle, one gets totally different depth-percentages. A pavilion angle around 41° will give a pavilion depth around 43% in a round. In a princess, the same angle will give a pavilion depth around 60%. Same angle, different figures.
Hope this clears up the matter somewhat,