Continuation of "Drop a normal" topic

Ever since I learned about the Steiner's theorem, the weakness of my constructions using the compass once or the square once was clear to me. They are constructions for basic steps such as drop a normal or draw a parallel. A complex geometrical construction takes many basic steps and if I choose the single circle center and/or radius or the single square center, half-diagonal, and/or orientation for one basic step, I will not be able to choose them for the next basic step. I never saw these construction as anything but stepping stones in the process of finding and learning the basic construction where the circle or square are given, period. Because only in this way I can proceed in a complex geometrical construction. I could not find these basic constructions in the library and I could not find them on the web.

Now, beside the geometrical constructions with one circle or one square given, period, there are (beautiful) geometrical construction in which we use the compass liberaly, selecting the center and/or radius every time. It seems to follow from the Steiner's theorem, that the constructions using the compas liberaly can be all performed using the square liberaly, constructions I did not know about, probably no less beautiful than the compass constructions. In order to think about or try such construction, it is necessary to know what limitations should be observed in placing the square. It does not matter that there is no square drawing tool, I can always draw a square somehow and pretend that it has been drawn by the tool. Just like we draw parallels by shifting triangle shaped rulers, because we know that we could construct them if necessary. It does not take away the beauty of the construction. I am almost sure that choosing the square center and/or half-diagonal should be allowed (in constructions using the square liberaly!!!), but I am still uncertain about choosing the square orientation - I will have to think about it. I do not see any reason for disagreement.

Regards, Vladimir