On-the-square meaning

Mounting his own pulpit in St Mark's he quietly related the events of the day to the faithful assembled in the church, and then withdrew to his cell, while the mob on the square outside was clamouring for his blood.

Continuing these experiments, they found that in acetylene gas under ordinary pressures the decomposition brought about in one portion of the gas, either by heat or the firing in it of a small detonator, did not spread far beyond the point at which the decomposition started, while if the acetylene was compressed to a pressure of more than 30 lb on the square inch, the decomposition travelled throughout the mass and became in reality detonation.

They were decapitated on the square outside the Hradcany palace where the estates met on that day (August 22).

Eventually he settles on the square based on the diagonal of the original square.