The Da Vinci Notebooks at sacred-texts.com
The arch is nothing else than a force originated by two weaknesses, for the arch in buildings is composed of two segments of a circle, each of which being very weak in itself tends to fall; but as each opposes this tendency in the other, the two weaknesses combine to form one strength.
As the arch is a composite force it remains in equilibrium because the thrust is equal from both sides; and if one of the segments weighs more than the other the stability is lost, because the greater pressure will outweigh the lesser.
Next to giving the segments of the circle equal weight it is necessary to load them equally, or you will fall into the same defect as before.
An arch breaks at the part which lies below half way from the centre.
If the excess of weight be placed in the middle of the arch at the point a, that weight tends to fall towards b, and the arch breaks at 2/3 of its height at c e; and g e is as many times stronger than e a, as m o goes into m n.
The arch will likewise give way under a transversal thrust, for when the charge is not thrown directly on the foot of the arch, the arch lasts but a short time.