On the length of beams.

A beam that is longer than twenty1 times its greatest width will not be very permanent, and it will break in half.  And remember that the part that goes into the wall must be steeped with hot pitch and bound with oaken boards, also steeped.

Every beam ought to pass through its walls and be fixed on the other side of these walls with sufficient chains, because one often sees earthquakes2 cause beams to leave the walls and then ruin the walls.3  And the floors where these are chained will keep the walls fixed together, and the walls will fix the floors.

I remind you again never to put plaster over timbers, since, with the growing and shrinking of the timbers4 due to the humidity and dryness, these floors5 will often crack, and once cracked, their divisions will gradually produce dust and make an ugly impression.

Again, I remind you not to make floors supported by arches and beams, since, with time, a floor supported by beams will droop somewhat at the middle,6 and the part of the floor supported7 by an arch will remain in its place, whence:

Proposition.8

Floors that are supported by two different natures of supports begin, after time, to appear to be made like hills.9

c d – a b

[III]

Window a is well placed under window c, but window b is poorly placed under pier10 d, because this pier is without support or foundation.  Therefore, remember never to make a break under the piers between windows.

On covering pieces of wood with plaster.

If you cover timber with plaster, as do some when making reinforcements within walls, using beams or other pieces of wood, the plaster on these pieces of wood will separate from the other11 plaster dressing the walls, and this will open fissures, so that within a short time12 the timber will be uncovered.  And this derives from the expanding of the timber when it incorporates humidity into itself and its shrinking when it releases this humidity.

c r m o c K – d S n p – y 7 – e a l – 1 2 3 4 5 6 7 – z 6 – f b

6 7 ; x z

[IV]

This wall under the arch, e f,13 will break, because the seven whole bricks are not sufficient to support the spring of the arch above them; and these seven bricks will break exactly in the middle, as appears between a and b.

The reason is that brick a only has weight a K on it, and the last brick under the arch has on it all the weight from c d to K a.14  c d appears to exert force on the arch toward the shoulder at point p, but weight p [o makes] resistance15 to this, so the whole weight goes to the root of the arch.

Therefore, make [the roots] of the arches as shown between 7 and 6, which are twice as strong as those shown between x and z.16