equal strength [throughout] that portion will give way soonest which
is farthest from its attachment; whence it follows that _d_ being
equally distant from _f, e_ .....

If the centering of the arch does not settle as the arch settles,
the mortar, as it dries, will shrink and detach itself from the
bricks between which it was laid to keep them together; and as it
thus leaves them disjoined the vault will remain loosely built, and
the rains will soon destroy it.

786.

ON THE STRENGTH AND NATURE OF ARCHES, AND WHERE THEY ARE STRONG OR
WEAK; AND THE SAME AS TO COLUMNS.

That part of the arch which is nearer to the horizontal offers least
resistance to the weight placed on it.

When the triangle _a z n_, by settling, drives backwards the 2/3 of
each 1/2 circle that is _a s_ and in the same way _z m_, the reason
is that _a_ is perpendicularly over _b_ and so likewise _z_ is above
_f_.

Either half of an arch, if overweighted, will break at 2/3 of its
height, the point which corresponds to the perpendicular line above
the middle of its bases, as is seen at _a b_; and this happens
because the weight tends to fall past the point _r_.--And if,
against its nature it should tend to fall towards the point _s_ the
arch _n s_ would break precisely in its middle. If the arch _n s_
were of a single piece of timber, if the weight placed at _n_ should