triangle _c n b_ has no weight upon it.

784.

I here ask what weight will be needed to counterpoise and resist the
tendency of each of these arches to give way?

[Footnote: The two lower sketches are taken from the MS. S. K. M.
III, 10a; they have there no explanatory text.]

785.

ON THE STRENGTH OF THE ARCH IN ARCHITECTURE.

The stability of the arch built by an architect resides in the tie
and in the flanks.

ON THE POSITION OF THE TIE IN THE ABOVE NAMED ARCH.

The position of the tie is of the same importance at the beginning
of the arch and at the top of the perpendicular pier on which it
rests. This is proved by the 2nd "of supports" which says: that part
of a support has least resistance which is farthest from its solid
attachment; hence, as the top of the pier is farthest from the
middle of its true foundation and the same being the case at the
opposite extremities of the arch which are the points farthest from
the middle, which is really its [upper] attachment, we have
concluded that the tie _a b_ requires to be in such a position as
that its opposite ends are between the four above-mentioned
extremes.