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85.
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.
The adversary says that this arch must be more than half a circle,
and that then it will not need a tie, because then the ends will not
thrust outwards but inwards, as is seen in the excess at a c, b
d. To this it must be answered that this would be a very poor
device, for three reasons. The first refers to the strength of the
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