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curve. To prove this let the weights be at n m which will break
the arch a, b, f. I say that, by the foregoing, as the
extremities c and a are equally pressed upon by the thrust n,
it follows, by the 5th, that the arch will give way at the point
which is furthest from the two forces acting on them and that is the
middle e. The same is to be understood of the opposite curve, d g
b; hence the weights n m must sink, but they cannot sink by the
7th, without coming closer together, and they cannot come together
unless the extremities of the arch between them come closer, and if
these draw together the crown of the arch must break; and thus the
arch will give way in two places as was at first said &c.
I ask, given a weight at a what counteracts it in the direction
n f and by what weight must the weight at f be counteracted.
7
78.
ON THE SHRINKING OF DAMP BODIES OF DIFFERENT THICKNESS AND
WIDTH.
The window a is the cause of the crack at b; and this crack is
increased by the pressure of n and m which sink or penetrate
into the soil in which foundations are built more than the lighter
portion at b. Besides, the old foundation under b has already
settled, and this the piers n and m have not yet done. Hence the
part b does not settle down perpendicularly; on the contrary, it
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