Fig. 3. 
¢ 
L oad 
its beauty or deformity, it being a matter not fubje@ to mathe- 
matical argument, his eriticifm on that head cannot be brought 
to the like decifive teft 23 the former, and therefore we fhall not 
pretend to controvert it. u 
20. Tue depreffed or fcheme Gothic arch is deieabed from 
centres, lying below the right line joining the capitals of the 
pillars from which it fprings: thus the arch BF D is defcribed 
from the centres m, 2, which lie below the horizontal line BD. 
Its ftrength is eafily computed by continuing the arch FD to 
the horizontal line RS which paffes through the centres m, #: 
and then, proceeding as before, the ftrength of the Gothic arch 
BFD will be to the ftrength of a femicircular arch of equal 
fpan, as FG3x KD to mS¢, that is, becaufe both FG and KD 
muft always be lefs than mS, in a ratio of lefs inequality. And 
the ftrength of the two Gothic arches BE D, BF D will be to each 
other in the dire@ duplicate ratio of their radii of curvature, and 
the inverfe triplicate ratio of the perpendicular heights of the 
arches above the lines of their centres. The ftrength alfo of the 
Gothic ,arch of four centres may be eftimated in the fame 
mannet. 
21. But as the buildings ere€ted on Gothic and femicircular 
arches are never fo formed as to render them curves of perfe@ 
equilibration, but are generally terminated by an horizontal right 
line, it will be neceffary to compare them in this refpe@ ; and we 
fhall find, that though the ftrength of the Gothic arch, when in 
equilibrio, 
