ee! 
one fegment about the fulcrum 7, and the other about the fulcrum ¢; 
and therefore the force of the vouffoir, acting on the levers Hz, 
H 7, is dire@ly as the perpendiculars ¢p, rg, let fall from the 
fulcrums on the line of direG@ion Hg, that is, dire&tly as the 
fine of the angle ¢Cp, or Hg K. \ 
13. Hence therefore if a weight, like a wall, be incumbent 
on the arch EABF, ftanding in a vertical plane, if the height 
of the wall on any point be in a ratio compounded of the recipro- 
cal triplicate ratio of the fine of the angle formed by the curve 
and vertical line, and the reciprocal fimple ratio of the radius of 
curvature in that point, all the vouffoirs will endeavour to fplit 
the arch with equal forces, and therefore will be in perfec 
equilibrium with each other. On this general propofition depends 
the theory of the conftruction of arches. 
14. Burt fince the materials with which arches are conftructed 
are not of infinite ftrength, there muft be a certain degree of 
preffure, which will rend even an arch whofe parts are in perfect 
equilibrium. Now the ftrength of an arch, in its different points, 
is as the greateft weight which it is able to bear on thofe points 
without breaking; that is, in a ratio compounded of the reci- 
procal triplicate ratio of the fine of the angle formed by the 
curve and vertical line in its different points, and the reciprocal 
fimple ratio of the radius of curvature in the fame points, On 
this principle the comparative ftrength as well of different arches 
as of the fame arch in its different points may be eafily afcer- 
tained. 
15. Let 
