[ 86 ] 
K N which paffes through the point of conta@; and N T the ordinate 
to the axis: Alfolet BK=c, KE=¢, ET=x, K A=, and K C=g, 
then K V=; Hs (Pr. 48. L.1. Ham. Con.); and p= = (Cor. I. 
—X>5 
Pr.31.L.1. Ham.Con.) therefore _ ; real : I (rad.): Sine of the angle 
K VN or MN A, which is therefore equal to a and its cube 
Sha eeees j 4 
rs ; alfo R, the radius of curvature at the point N 
is equal to - (Cor. Pr.18. L.5. Ham.Con.) = £. ; therefore R ~ Sin. ° 
of MNA= eee ; and the height of the wall above the point 
N, which is reciprocally as R x fin.? MN A, will be dire@lly as 
14 
ress = 5, which at apis Digseaa Bas and confequently the heightof the 
4 ? 
wall above N is to the height above E as 5 ,5=,3 to—>, or as ¢? to 
?-x” that is, as EK? to NM}; or as HK? to nM’; therefore 
the heights of the wall above each point N of the ellipfe and the 
correfponding point x of the femicircle are equal. Confequently 
when the altitude over the vertex of the arch is given, and 
the termination of the wall horizontal, there will be a 
lefs deviation from a true balance in the higher arch, that is, in 
the ellipfe; and the height over the point N is to a, the given 
E K; 
height over E, as E K* to NM}, therefore equal to ax—— hat and 
EK; 
i x 
the height over # equal to ax 
; and the difference equal to 
mM3—N M3 mM—NM 
ich i han ax E K x mee 
which is greater t E aE iar 
ax E K*x , that 
NM? xmM3 
NM i 
is, greater than ax EK Saag which is greater than NM, the 
difference 
