as are terminated by Planes , &c. 
251 
V I -f- r* V' 1 -J- r a 
We have yet to find the value of C; and at first we get 
c = r— f - = r— a - _ 
J (a*+ T*)i J («*+(!+ r*)Trf ** J 1 + L^ Vl 
+ r a 
z 
a 
f /_•_ +r)i’ 
\i + r 1+ tf a j 
which again integrated, becomes 
C = L (— + s/\ + -’) — —= L (- + v/-r-. + ■?) 
\a 1 ^ 1 a* I Vj-fr* \ a ' ^ i-f-r* ' a % ] 
+ — Z=r L . 
vi+r 1 
The expressions we have thus arrived at, for the action of 
a right angled triangle, are of such continual use in the fol- 
lowing propositions, that it will be convenient to represent 
them by some concise symbol ; and as they are functions of 
a> b, and r we may put 
A = arc (tang. == ^s / 1 -f- ^ b') — arc (tang. = ~) = 
<p ( a , 6, r) — arc (tang. = —]. 
B = -4=L (2LLiIl* + v / 1 -f — L (- f6+ 
A/j + r 2 \ « 1 1 «* j \ Vcf+b* I 
= x{“> b > r )- 
C = L(i + /^|-iL[^ + /^F] 
= xp (a, 6, r). 
Cor. 1 . If, whilst r remains constant, b and a are supposed 
to vary, but so as to preserve the same ratio to each other, the 
