GEOMETRICAL PROBLEMS. 
/ Z 
PROBLEM LXXV. 
Supposing the right-lines m,n,p,to represent the lengths 
. of three staves erected perpendicular to the horizon, in the 
given points A, B, C ; to find a point P, in the plane of 
the horizon ABC, equally remote from the top of each 
staff. 
by the perpendiculars LIST and IK, cutting AB 
in N and K; make KP and NP perpendicular to BC 
and BA, and the intersection P of those perpendiculars 
will be the point required, 
DEMONSTRATION. . 
Conceive the planes AEFB and BCHG to be turned 
up, so as to stand perpendicular to the plane of the ho 
rizon ABC and intersect it in the right lines AB and 
BC ; then, because BF and BG are equal to each other, 
and perpendicular to the plane of the horizon, it i 
c c 4 
CONSTRUCTION. 
Join A, B and B, C, and make AE and BF per 
pendicular to AB y also make BG and CH perpen- 
cular to BC, and let AE be taken m, CH rr p, and 
BF and BG each — n: draw EF and GH. which bisect